Anomalous Current and Voltage Fluctuations in High Power Impulse Magnetron

Sputtering

By

Scott Kirkpatrick, Ph.D.

A DISSERTATION

Presented to the Faculty of

The Graduate College at the University of Nebraska

In Partial Fulfillment

for the Degree of Doctor of Philosophy

Major: Engineering

Under the Supervision of Professor Suzanne L. Rohde

Lincoln, Nebraska

August, 2009

UMI Number: 3365710

INFORMATION TO USERS

The quality of this reproduction is dependent upon the quality of the copy

submitted. Broken or indistinct print, colored or poor quality illustrations and

photographs, print bleed-through, substandard margins, and improper

alignment can adversely affect reproduction.

In the unlikely event that the author did not send a complete manuscript

and there are missing pages, these will be noted. Also, if unauthorized

copyright material had to be removed, a note will indicate the deletion.

______________________________________________________________

UMI Microform 3365710Copyright 2009 by ProQuest LLC

All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

_______________________________________________________________

ProQuest LLC 789 East Eisenhower Parkway

P.O. Box 1346 Ann Arbor, MI 48106-1346

Anomalous Current and Voltage Fluctuations in High Power Impulse Magnetron

Sputtering

Scott Kirkpatrick, Ph.D.

University of Nebraska, 2009

Adviser: Suzanne L. Rohde

The objective of this work was to study dc and High Power Impulse Magnetron

Sputtering (HiPIMS) plasmas in order to better understand the various aspects of

sputtering; such as rate, uniformity and current and voltage characteristics. The results

compare known characteristics for general plasmas as applied to dc and HiPIMS plasmas.

Methods are put forth to better describe these plasmas. These include dielectric constant

analysis, circuit equivalent models, fluid based models and other computational models

to predict current and voltage vs. time curves for HIPIMS.

Models describing the plasma behavior are important due to the nature of HiPIMS

plasmas. HiPIMS systems generate very high intensity discharges resulting in a higher

degree of ionization of the sputtered flux. Consideration of ionized flux from a HiPIMS

process is fundamental to understanding the scattering behavior within the plasma and

electric fields within the plasma. Various models are explored for their contributions to

provide a better overall understanding of the magnetron process. These models include

capacitor and inductor networks, and mathematical approximations to specific behaviors

such as an ion matrix sheath. This dissertation focuses on developing methods to predict

the characteristic current-voltage behavior for HIPIMS. Analysis of the fluctuations

providing a clearer picture of the plasma behavior has been developed. This

understanding provides a groundwork for a number of expectations and improvements to

the HiPIMS and related processes. This dissertation links, plasma immersion ion

implantation ion matrix sheath theory (PIII), and ion sheath transit times to the

fluctuations.

Anomalous Current and Voltage Fluctuations in High Power Impulse Magnetron

Sputtering

Scott Kirkpatrick, Ph.D.

University of Nebraska, 2009

Lay Abstract

Adviser: Suzanne L. Rohde

High Power Impulse Magnetron Sputtering (HiPIMS) is a process for improving

deposited thin films applicable from filling vias within semiconductor devices to

depositing improved barrier protection in potato chip bags. In order to coat predictably,

and evenly over any number of possible source materials; the process must be better

understood. To date, anomalous fluctuations of voltage and current have been observed

but not quantified.

This dissertation develops tools to help define oscillation sources and their significance to

functioning magnetron plasmas through a methodology of equation analysis,

computational modeling, and experimental solutions. It is the goal of this dissertation to

better understand the root causes of the current and voltage fluctuations within the

HiPIMS process which may lead to new designs of power supplies that may optimize the

process and be applicable for industrial use of the HiPIMS technology.

This dissertation has found models and theory to support ion based fluctuations in the

sheath, and an ion matrix sheath behavior in the current and voltage curves of a HIPIMS

supply. The combination of sheath instabilities and an ion matrix sheath explain the

anomalous behavior of HIPIMS systems.

.

vi

Acknowledgements

I would like to thank my advisor Dr. Suzanne Rohde for the opportunity and

encouragement to research HiPIMS as well as her encouragement of my independent

thought. I would like to thank my committee for their valued opinions throughout the

graduate process. I would also like to thank Dr. Ulf Helmersson for his tutelage, support

and introductions to a great number of brilliant scientists. I would also like to thank Dr.

Nils Brenning, Dr. Jon Tomas Gudmundsson and Daniel Lundin for their valued plasma

discussions, in spite of being an ocean apart most of the time.

vii

Table of Contents

Chapter 1 Introduction ................................................................................................ 1

1.1 HiPIMS (High Power Impulse Magnetron Sputtering) ............................................ 1

1.2 Direct-Current Magnetron Sputtering Improvements ............................................. 4

1.3 Direct-Current Magnetron Sputtering Current ........................................................ 5

1.3.1 Particle-in-cell (PIC) collision model ...................................................................................... 6

1.3.2 Diffusion model ....................................................................................................................... 6

1.4 Motivation and Objectives ........................................................................................... 7

Chapter 2 Sputtering Background .............................................................................. 9

2.1 Introduction to Sputtering ........................................................................................... 9

2.2 Temperature Effects in Sputtering ........................................................................... 10

2.3 Sputtering Techniques ............................................................................................... 12

2.3.1 Direct-current sputtering........................................................................................................ 13

2.3.2 Rf Sputtering ......................................................................................................................... 15

2.3.3 Reactive sputtering ................................................................................................................ 15

2.3.4 Pulsed dc sputtering ............................................................................................................... 16

2.4 Magnetron Sputtering ................................................................................................ 17

viii

2.5 High Power Pulsed Magnetron Sputtering .............................................................. 19

2.6 HiPIMS and dc Magnetron Sputtering Plasmas ..................................................... 20

Chapter 3 Low Pressure Gasses ................................................................................ 23

3.1 Advantages of Low Pressure ..................................................................................... 23

3.2 Gases at Low pressures, Collision Frequency and Mean Free Path Derived ....... 25

3.2.1 Gas pressure, temperature and atom density relationship ...................................................... 25

3.2.2 Collision frequency and mean free path ................................................................................ 26

Chapter 4 Plasma Definitions ................................................................................... 29

4.1.1 The Debye length .................................................................................................................. 30

4.1.2 The Boltzmann relation ......................................................................................................... 31

4.1.3 Boltzmann relation derivation ............................................................................................... 31

4.1.4 Debye length derivation......................................................................................................... 32

4.1.5 Boltzmann and Debye length assumptions and limitations ................................................... 34

Chapter 5 Plasma Sheath .......................................................................................... 35

5.1.1 Plasma Sheath as a dielectric ................................................................................................. 35

5.1.2 Plasma pre-sheath and floating wall potential ....................................................................... 37

5.1.3 Child-Langmuir law sheath ................................................................................................... 44

Chapter 6 The Plasma as a Fluid ............................................................................. 46

ix

6.1 Diffusion in a plasma .................................................................................................. 46

6.2 Charge Balance and Ambipolar Diffusion ............................................................... 47

6.3 Magnetic Effects in a Plasma ..................................................................................... 48

6.3.1 Magnetic effects on a particle ................................................................................................ 48

6.3.2 Magnetization of a plasma ..................................................................................................... 49

6.3.3 Magnetic field effects on diffusion ........................................................................................ 50

6.3.4 Bohm diffusion ...................................................................................................................... 51

6.3.5 Drift velocities in a fluid ........................................................................................................ 52

Chapter 7 Waves and Plasma Oscillations ............................................................... 54

7.1.1 Sinusoidal equations of particle motion ................................................................................ 54

7.1.2 Development of the plasma frequencies ................................................................................ 54

7.1.3 Electrostatic wave propagation .............................................................................................. 57

7.2 The plasma as a Dielectric ......................................................................................... 60

7.2.1 Electromagnetic wave propagation ........................................................................................ 60

7.2.2 Dielectric tensor..................................................................................................................... 61

7.2.3 Geometric oscillations ........................................................................................................... 62

7.3 Summary ..................................................................................................................... 63

Chapter 8 General Expectations for a dc Magnetized Plasma ................................ 65

x

8.1 Power Law and Child Law Sheath ........................................................................... 65

8.2 Plasma Frequencies .................................................................................................... 66

8.2.1 Electromagnetic wave propagation ........................................................................................ 67

8.2.2 Geometry based frequencies .................................................................................................. 72

8.2.3 Frequency matching .............................................................................................................. 75

8.3 Summary ..................................................................................................................... 75

Chapter 9 Case Study: Analysis of Prior Magnetron Models ................................. 77

9.1 Oscillations in Magnetron Plasmas ........................................................................... 77

9.2 Collisional Model and Particle in Cell ...................................................................... 89

9.3 Conclusions ................................................................................................................. 90

Chapter 10 Plasma circuit equivalent model.............................................................. 92

10.1 Magnetron circuit ....................................................................................................... 93

10.2 Turbulence effect ........................................................................................................ 96

10.3 Conclusions ................................................................................................................. 99

Chapter 11 Experimental Data ................................................................................. 100

11.1 Experimental Setups ................................................................................................ 100

11.1.1 The “Maggie” Chamber ............................................................................................. 100

xi

11.1.2 Linköping University chamber .................................................................................. 102

11.2 Current and voltage vs. time data collection for each system .............................. 104

11.3 Physical data range ................................................................................................... 108

11.4 Current and voltage vs. time for each element ...................................................... 110

Chapter 12 Results and Discussion .......................................................................... 116

12.1 Current and Voltage Characteristics ...................................................................... 117

12.1.1 Current and voltage curves for selected pulses .......................................................... 120

12.1.2 Maximum current vs. maximum voltage ................................................................... 122

12.2 Average Resistance vs. Applied Voltage ................................................................. 124

12.3 Modified magnetron I-V fit ..................................................................................... 129

12.4 Fluctuations ............................................................................................................... 133

12.5 Plasma immersion ion implantation matrix sheath model ................................... 135

12.6 Plasma sheath instability ......................................................................................... 141

12.7 HiPIMS plasma analysis .......................................................................................... 144

12.8 Sheath and PIII Implications .................................................................................. 148

Chapter 13 Summary and future work ..................................................................... 149

13.1 Summary ................................................................................................................... 149

xii

13.2 Future work .............................................................................................................. 152

13.3 Conclusion ................................................................................................................. 154

References ...................................................................................................................... 155

Appendix A Current and Voltage Curves vs. time for select elemental Targets at UNL

......................................................................................................................................... 171

A.1 Current and voltage vs. time curves for copper ........................................................... 171

A.2 Current and Voltage Curves for titanium .................................................................... 177

A.3 Current and Voltage Curves for silver ......................................................................... 200

Appendix B Current and Voltage characteristic curves for Aluminum and Chromium

at a range of pressures from LIU system ...................................................................... 209

B.1 Current and Voltage Curves for aluminum ................................................................. 209

B.2 Current and Voltage curves over a range of pressures for chromium ...................... 251

xiii

Table of Figures

Figure 2-1. Sputtering of metal (Me) by ionized argon. .................................................. 10

Figure 2-2. The effects of argon pressure and substrate temperature on film structure by

Thornton (2). ............................................................................................................. 11

Figure 2-3. Typical regions within a dc plasma discharge (after Lieberman and

Lichtenberg) (22). ..................................................................................................... 14

Figure 2-4: Two dimension electron “hopping” for magnetron sputtering. On average,

the electron moves to the right showing basic concept of electron “drift”. .............. 18

Figure 2-5. Current and Voltage vs. time for a typical HiPIMS discharge ...................... 20

Figure 2-6. Macak et al demonstrated the shift in ions from the inert gas to metal ions

(73). Optical emmision signals for argon and titanium are overlayed with target

current and voltage. The inset shows an ion probe signal broken into argon and

titanium components from the optical emission data as deconvoluted by Macak et al

(73). ........................................................................................................................... 21

Figure 3-1. The cylinder schematically drawn in cross section is the volume traversed by

an atom through a gas. The cylinder is how far on average a particle will travel

before one collision will occur. The radius is 2 atoms in size to allow for the

colliding atoms to be considered points rather than spheres. .................................... 27

xiv

Figure 4-1. Negative charges are schematically drawn depicting a plasma attracted to and

effectively shielding a positively charged plate. Dotted line indicates approximate

Debye length. ............................................................................................................ 30

Figure 5-1. A schematic representation of a plasma sheath between a wall and a plasma;

and the plasma density profile is shown as a cutoff with the ions and electrons

dropping to zero at the sheath edge. The sheath thickness is “s”. ........................... 36

Figure 5-2. A description of the plasma sheath using a pre-sheath region of reducing

plasma density followed by a sheath containing more ions than electrons due to the

difference in the thermal velocity of ions and electrons is schematically depicted.

The electron (dotted line) and ion density (solid line) are equal within the pre-sheath

and bulk plasma. ....................................................................................................... 38

Figure 5-3. The theoretical ion velocity dependence on initial ion velocity. Initial ion

velocities of: zero, half the bohm velocity (KT/M), the Bohm velocity, and twice the

Bohm velocity, are shown. As the ion velocity reaches the Bohm velocity, the

sheath has a smaller relative influence. ..................................................................... 41

Figure 5-4. Ion density for various initial velocities with respect to the Bohm velocity

(kT/M) compared to the electron density (Ne). Velocities graphed are zero initial

velocity, half the bohm velocity, the Bohm velocity, and twice the Bohm velocity.

Only the Bohm velocity meets the initial assumption that the number of ions is equal

to the number of electrons and also maintains the assumption of more ions than

electrons (Ne) within the sheath. ............................................................................... 42

xv

Figure 7-1. A displaced electron cloud (downward cross-hatching) is schematically

drawn over a set of stationary ions (upward cross-hatching). An enclosed surface

for finding the electric field over a region using Gauss's law is also drawn. ............ 55

Figure 8-1. The square of the theoretical refractive index (N2) for a high density

magnetized plasma parallel to the magnetic field predicted using Equation (8-3) as a

function of frequency. The value is negative resulting in an imaginary refractive

index, not allowing waves to propagate. The parameters are 200 gauss, 1019 ions per

m3, argon gas, ignoring collisions. ............................................................................ 68

Figure 8-2. The square of the theoretical refractive index (N2) for a high density

magnetized plasma perpendicular to the magnetic field (extraordinary wave)

predicted using Equation (8-6) plotted with respect to frequency. The parameters

are 200 gauss, 1019 ions per m3, argon gas, ignoring collisions................................ 70

Figure 8-3. The square of the refractive index (N2) plotted with respect to frequency for

special right handed polarization propagation parallel to the magnetic field.

Resonance occurs around 108 Hz (not shown). The parameters are 200 gauss, 1019

ions per m3, argon gas, ignoring collisions. .............................................................. 71

Figure 8-4. The square of the refractive index (N2) plotted with respect to frequency for

special left handed polarization propagation parallel to the magnetic field.

Resonance occurs around 104 Hz. The parameters are 200 gauss, 1019 ions per m3,

argon gas, ignoring collisions. .................................................................................. 72

xvi

Figure 8-5. The change in the configuration of the plasma from a uniform plasma density

to a non-uniform plasma density, due to circular geometry. a) The first section

shows an initially uniform plasma density, with a small region ∆ marked, and b)

then the electrons move in their cyclotron path, resulting in c) the regions subtended

in part “a)” switching places, generating a plasma density fluctuation, not previously

present. The plasma density change will result in an outward pressure gradient .

................................................................................................................................... 73

Figure 8-6. A possible oscillation that can develop alongside the pressure gradient and

drift within the magnetic trap is schematically drawn (75). ..................................... 74

Figure 9-1. The dependence of electron density with respect to electron density divided

by the total number of charge carriers. This plot allows the establishment of

variable dependence. The power value of “-.031” indicates a small dependence,

with the relative local density decreasing as the total plasma density increases. The

power value of “.0626” indicates a small dependence, with the relative density

increasing as the total plasma density increases. ...................................................... 83

Figure 9-2. The electrons move along lines of flux above the target. The width w of the

track followed by the electrons is in part due to the gyroradius for the electron.

Higher voltage electrons (grey) will have larger width erosion tracks. Schematic

drawn after Liebermann and Lichtenberg (22). ........................................................ 84

xvii

Figure 9-3. The the square of the refractive index (N2) vs. frequency (f) in Hz for the

right hand polarized wave, as known as the whistler mode. The values for this

calculation were 1016 m-3 density, argon gas and 132 Gauss magnetic field. ........... 85

Figure 9-4. Goree and Sheridan's observed frequency spectrum for variation in density

(28). The graph shows a normalized plot of the fluctuation in density with respect to

the frequency of the fluctuation. ............................................................................... 86

Figure 9-5. The frequency (f) in Hz vs. the square of the refractive index (N2) for the left

hand polarized wave is graphed. The values for this calculation were 1016 m-3

density, argon gas and 132 Gauss magnetic field. .................................................... 87

Figure 9-6. The frequency (f) in Hz vs. the square of the refractive index (N2) for the

extraordinary wave is graphed. The values for this calculation were 1016 m-3

density, argon gas and 132 Gauss magnetic field. .................................................... 88

Figure 10-1. An illustration of the magnetron plasma represented as a series of capacitors

and inductors; resistive components have been removed for clarity. ....................... 92

Figure 10-2. The model for the power supply (a), and the model for the plasma (b) is

schematically depicted. A capacitor set is shown for both sheaths. The flux lines

are modeled as inductors parallel and capacitors perpendicular to the plasma. The

flux lines that are modeled are overlaid as dotted grey lines. ................................... 94

xviii

Figure 10-3. The Current and Voltage vs. time curve for the power supply through a

resistive load ( grey dashed lines) and the I and V vs. t curve for the plasma model

without resistive variation (solid lines). .................................................................... 95

Figure 10-4. The simplified network with a pair of choppers (modulated resistivity) used

to simulate the plasma as a pair of capacitors with parallel resistors to conduct the

power......................................................................................................................... 97

Figure 10-5. The dc behavior for Voltage and RMS current supplied to the cathode as

depicted by a simplified power system model is graphed as current vs. time. The

upper line operates the chopper circuit at 10 kHz, and the lower line is at 1Hz. ...... 98

Figure 11-1. A schematic diagram of the magnetron sputtering system at UNL

“Maggie”. ................................................................................................................ 101

Figure 11-2. A confirmed model of the magnetic field direction, and strength of the

"maggie chamber". The contour lines represent magnetic field strength of 10 gauss

increments, and the arrows indicate magnetic field direction. ................................ 101

Figure 11-3. Schematic Diagram of the Swedish HiPIMS system. Courtesy Johan

Böhlmark, Chemfilt Ionsputtering AB ..................................................................... 103

Figure 11-4. The applied magnetic field of the magnetron. The numbers are given in mT.

The data were taken using a Hall probe. The solid lines represent the direction of the

magnetic field, while dashed lines represent the magnetic field strength. Courtesy

Johan Böhlmark, Chemfilt Ionsputtering AB. ......................................................... 104

xix

Figure 11-5. Typical discharge for UNL HiPIMS system, current and voltage for

titanium at 3mTorr of argon and 1144 Volts, scaled to a similar time frame to LiU

data. ......................................................................................................................... 106

Figure 11-6. Typical discharge for UNL HiPIMS system, current and voltage for

titanium at 3mTorr of argon, and 1144 Volts applied discharging to about 500 V. 107

Figure 11-7. Typical discharge for Linköping system. Voltage applied to aluminum at

22.5 mTorr starting at about 832 Volts initially applied, discharging to about 500

volts. ........................................................................................................................ 108

Figure 11-8. Current and voltage curves for copper at 3mTorr and 830 Volts initially

applied. .................................................................................................................... 110

Figure 11-9. Current and voltage characteristics for titanium at 820 Volts initially

applied and 3mtorr with the coil off. ...................................................................... 111

Figure 11-10. Current and voltage characteristics for titanium at an initially 820 Volts

and 3mtorr and a coil current of 5 amps. ................................................................ 112

Figure 11-11. Current and voltage characteristics for silver at an initially applied 820

Volts and 5mtorr. .................................................................................................... 113

Figure 11-12. Current and voltage curves for aluminum at 5 mTorr and 830 Volts

initially applied. ...................................................................................................... 114

xx

Figure 11-13. Current and voltage curves for chromium at 5 mTorr and 830 Volts

initially applied. ...................................................................................................... 115

Figure 12-1. Titanium at 3mTorr with 550V applied. A clear lag (shaded region)

between current flow and voltage applied may be seen. ........................................ 117

Figure 12-2. Titanium current and voltage curves at 1200V, a clear second region is

present in the current curve after the initial peak. Typically there is an initial current

from the argon ions, and then a second peak from the metal ions is detected. The

current peaks have corresponding voltage drops. ................................................... 118

Figure 12-3. 5 mTorr aluminum at 1700V applied voltage indicating several behaviors

present in HiPIMS current and voltage curves. An initial voltage drop again is

followed by a second voltage drop. A periodic oscillation increases in frequency

and amplitude during the discharge of the supply overlaying the region of the second

voltage drop. ........................................................................................................... 119

Figure 12-4. Shows voltage vs. time for chromium at 5 mTorr for 600 through 1700

starting voltages. (a) is 600 volts initially applied, (b) is 800 Volts initially applied

(c) is 1100 Volts initially applied (d) is 1300 Volts initially applied and (e) is 1700

Volts initially applied. ............................................................................................. 120

Figure 12-5. Shows voltage vs. time for aluminum at 5 mTorr for 600 through 1500

starting voltages. (a) is 600 volts initially applied, (b) is 900 Volts initially applied

(c) is 1050 Volts initially applied (d) is 1250 Volts initially applied and (e) is 1500

Volts initially applied. ............................................................................................. 121

xxi

Figure 12-6. A graph of peak applied voltage vs. peak developed current is plotted for

various pressures of argon. Error in the applied voltage measurement is +/- 10

Volts. ....................................................................................................................... 122

Figure 12-7. Chromium graphs of voltage applied vs. the maximum current. The two

sets are different magnet arrays used in the same cathode body. The weaker magnet

set (diamonds) generated voltages in the 100’s of amps. The stronger magnetic field

(squares) generated larger peak maximum currents. .............................................. 123

Figure 12-8. Current maximum vs. maximum applied voltage for aluminum at both 5 and

20 mTorr. The values appear to converge toward a single value. ......................... 124

Figure 12-9. The resistance as a function of applied voltage for chromium at a range of

pressures. All the pressures appear to converge to one resistance at high applied

voltages. .................................................................................................................. 126

Figure 12-10. The resistance as a function of applied voltage for aluminum at 5 and 20

mTorr. Similar to the chromium, the different pressures appear to converge to one

resistance. ................................................................................................................ 127

Figure 12-11. The pressure and material dependence of the resistance from the plasma

may be observed through the voltage vs. resistance curve. The chromium data is in

gray (triangles, asterisks, bullets and plusses), and aluminum data is black

(diamonds and squares). The scale of this graph has been adjusted to have a non zero

lower limit in order to see that the curve continues at the small resistance values. 128

xxii

Figure 12-12. A new asymptotic approach for the minimum resistance in comparison to

the original magnet array for the same pressure may be seen in the figure. The

lower magnetic field data set is black squares. The larger magnetic field data set are

dark circles. The increased B field achieves a lower minimum resistance. ........... 129

Figure 12-13. A fit to the current maximum vs.-applied voltage maximum curve by

adding an "n=1" term to the system for 15 mTorr chromium. The graph also helps

demonstrate that at large currents, the "n=1" term will become dominant. ............ 131

Figure 12-14. A fit to the current maximum vs.-applied voltage maximum curve by

adding an "n=1" term to the system for 5 mTorr aluminum. This helps demonstrate

the broad application of this fit through demonstration on separate material and

pressure. .................................................................................................................. 132

Figure 12-15. The derivative of the voltage vs. time (left axis) and the current vs. time

(right axis) graphs. The voltage oscillations decrease in frequency during the length

of the pulse. ............................................................................................................. 133

Figure 12-16. The correlation between current flow and fluctuations on the I-V curves

has been highlighted. a) and b) show the behavior for an applied voltage of -1500

dv/dt is appr 1e9 and the current approaches 800 amps for aluminum. c) and d) show

the behavior for an applied voltage of -700V, dV/dt is almost 1e8, and the current

approaches 60 amps also for aluminum. ................................................................. 135

xxiii

Figure 12-17. Illustrated is the sheath moving away from the cathode exposing a matrix

sheath of ions. The large group of initially exposed ions creates a spike in current.

................................................................................................................................. 136

Figure 12-18. The normalized current vs. normalized time for the plasma immersion

effect from Lieberman(90). The dashed line is the theoretical values, the solid line

is the experimental (22). ......................................................................................... 138

Figure 12-19. The current vs. time and voltage vs. time for titanium at 1245 volts

initially applied and 3mTorr. The initial peak has strong similarities to the matrix

sheath model. .......................................................................................................... 139

Figure 12-20. A graph of 3 separate current vs. time graphs from Arbel et al. (95). The

time scale is 200 ns/div. a) shows the behavior of a stable discharge with 10 mA/div;

(b) shows an oscillation slightly above discharge threshold for instability with

20mA/div; and (c) shows a current well above the threshold current at 40 mA/div.

................................................................................................................................. 142

Figure 12-21. The oscillations in the current and voltage for aluminum at 22.5 mTorr and

1800 V maximum applied voltage. After the intial ringing dies down, a set of

oscillations develops during the discharge. ............................................................ 143

Figure 12-22. Current and voltage are graphed with respect to time from Chistyakov's

patent Figure 5C. The figure shows a dramatic increase in current being generated

by a quick change in the applied voltage. As may be seen by the drawn in peaks, the

frequencies are close to the Nyquist rate of the measurement. ............................... 147

xxiv

1

Chapter 1 Introduction

In the thin film industry, improvements in film quality have been observed and achieved

through increased heat and energy at the growing film surface (1) (2). Techniques used

to deliver this energy to the growing film have evolved from wafer heating (2), to wafer

bias (3) (4), to ionizing the incoming flux (5) (6). While there are a number of different

methods for ionizing the incoming flux to the substrate; however the focus of this

dissertation is on a method commonly described as High Power Impulse Magnetron

Sputtering (HiPIMS) (7) or High Power Pulsed Magnetron Sputtering (HPPMS) (8). The

goal of this dissertation is to develop a better understanding of the underlying

relationships that resulted in anomalous oscillations of the power supplied during

HiPIMS. This goal will be achieved by: introducing the underlying concepts of plasmas

and their applications to sputtering and direct current (dc) discharges; developing

computational models from these concepts; and finally comparing these models to

collected experimental data to develop predictions for the fluctuations in the discharge.

This dissertation in turn will provide the groundwork for improved HiPIMS power

supplies and system designs.

1.1 HiPIMS (High Power Impulse Magnetron Sputtering)

High Power Impulse Magnetron Sputtering (HiPIMS) is a process that develops a highly

ionized sputtered flux through pulsing high voltages (approximately 1kV or greater) and

currents (up to 1000 amps) into targets for short durations (10-200 microseconds) (9). It

has been previously demonstrated that increased ionization of the material to be deposited

2

results in improved film quality (5). HiPIMS processes show promise for increasing ion

densities, via filling, and improved film growth (10) (11) (12). HiPIMS has also been

reviewed for its use as a pre-treatment for various reactively sputtered coatings (13).

HiPIMS has an advantage over other ionization techniques, as the primary required

modification is simply a pulsed power supply. A characteristic HiPIMS pulse has an

initial voltage region before the plasma ignites, followed by a discharge curve ending

when the plasma is no longer sustainable (11). A typical design for the supply is to store

the power to be supplied to the plasma in a capacitor. This results in an ever dropping

voltage across the cathode as the capacitor loses charge. Various designs provide

additional inductors, ringing circuits or solid state devices to trigger the plasma and

maintain a selected voltage for as long as possible (8) (9) (14) (15).

HIPIMS systems generate a significant fraction of ionized species in the sputtered flux;

this ionization increase results in different deposition rates and profiles compared to those

of dc sputtering (7) (16). Electric fields applied to the substrate during HiPIMS have also

been found to significantly affect the deposition rate, as has varying the magnetic field

strength of the cathode (7) (16) (17). Magnetic and electric fields of the magnetron are

known to vary radially and vertically from a target surface for dc sputtering (18).

Therefore current simple collisional Monte Carlo simulations of deposition profiles are

no longer sufficient for HiPIMS discharges. In order to successfully predict the

deposition profile for an ionized source, electric and magnetic fields within the plasma

need to be considered.

3

HiPIMS sources utilize several power supply designs (8) (9) (15) (19). The one clear

behavior all of these designs have in common is a high current which develops extremely

large powers for brief instances in time. A second common characteristic would be

unintentional fluctuations within the target’s current and voltage vs. time curves. Most

HiPIMS research to date has focused in the area of the improved film characteristics

provided with the increased ionized sputtered material (10), or applying the ionized flux

source in new multi-step processes (13). To date, two current/voltage fluctuations

phenomena have been explored within the HiPIMS literature, arcs (8) and a high current

phenomena induced by a preprogrammed variation in supplied power (20). The first

fluctuation to be studied in more detail was arcing. Occasionally during the pulse, the

voltage may plummet and current dramatically increase as an arc develops. In order to

prevent such behavior, arc suppression circuitry has been developed (8). The second

phenomena was initiated by a power supply design with the apparent purpose to allow

programmed high voltage waveforms of any shape with the current available for

sustained high voltage pulses (20). The inventor’s data show a marked improvement in

discharge current when the applied voltage begins to oscillate. The data would initially

seem to show that by just a small oscillation in the voltage, a dramatic increase in current

is possible. The data provided however appears to be attempting to sample an oscillation

above its Nyquist frequency, making the determination of amplitude suspect (20).

Regardless of the measurement, a basic demonstration that oscillations may drive greater

dc currents has been claimed.

4

1.2 Direct-Current Magnetron Sputtering Improvements

In order to begin to understand the HiPIMS process, it is useful to first step back and look

at what has been done with dc magnetron sputtering. In general, processing plasmas are

considered as a pair of sheaths and a uniform plasma between the sheaths (21). Direct-

current (dc) plasmas include anode and cathode sheaths, and require secondary electron

emission along with a large enough anode-cathode distance to maintain the plasma

through collisions (22). Magnetron sputtering adds a magnetic field to the dc processing

plasma allowing shorter substrate to target distances by turning the electron’s trajectory

into a helix, and thus providing the required collisions in smaller distances (23).

Unbalanced magnetron sputtering further improves the film quality through greater

plasma densities, which result from increasing the outer magnetic field strength of the

magnetron (24). Numerous types of dc magnetrons now exist, circular, rectangular,

planar, and cylindrical; some contain anodes in the center, some have floating darkspace

shields (23) (25). Each design results in different electric field patterns; the sputtered

flux in dc magnetron sputtering, however, would remain mostly unaffected. The minimal

effect on dc sputtering is related to the small percentage of ionized material, however, in

processes with highly ionized flux, such as HiPIMS the ions’ trajectory will be affected

by the electric and magnetic fields present in the magnetron plasma.

An impending process driven need to understand the role magnetic and electric fields

have within the plasma is now becoming a reality with the advent of ionized deposition

processes. In a qualitative manner the processing community can simply understand that

increased electron trapping and electron density will require increased ion trapping

5

through ambipolar diffusion and thus affect deposition profiles (16) (17). This

understanding falls clearly short of providing a predictable model applicable to various

magnetron designs or process parameter settings to generate accurate film rates and

uniformity. In order to accurately model the movement of the ions, the electric and

magnetic fields governing the ion’s path as well as collisional occurrences must be

considered. In order to predict the electric and magnetic fields the ions will encounter,

the electrical behavior of the magnetized plasma must be scrutinized.

The common thread within these HiPIMS challenges is a need for a better understanding

of the HiPIMS plasma. The focus of this dissertation is to analyze what effects and

contributions, plasma oscillations may have, in HiPIMS plasmas.

1.3 Direct-Current Magnetron Sputtering Current

Oscillations and current transport within the plasma of dc magnetrons have been a subject

of interest for many years (23) (26) (27). In 1975, Thornton theorized that diocotron type

waves and other turbulent oscillations were responsible for successful electron transport

within cylindrical magnetrons (23). Sheridan and Goree have since provided a wealth of

publications indicating the importance of collisions and ions to the magnetron behavior

(28) (29) (30) (31) (32) (33). More recently, Martines, et al. and others have renewed

some interest in reviewing the contribution of oscillations within the plasma (27) (34)

(35).

In 1989 Sheridan et al. began to investigate the concept of oscillations and how to model

the magnetron plasma (28) (31). First, Sheridan et al. performed experiments at low

6

sputtering intensities and analyzed the oscillations below 1MHz (28). Second, Sheridan

et al found that any relationship described needs to follow a dependence on the mass of

the gas (29). Third Sheridan et al. attempted to demonstrate through particle-in-cell

modeling that collisions were an important factor in electron transport, and a more likely

candidate than oscillations for the observe current flow (31).

1.3.1 Particle-in-cell (PIC) collision model

Goree and Sheridan then developed a particle-in-cell (PIC) simulation of electrons

escaping the surface of a magnetron and tracked their movements in a set of articles (31)

(32). 2-d simulations were carried out with and without collisions. However, their model

finds that significant numbers of the electrons fully use up their energy ionizing argon.

Their PIC model would result in a buildup of spent electrons within the magnetic trap.

Thus, the model does not appear to be charge/current flow balanced. Ideally each

electron would be tracked until the electron finds a wall or is otherwise neutralized.

Through more powerful computing, more self-consistent models are being developed

(36). New factor that is also missed in the PIC model is the countering magnetic field

that will develop from the electron current. As the plasma becomes denser, this may be

expected to become a significant contribution.

1.3.2 Diffusion model

Clearly there is still a need to describe the traversal and flow of electrons across magnetic

field lines beyond the expectations derived from following single electrons. Often this

gap has been filled by the semi-empirical formula of Bohm diffusion. Although Bohm

7

diffusion may approximately be derived, and describes a relationship between expected

electric fields within a plasma, the term tends to be used as a catch-all for electrons

unexpectedly penetrating magnetic barriers.

Recent experiments in analyzing plasmoid penetration of magnetic barriers have

indicated fast electron transport mechanisms exceeding Bohm diffusion (37). This

transport has been reported to be the result of oscillations in the range of the lower hybrid

frequency (38). There is therefore a need to look into the expected methods of transport

within a plasma as well as the frequencies present within magnetized plasmas.

1.4 Motivation and Objectives

Collisions and collision models fail to completely account for the behavior of magnetron

cathodes as may be seen by the lack of agreement between ionizing collisions modeled

and ionizing collisions required to maintain the plasma (30) (32) (39). These problems

are greatly magnified with the high current densities of HiPIMS.

The overall goal of this dissertation will develop a better understanding of the underlying

relationships that may result in oscillations of the power supplied during HiPIMS.

Specifically, this dissertation will:

• develop a basic model for magnetron plasmas that attempts to include

oscillations;

• explore the frequency instabilities that would be present in a magnetron;

8

• analyze the HiPIMS characteristic power curves for fluctuations and associate

these fluctuations with expected frequencies within the plasma; and

• generate a solution to the experimental solutions by applying related fields of

study.

Overall, the goal of this dissertation is to knit together the wave carrying capability of the

magnetized plasma and the observed plasma oscillations into a partial explanation for the

current carried by the plasma thus providing an improved understanding of HiPIMS and

magnetron plasmas.

9

Chapter 2 Sputtering Background

Magnetron sputtering is an important industrial process for a wide variety of products

from automobiles to semiconductors (5) (11) (24) (40). Although the basic concept of

increased current from improved path length by using magnetic trapping regions near the

cathode is well understood, the mechanisms of current flow, and the plasma behavior are

still areas of active research.

2.1 Introduction to Sputtering

Sputtering can be described as the ejection of material from a solid or molten source (or

target) by kinetic transfer from an ionized particle (41) (42). In Figure 2-1, argon atoms

are ionized and accelerated through a potential difference; the Ar+ ions then collide with

the negatively biased cathode surface, or target. Each ion collision with the cathode has

the potential to cause ejection of one or more atoms (labeled “Me” in Figure 2-1) from

the surface of the cathode. Through the process of kinetic energy transfer, the ejected

material moves away from the cathode in a linear fashion, and thus vapor atoms condense

on all surfaces in line-of-sight of the cathode. The sputtered material depositing on a

surface tends to have higher kinetic energy, imparted by the high-energy Ar+ ions, than

thermally evaporated atoms. The ejected material therefore often has higher mobility

than an evaporated material and this generally results in larger grain sizes (43), better

adhesion, and more dense film structures.

10

Figure 2-1. Sputtering of metal (Me) by ionized argon.

A wide array of materials can be sputtered regardless of their melting temperatures,

sputtering also works well with alloy sources. Although different atoms have varying

sputtering yields, a low sputtering yield material would quickly become overabundant,

and sputter at a higher rate due to an increased surface concentration. This results in film

chemistries that are quite close to those of the source material. The reader is referred to

The Materials Science of Thin Films by Ohring, (44) Thin Film Processes by Vossen and

Kern, (45) Principles of Plasma Discharges and Materials Processing by Lieberman and

Lichtenberg, (46) Handbook of Thin Film Technology by Maissel and Glang (41) and the

chapter on “Unbalanced Magnetron Sputtering” in Physics of Thin Films 18, Plasma

Source for Thin Film Deposition and Etching by S. L. Rohde, (24) for more detailed

information on sputtering and its variations.

2.2 Temperature Effects in Sputtering

Sputtering is a type of physical vapor deposition (PVD), where mostly individual atoms

collect on a substrate. Often PVD systems may also include heating, cooling and

Ar+

Me

Me

11

substrate bias capabilities in order to affect the density, uniformity, and crystallinity of

the thin film. As illustrated in Figure 2-2, heating helps nucleation of a crystalline film.

Similar to heating, the substrate bias increases the mobility of atoms on the surface of the

sample lowering the temperature at which crystalline material will be formed (47). The

substrate bias extracts positive ions out of the plasma and bombards the substrate (ion

bombardment), the voltage is slightly more negative than the potential of the plasma near

the substrate.

Figure 2-2. The effects of argon pressure and substrate temperature on film structure by Thornton

(2).

Substrate ion bombardment not only lowers the temperature at which a crystalline

material will form, but also helps to densify the material being deposited. Sputtering

12

ejects material that moves in a “line-of-sight” direction from the cathode and then

deposits on a surface. The bombarding ions act to smooth the surface by exciting the

surface atoms, thus increasing their mobility, and also by resputtering material from the

substrate. If the bombardment energy is not high enough, the film density will not

noticeably change; if the incident ion energy is too high, the film will become stressed

and may delaminate. Ion bombardment may also affect the crystallite size, and the

crystalline orientation (48) (49). Heating the substrate and ion bombardment are

important techniques, because they give the researcher more flexibility in controlling

certain film characteristics of the sputtered film.

2.3 Sputtering Techniques

There are many methods used to accomplish the sputtering of a target. Direct-current

sputtering was the original method and is named because it keeps the target at a constant

(dc) potential. Radio frequency (rf) sputtering uses a varying target potential and can be

used to sputter non-conductive materials. Reactive sputtering occurs when a gas that will

react with the target is introduced into the system and the reacted compound creates the

thin film. In general, a pulsed dc power supply is used in conjunction with reactive

sputtering. One major improvement over dc sputtering was the use of magnets behind

the target in order to increase target current and deposition rates. This is called

magnetron sputtering and can be used with either a dc or rf power supply. Each of these

methods: dc, rf, reactive, pulsed dc, and magnetron are described in more detail below.

13

2.3.1 Direct-current sputtering

The two basic requirements for dc plasma sputtering are a conductive cathode and

electron emission from the cathode. The cathode is a conductive target to which a large

negative potential voltage has been applied, while the anode is typically the metallic

chamber walls, but can also be a grounded or positively biased electrode. The processes

by which electron emission occurs and the resulting dc plasma discharge are described

below.

First, an inert gas, typically argon, is introduced into a chamber and serves as a medium

for the discharge. An ionizing event occurs similar to the ionizing event in a Geiger

counter, resulting in the formation of an Ar+ ion. If sufficiently close to the target, Ar+

ions will be accelerated towards the cathode, while the electrons near the anode are

accelerated towards the anode. The Ar+ ions colliding with the target cause ejection of

material, electrons, and x-rays, in addition to target heating. The ejected electrons are

accelerated away from the electrode through the cathode fall region (Figure 2-3), causing

more ionization, and if enough secondary electrons are produced at the target the

sputtering process becomes self-sustaining. The result is a sputtering plasma containing a

near-equilibrium number of positively ionized particles, such as ionized argon, and

negatively charged particles, such as electrons.

Figure 2-3 is a schematic sketch of a typical dc discharge. The cathode fall region is

where the largest voltage drop occurs. As the secondary electrons are accelerated away

from the cathode, the electrons will produce ionizing events as they collide with the gas

atoms in the chamber. These ionizing events will create exponentially more electrons.

14

Figure 2-3. Typical regions within a dc plasma discharge (after Lieberman and Lichtenberg) (22).

The large numbers of high-energy electrons create a region where a large number of ions

are produced (the negative glow region). Substrates are typically placed in the negative

glow region. Electrons drop most of their potential within the cathode fall, and are

slowing down as they pass through a region with more electrons than positive ions known

as the faraday dark space region, the electrons in this region collide with atoms and other

electrons slowing them down even further before entering the positive column. The

positive column is a region with a small potential gradient toward the anode, and nearly

the same number of positive and negative carriers. At the end of the positive column,

there is a region where the electron mean free path is typically larger than the distance to

the wall. In this region, all electrons are accelerated toward the wall creating a sheath

region. This region is described as the anode dark space. Thus a dc discharge will

typically have five different regions: cathode fall, negative glow, Faraday dark space,

positive column, and anode dark space. Within a magnetron sputtering cathode, most

Anode Cathode

Cathode Fall

Negative Glow

Faraday Dark Space

Positive Column

Anode dark space

Target

15

notable is the cathode fall and the dense positive column region which begins

immediately within the magnetic trap.

2.3.2 Rf Sputtering

Sputtering with rf removes the requirement that the cathode be conductive (50). In rf

sputtering, the potential applied to the target alternates from plus to minus at a high

enough frequency (>50 kHz) so that electrons can directly ionize the gas atoms, and thus

supply current to the target through capacitive coupling (51). In this case the sputtering

occurs both at the walls and at the target. The amount the walls are sputtered is

correlated with the ratio between the target and wall areas. The area that is smaller (e.g.

the target) has a higher rate of sputtering. The primary advantage of this type of

sputtering is that the target material need not be conductive, since the capacitive current

will travel through a non-conductive material.

2.3.3 Reactive sputtering

Reactive sputtering is a method to produce a compound film from a metal or metal alloy

target (52) (53) (54) (55). In reactive sputtering a reactive gas, such as oxygen or

nitrogen, is added to the inert (working) gas, typically argon. Formation of the reactive

compounds may occur in three regions, on the target, in the gas and on the surfaces.

Some of the reaction occurs at the target, a very small amount reacts in the gas, and the

remainder must react at the surfaces or be pumped away. The amount of reactive gas is

very important as an excessive amount of reactive gas reduces the sputtering rate since,

as most reactive compounds have a lower sputtering yield, and not enough gas results in

16

substoichiometric films (56). A fine balance must be made between reactive gas flow

and sputtering rate. This makes reactive sputtering an interesting challenge.

The behavior of the plasma in reactive sputtering is further complicated since different

materials emit varying amounts of electrons and have different sputtering yields; in

addition, the reactive gas will ionize along with the working gas. Reactive gases have a

number of effects on the target and the characteristics of the plasma, one of which is a

hysteresis effect (57) (58). For instance, aluminum oxide has a significantly lower

sputter yield and emits more electrons than aluminum resulting in deposition rates five

times lower than the metal deposition rate (1) (59). Different electron emissions mean

that the discharge currents may be drastically different for the same applied voltage

between the metal and the metallic compound. The changes in plasma characteristics are

thus further complicated and cannot be clearly explained for all compounds, but may help

indicate how much of the target is covered by the reactive compound. It is desirable to

sputter mostly metal in order to keep high sputtering rates, but form enough of the

metallic compound so that the film formed is stoichiometric. There are a number of

approaches detailed in the literature that try to avoid the reduction in sputtering rate for

reactive sputtering and the reader is referred to the following references for more

information (60) (61) (62) (63) (64).

2.3.4 Pulsed dc sputtering

During reactive sputtering many metals form compounds that are dielectrics. As the

dielectric forms, the target begins to build charge, and this charge reduces the potential

the plasma sees. If the dielectric layer builds up too much charge, the dielectric will

17

break down causing arcing; pulsed dc sputtering has been used in order to combat this

arcing (65). In pulsed dc sputtering the target is oscillated between an assigned negative

voltage (≅400V) and a positive voltage which is approximately 10% of the assigned

voltage at a high frequency (50-250 kHz). The positive voltage is a small percentage of

the negative set point in order to prevent sputtering of the anode. The anode may be the

walls; similar to the case with normal non-reactive sputtering, but the anode must be

protected from the sputtering target in order to act as a stable ground plane for the system

without building up a dielectric layer. One alternative method uses a second target as the

anode; in this case, the pulsing alternates which target is sputtering, and which acts as the

anode.

2.4 Magnetron Sputtering

Sputtering processes do not typically provide large discharge currents, or high deposition

rates, however the use of magnetic discharge confinement drastically changes this.

Magnets carefully arranged behind the target generate fields that trap the electrons close

to the target (66). Electrons ejected from the target are affected by an electric force due

the negative potential of the target as well as a magnetic force (“F”) due to the magnets

placed behind the target (cathode) as given by

(2-1) )( BvEF ×+= q .

18

Where “ ” is the charge, “E” is the electric field, “B” is the magnetic field, and “v” is the

velocity of the charged particle. Instead of just accelerating towards the negative anode

as in the dc sputtering case, the electrons are instead made to “hop” along near the target

surface. A simple two dimensional model is shown in Figure 2-4 with E = 100 V in a

direction perpendicular to the target surface (which is chosen to be the x-direction), B =

15 Gauss in a direction parallel to the target surface (which is chosen to be the y-

direction), and v is the is an initial electron velocity of 1x104 m/s. The electron only goes

so far away from the target before turning around and nearly hitting the target again, thus

creating a hopping behavior. The end result for the electrons is that they have an average

velocity perpendicular to both the electric and magnetic fields. The path length of the

electrons therefore increases near the cathode improving the ionization of the gas near the

target. This local increase in ionization produces more ions that can then be accelerated

toward the cathode, which in turn provides higher sputtering rates.

Figure 2-4: Two dimension electron “hopping” for magnetron sputtering. On average, the electron

moves to the right showing basic concept of electron “drift”.

0.00

0.20

0.40

0.60

0.80

1.00

0.00 1.00 2.00 3.00 4.00 5.00 6.00

z distance

x di

stan

ce

19

2.5 High Power Pulsed Magnetron Sputtering

The HiPIMS process is a sputtering process which results in large amounts of ionized

flux through high discharge current densities (12). The large current densities and

associated power levels are prevented from destroying the target/magnetron by applying

the power in bursts or pulses with small duty cycles thereby reducing the average power

to the cathode. The ionized flux of HiPIMS results in numerous advantages in

applications such as via or trench filling and improved film growth (10) (67). A

characteristic HiPIMS pulse (see Figure 2-5) has an initial voltage spike and a small

plateau region dependent on plasma ignition time, followed by a discharge curve ending

when the plasma is no longer sustainable (11). HiPIMS supplies store power to be

supplied to the plasma in a capacitor or bank of capacitors. This results in a dropping

voltage across the cathode as the capacitor loses charge. Various designs have been

developed to provide additional inductors, ringing circuits, arc suppression and/or solid

state devices to trigger the plasma and maintain a selected voltage for as long as possible

(8) (12) (14) (15).

HiPIMS supplies increase the significant ionized species in the sputtered flux; this

ionization shift results in different deposition rates and profiles from those of dc

sputtering (68). Statically applied magnetic and/or electric fields applied to or near the

substrate have been found to significantly affect the deposition rate for HiPIMS processes

which is not typical for DC sputtering processes (7) (16) (17). Electric fields of the

magnetron are known to vary radially and vertically from a target surface for dc

20

sputtering (18). Therefore, simple Monte Carlo simulations of deposition profiles are no

longer sufficient.

Figure 2-5. Current and Voltage vs. time for a typical HiPIMS discharge

2.6 HiPIMS and dc Magnetron Sputtering Plasmas

Studies of dc Magnetron and HiPIMS sputtering plasmas show fluctuations within the

electric field of the plasma (12) (27) (28) (35) (69) (70). These fluctuations have been

shown to have stronger occurrence at various frequencies. For example, Goree and

Sheridan have shown a strong frequency at the ion cyclotron resonance (104 Hz) (28);

and Martines et al. shows a series of frequencies in the azimuthal direction on the order

of 105 Hz (27).

0

100

200

300

400

500

600

700

800

900

0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04time (s)

Volta

ge (V

)

0

20

40

60

80

100

120

140

160

180

200

Cur

rent

(A)

Cr

21

In HiPIMS numerous frequencies may be seen developing in the target voltage after the

initial ringing of the power supply has died off (71), however variation in power supply

design makes this difficult to pinpoint. HiPIMS has several intriguing plasma properties

where after an initial argon ion plasma, the plasma shifts to a metallic ion based plasma

as shown in Figure 2-6 (72) (73). This shift in ions presents interesting plasma behavior.

The films produced using this HiPIMS technique are denser than sputtered films (10)

indicating higher energy/temperature of the incoming metal flux to the substrate.

Figure 2-6. Macak et al demonstrated the shift in ions from the inert gas to metal ions (73). Optical

emmision signals for argon and titanium are overlayed with target current and voltage. The inset

shows an ion probe signal broken into argon and titanium components from the optical emission data

as deconvoluted by Macak et al (73).

Typical I-V characteristics in a dc magnetron discharge follow the formula (7) (16) (17):

22

(2-2) nkVI =

Where I is the current and V is the applied voltage and k and n are empirical constants

developed for the individual system. Typical magnetron sputtering “n” values for

effective confinement fall in the range of five to nine (17) whereas “n” values on the

order of one have been shown to indicate a lack of confinement (74). HiPIMS plasmas

have also been shown to follow the same behavior with a transition to an n=1 region at

voltages over 700 V (16) (72). In order to better understand the HiPIMS plasmas and

their parent sputtering characteristics, a careful study of the dc magnetron plasmas is

required. Studying the behavior of gasses will help develop the knowledge needed for

plasmas.

23

Chapter 3 Low Pressure Gasses

Within “Introduction to Plasma Physics” Francis Chen (75) defines a plasma as “a quasi-

neutral gas of charged and neutral particles which exhibits a collective behavior.” By

considering the “gas” a “fluid” a number of the same formulae developed for plasmas

similarly correspond to the electromagnetic behavior of free electrons in metals and other

solids. Within the present dissertation the focus is on gaseous plasmas. The basic

constituents are free electrons, at least one species of at least singly ionized ions, and

neutral gas atoms. The following chapters will develop behaviors for the above parts of

the plasma, starting with defining the behaviors of a gas, followed by basic plasma

behavior and incrementally applying previous section realizations to develop various

equations for plasmas. After which general methods for generating and maintaining

plasmas will be discussed, this will then tie in to applying plasmas to thin film deposition.

3.1 Advantages of Low Pressure

Low pressure depositions occur whenever a chamber is evacuated and includes processes

such as thermal evaporation, electron-beam evaporation, and sputtering. Vacuums have

many advantages when it comes to making thin films. These advantages stem from the

fact that pressure is inversely related to the number of molecules in a given volume as

shown by the ideal gas law:

(3-1) NKTPV =

24

where P is the pressure, V is the volume, N is the number of molecules, K is Boltzmann’s

constant (1.38x10-23 J/K) and T is the gas temperature in K. The number of molecules

per cm3 is 1019 at room pressure (about 760 torr) and is only 109 at a pressure of 1x10-7

torr (a typical base pressure). Therefore the likelihood of impurities in a sample,

especially reactive species such as oxygen which occur naturally in air is decreased by a

factor of 1010.

The other main advantage of using a vacuum process in order to deposit a thin film is the

long mean free path of the desired material atoms. In general, the mean free path is

longer than the distance from the source to the substrate. This means that the source

atoms will not collide with other atoms on the way to the substrate and this creates a

process in which a substrate that is placed in the line of sight of the source will receive

most of the source atoms. The mean free path of an atom can be determined by:

(3-2) P

KTmfp

σλ

2=

where λ is the mean free path of an atom and σ is the interaction cross section. The mean

free path is only a few nanometers at atmospheric pressure, but is a few centimeters at the

typical sputtering pressure of 2 to 10 mTorr.

Low pressure therefore facilitates not only the elimination of contaminants including

oxygen, but also a longer mean free path allowing substrates to be placed at a reasonable

distance from the source without compromising deposition rates.

25

3.2 Gases at Low pressures, Collision Frequency and Mean Free Path

Derived

In order to understand plasmas the concept of a gas and fluid must first be described. A

gas may be considered a fluid with no local ordering of the atoms/molecules, where the

atoms/molecules may be considered individual particles. These particles move about

with a distribution of velocities colliding with each other and the chamber walls. The

momentum delivered to the walls from the atom’s velocity is generally described as a

pressure. The velocity distribution is associated with the atom’s temperature through a

Maxwell Boltzmann relationship:

(3-3)

where “ ” is the number of molecules as a function of velocity, “ ” is the molecules per

volume, “ ” is the mass, “ ” is boltzmann’s constant, and “ ” is the temperature in

Kelvin.

3.2.1 Gas pressure, temperature and atom density relationship

Atoms/molecules in a gas have energy associated with their velocity. Each atom’s

velocity is not necessarily exactly the same; rather the atoms produce a distribution of

velocities. This distribution will change with temperature, and there are a number of

ways to describe such a distribution. The pressure may be related to the distribution of

the gas atoms at a given isothermal temperature by the formula:

(3-4) or also

26

Where is pressure, is number of atoms, is Boltzmann’s constant and is

temperature in Kelvin. The above formula may be rewritten as the relationship:

(3-5) 3.25 10

with in atoms per cubic centimeter and p in Torr at standard temperature.

3.2.2 Collision frequency and mean free path

Atoms within a gas are typically traveling with high velocity. The velocities of the atoms

vary and may be predicted to approximate a Maxwell Boltzmann distribution described

previously. The distribution can be described using the terms of the most probable

velocity (u ), the average velocity (u), and the root mean square velocity u . The

values for each are different due to the large tail at higher velocities in the distribution

and given by the formulae (22):

(3-6) u

(3-7) u

(3-8) u

where, “ ” is the temperature and “ ” is the mass of the gas atoms. At room

temperature for argon this results in average velocities on the order of hundreds of meters

per second. It is highly unlikely however, for an atom to travel a distance of hundreds of

meters in a single direction in a second due to the presence of other atoms for collision.

27

As previously defined, the average distance traveled before a collision occurs for an atom

is described as the mean free path. The distance traversed by an atom before a collision

may be written as a volume of a cylinder carved out of space while considering the size

of the atom as the radius for the cylinder as shown in Figure 3-1, in order to simplify the

setup assuming the second atom as a point and supplying its radius to the traversing atom

provides us with a volume of space that an atom travels. Given an atom density (number

of atoms per cubic meter), it is possible to determine the volume of space to be covered in

order to encounter one atom as the inverse of this density; thus providing a second

volume to equate to our first volume that the atom has traversed. Once an atom has

traversed a volume equal to the volume within which one atom is contained, a collision is

expected to occur.

Figure 3-1. The cylinder schematically drawn in cross section is the volume traversed by an atom

through a gas. The cylinder is how far on average a particle will travel before one collision will occur.

The radius is 2 atoms in size to allow for the colliding atoms to be considered points rather than

spheres.

λ

28

Thus yielding the equation:

(3-9) or 1

where is the collision cross-section defined in this case, by , is the length of

the mean free path and is the density. (Note: This equation is another form of equation

(3-2) where ng has been substituted in for p/KT). By applying the average velocity “u” of

the atoms in the gas we can develop an expression for how long before a collision occurs

“ ” and how frequently collisions occur “ ” with the equations (22):

(3-10) and u

Free electrons and ions within a plasma have the same behaviors as the gases, but with

the additional twist of interactions that result from their charge. This produces new types

of collisions such as electron-neutral, ion-electron and ion-neutral, as well as cumulative

behaviors from the electric and magnetic interactions of charged particles.

Collisions are key to understanding of dc sputtering and HiPIMS plasmas. Energetic

electrons collide with argon atoms generating argon ions. These ions are accelerated

toward the cathode with enough velocity to collide with and eject material for deposition

as well as more electrons for ionization. The collision frequency also plays an important

role in the behavior of waves and diffusion. Now that low pressure gases have been

developed, the physical description of a plasma may be described.

29

Chapter 4 Plasma Definitions

A gas behaves as a plasma whenever there are enough ions to screen out an electric field.

For example, if a positively charged plate is placed within a plasma, positively charged

ions will be repelled, and negative charged ions and electrons will be attracted. This

movement of charge will occur until the charged plate has enough surrounding charges

within the plasma to negate the plate’s effect on the electric field within the plasma. The

movements of these charges all depend on forces. The equation governing most of these

behaviors is the force equation which in general terms may be written as (22):

(4-1) mn ·

where, m is the mass, n is the density and is the velocity vector. The force equation

above relates the acceleration of the particles within the fluid to the forces from electric

and magnetic fields; pressure gradients; and collisions.

In addition to Equation (4-1), the continuity equation also plays a role in governing

charge motion and it states that the number of particles in a volume can change only

when a flux of particles crosses its enclosed surface, described mathematically by the

equation:

(4-2) · 0.

30

4.1.1 The Debye length

The distance an electric field penetrates into a plasma is related to the Debye length.

Using the plate example from the previous section, the distance of the plate’s influence

on the electric field within the plasma is defined as the Debye length (see Figure 4-1).

Figure 4-1. Negative charges are schematically drawn depicting a plasma attracted to and effectively

shielding a positively charged plate. Dotted line indicates approximate Debye length.

The freely moving ionized particles within the plasma will develop an oppositely charged

region next to a charged plate. The particles providing the charge however, still have

their thermal energy and therefore velocity. This prevents the charged region from

becoming infinitesimally small as the free electrons move about due to their thermal

energy. The equation describing the Debye length is:

(4-3)

V + -

++++++++++

-

-

-

-

-

-

-

-

-

-

31

4.1.2 The Boltzmann relation

The Debye length equation relates the energy of the electrons ( ) to the electric

potential ( ) within the plasma from Poisson’s equation

(4-4) 4 ,

through the Boltzmann relation

(4-5)

where is the electron density, and is the ion density. The Boltzmann relation is

generated by looking at the behavior of the electrons within the plasma in equilibrium

due to the interactions between electric field forces and pressure gradients applied to the

electron fluid.

4.1.3 Boltzmann relation derivation

The attraction and expected movement of the charged particles to the plate of Figure 4-1

generates a pressure (change in density) imbalance on the electrons within the plasma

generating a force density ( ) on the charged particles which is counter balanced by

the force applied by the electric field ( ) created by the charged plate resulting in the

sum of force densities of (22):

(4-6) 0,

assuming an isothermal state and using equation (3-4) which applies when changes in

pressure are on a slow time scale, and equation (4-6) changes to:

32

(4-7) 0

Recognizing that ln , and by removing a factor of equation (4-7) may be

rewritten as:

(4-8) ln 0

then integrating provides the result:

(4-9) ln

where “ ” is a constant, rearranging terms, solving for , and recognizing the initial

condition of no electric field should result in a density of the plasma ( ) generates

the previously discussed Boltzmann relation:

(4-10)

As shown, the Boltzmann relation assumes that the electrons are isothermal within the

plasma, this assumption means that the electron temperature throughout the plasma is

expected to be the same temperature; and that any waves that are to be considered, are

slow enough to allow the electrons to distribute the energy, maintaining the constant

temperature assumption.

4.1.4 Debye length derivation

By substituting the Boltzmann relation into Poisson’s equation (4-4), and assuming the

ions are stationary such that the result is (22):

33

(4-11) 4

then, by expanding the exponential through a Taylor series ( ∑! ) we get:

(4-12) 4 1 1

Assuming that is much less than one, the system may be linearized by dropping the

terms after “n=1” as insignificant (for 0.1 the “n=2” term is only a 5% change and

at 0.01 the change is half a percent) equation (4-12) becomes:

(4-13)

By recognizing the form of the double derivative depending on itself, a function of

potential fitting this description would be of the form the double derivative

of which is:

(4-14)

replacing the generic term “c” and defining this term as the Debye length , and placing

equation (4-13) into the form of equation (4-14) using the equation (previously given

in equation (4-3) ) for becomes:

(4-15)

34

4.1.5 Boltzmann and Debye length assumptions and limitations

This characteristic length for an electric charge’s influence on a plasma has been

determined using several assumptions. The first assumption is the linearization of the

exponential within Boltzmann’s relation which assumes 1. Second, the Boltzmann

relation itself assumes isothermal electrons with no drift velocity. Finally the assumption

is made that the ions are stationary due to having a mass three to four orders of

magnitude greater than the electrons. Nevertheless, the Boltzmann relation and the

Debye length provide two quick and simple methods for comprehending the behavior of

the plasma, and its interaction with electric fields. The plasma is quasi-neutral allowing

small electric fields to propagate. Fields applied to a plasma will reduce by about two

thirds (1-e-1) every Debye length, and this is achieved by relatively small differences in

the density of electrons to ions that counteract the applied field according to the

Boltzmann relation.

35

Chapter 5 Plasma Sheath

As previously discussed, a set of ions, electrons or neutral gas atoms can be expected to

follow a Boltzmann distribution for their individual velocities. As shown in equation (3-

7), the average velocity of the particles is inversely proportional to their mass. The net

result of this mass dependence is the treating of the ions as “stationary” and considering

only the electrons as having a thermal velocity. Since the electrons are moving faster

than the ions it can be expected more electrons hit the walls or other objects within the

system more often than the ions. As electrons are lost, however, the potential of the

system will shift positive as there are now more ions than electrons within the plasma.

Eventually the system reaches an equilibrium state where the electrons bombarding an

object where the flux Γ is equal to the ions bombarding an object Γ such that Γ Γ ,

due to the net positive charge of the plasma attempting to hold in the electrons from

walls. A plasma as shown earlier with the Debye length as in equations (4-14) and (4-

15), attempts to shield out electric fields from the plasma, thus pushing the potential drop

and loss of electrons close to the walls (within a few Debye lengths of the wall). The net

results are 1) a small region where the electron density is less than the ion density and 2)

for a wall with zero net current, the number of electrons hitting the wall is equal to the

number of ions hitting the wall.

5.1.1 Plasma Sheath as a dielectric

The plasma sheath, the region where most of the potential is dropped, contains fewer

electrons and ions than the bulk plasma; and this region may be described by a number of

36

approximations. The first simple approximation for the sheath is assuming a thin layer of

a vacuum absent of any ions or electrons. The approximation assumes the number of

electrons and ions within the sheath are so small, that their contribution is negligible as

shown in Figure 5-1 (22) (76).

Figure 5-1. A schematic representation of a plasma sheath between a wall and a plasma; and the

plasma density profile is shown as a cutoff with the ions and electrons dropping to zero at the sheath

edge. The sheath thickness is “s”.

n0

x

n

wall sheath plasma

s

n = ne = ni

37

This approximation results in an air dielectric between two conducting surfaces, the wall

and the plasma. The capacitance ( of the sheath may then be written as:

(5-1)

Where s is the sheath thickness is the dielectric constant of a vacuum; is the area of

the sheath and is the thickness of the sheath.

5.1.2 Plasma pre-sheath and floating wall potential

A second approximation describing the sheath would be to reduce the electrons faster

than the ions as shown in Figure 5-2, and to gradually reduce the plasma density within

the sheath rather than abruptly cutting off the plasma. A floating wall would then have a

potential ( ) according to the following equation:

(5-2) ,

where is the electron temperature, and are the ion and electron masses

respectively. This shows that a floating wall would be expected to have a linear behavior

with respect to the electron temperature of the system.

38

Figure 5-2. A description of the plasma sheath using a pre-sheath region of reducing plasma density

followed by a sheath containing more ions than electrons due to the difference in the thermal velocity

of ions and electrons is schematically depicted. The electron (dotted line) and ion density (solid line)

are equal within the pre-sheath and bulk plasma.

The floating potential is derived by setting the electron flux to the wall equal to the ion

flux at the wall where (22):

(5-3)

is the ion flux where it is assumed the ions have the uniform Bohm velocity , and the

electron density may be described by (22):

(5-4)

n0

x

n

wall sheath plasma

s

pre-sheath

ne ni

39

that is assumed to be a Maxwellian distribution of electron velocities due to their thermal

energy. At the sheath-presheath edge the plasma density is expected to have become

reduced to a value from the bulk plasma density through the presheath due to a small

potential where the approximation of ne=ni still holds. The Bohm velocity may be

written as (22):

(5-5)

The Bohm velocity is the speed that the ions have been accelerated to during the pre-

sheath region, where the assumption of the ions and electrons quasineutrality may still be

assumed to hold, but that a small electric field is still present causing the ions to be

accelerated, and the electrons to follow the Boltzmann relation. The Bohm velocity is a

minimum velocity that the ions need entering the sheath in order for the ion density not to

decrease too dramatically. This is caused by applying the conservation of energy to the

assumption of constant flux within the sheath. Given that electrons initially escape more

readily from the plasma, the plasma is slightly positive and therefore the potential is

negative as the ions approach the wall within system setting up the energy conservation

equation (22):

(5-6) Φ x ,

where is the ion velocity at the edge of the sheath, and since the electric field is

negative, the velocity at any point is increasing as the ions approach the wall.

Unless ions are being created and destroyed, the flux may be assumed to be constant. A

constant flux means if there is an increase in velocity; the density must decrease to

40

maintain a constant flux. The equation describing this assumption is a form of the

continuity equation (4-2) (22):

(5-7)

where the flux at the sheath edge “ ” is equal to the density at any given

position times the velocity at that same position. Solving equation (5-6) for

velocity at any point in the sheath “ ” becomes (22):

(5-8)

Figure 5-3 shows the ion velocity curves with various initial sheath ion velocities as the

ions are accelerated across the sheath by the sheath potential. As the initial ion velocities

increase, the contribution that the sheath potential acceleration provides to the ions’ final

velocity is reduced.

41

Figure 5-3. The theoretical ion velocity dependence on initial ion velocity. Initial ion velocities of:

zero, half the bohm velocity (KT/M), the Bohm velocity, and twice the Bohm velocity, are shown. As

the ion velocity reaches the Bohm velocity, the sheath has a smaller relative influence.

If the ions had no or a very small initial velocity the flux caused by the ions would also

be very small. The less effect the sheath potential has on the ions, the smaller the change

in ion density that is required to maintain the assumption of a constant flux across the

sheath. The effect the assumption of constant flux and the accelerating ions may be seen

by applying the ion velocity from equation (5-8) into equation (5-7) the ion density

behavior within the sheath will follow:

(5-9) 1

Ion

velo

city

with

in sh

eath

Arb

itray

Uni

ts

Sheath Potential----> Towards wall

no initial

half

kt/m

2kt/m

kt/2m

42

Figure 5-4 shows the ion density through the sheath, using the assumption of constant

flux. The effect of initial velocity may be clearly seen in the plasma density. The

electron density has been assumed to follow the Boltzmann relation from equation (4-10),

and is also plotted as a reference point. Only solutions that have more ions than electrons

meet the criteria of the assumptions for the negative electric field.

Figure 5-4. Ion density for various initial velocities with respect to the Bohm velocity (kT/M)

compared to the electron density (Ne). Velocities graphed are zero initial velocity, half the bohm

velocity, the Bohm velocity, and twice the Bohm velocity. Only the Bohm velocity meets the initial

assumption that the number of ions is equal to the number of electrons and also maintains the

assumption of more ions than electrons (Ne) within the sheath.

ion

dens

ity w

ithin

shea

thA

rbitr

ay U

nits

Sheath Potential----> Towards wall

no initial

half

kt/m

2kt/m

Ne

kt/2m

43

A minimum velocity is required in order to maintain the constant flux assumption while

also maintaining the assumption of more ions than electrons within the sheath. This

minimum ion velocity assumes the Boltzmann relation is accurate for the presheath

electrons, which assumes isothermal and uniform electron densities.

The electron flux is developed from the assumption that the electrons have a distribution

of velocities and directions from their temperature which outweighs any drift velocity.

The average speed of the distribution is given by equation (3-7), ; and the

number of electrons flowing out in one direction is given by (22) (75):

(5-10)

So, by setting Γ Γ and substituting in for the Bohm velocity the relationship becomes

(22):

(5-11)

then by applying Boltzmann’s relation for the number of electrons, and setting the

potential to the potential of the wall with respect to the sheath-presheath edge, the result

is (22):

(5-12)

then taking the natural log and solving for the wall potential results in previously given

equation (5-2) (22):

44

(5-13)

This potential therefore assumes: the drift velocity of the electrons is small with respect

to the electron temperature; the electron temperature is uniform; the electrons are

isothermal; and that there is no ionization within the sheath. The potential at the wall

5.1.3 Child-Langmuir law sheath

The Child-Langmuir law sheath assumption allows the derivation of the Child-Langmuir

law of “space charge limited” current in a planar diode. The assumptions are: ignore the

contribution of electrons to the sheath current; equate the current to the flux of ions

across the sheath; and assume the energy developed by the ions in the presheath is

insignificant in comparison to the energy developed within the sheath. The resulting

Child-Langmuir law formula for current in a “space charge limited” diode is (22):

(5-14)

Where J is the ion current, is the permittivity of free space, is the potential applied

to the electrode, and is the sheath thickness. This defines the expected non-linear

relationship for plasma diodes. The ion current is simply the flux of ions as in equation

(5-3), multiplied by the charge of the ions, which assuming singly ionized species and

constant flux results in (22):

(5-15)

45

Setting equations (5-14) and (5-15) equal allows the calculation of the sheath thickness

“s” resulting in (22):

(5-16)

Then substituting in equation (5-5) for the Bohm velocity so that ; the

sheath thickness may be written as (22):

(5-17)

The Child-Langmuir current law for a planar diode has a non-linear dependency on

applied voltage, and is inversely proportional to the square of the sheath thickness. In

comparison to the magnetron I-V characteristic in equation (2-2), the “n” would be 3/2

rather than “n” which ranges between 3 and 15 for dc magnetrons (23).

The sheath thickness varies with less than a linear behavior with respect to all of the input

parameters (all input parameters have a power magnitude less than one). The sheath

thickness increases the most with applied voltage, but only at . Sheath thickness

varies by the inverse square of plasma density, and only changes by the inverse fourth

root of electron temperature. Now that the sheaths have been described it is time to look

between the sheaths and develop a description of the plasma.

46

Chapter 6 The Plasma as a Fluid

The basic diffusion and fluid equations allow the development of equations to describe

the diffusion behavior of the plasma which is a critical step in understanding the HiPIMS

and sputtering behavior.

6.1 Diffusion in a plasma

The application of the diffusion coefficient is one method used to develop an expression

for the plasma as fluid motion. As the plasma is a fluid, Fick’s first and second laws of

diffusion can apply. Fick’s first law suggests that flux will flow away from a high

concentration to a low concentration. Fick’s first law may be written as:

(6-1)

Where Γ is the flux, D is the diffusion coefficient, and n is the density.

Fick’s second law describes the change in density over time due to a concentration

gradient as:

(6-2) ,

where is the change in density with respect to time. In effect, a plasma will have a

driving force which will be attempting to make the plasma uniform over the region within

which it is contained. A second driving force within plasmas is the electric field. This

leads to the particle flux equation (22):

47

(6-3) ,

where is the mobility constant for that species. “ ” may be found by taking the charge

of the species and dividing by the mass “ ” and the collision frequency ” ”:

(6-4)

And the diffusion constant may be found by:

(6-5) and for hard sphere scattering

with being the Boltzmann constant and temperature respectively. The components of

the electric field force are seen in the first term of equation (6-3). The second term is the

pressure from a concentration gradient.

These basic plasma behaviors include the decay of variations in plasma densities.

Variations in plasma density should be expected to disperse over time, and more complex

and/ higher order functions may be expected to die out first very similar to the way higher

overtones are the first to die out when a piano key is struck.

6.2 Charge Balance and Ambipolar Diffusion

There are a large number of charged particles within the sputtering plasma, and even

more within a HiPIMS plasma. The plasma contains nearly an equal number of electrons

and ions. This behavior leads to the assumption of “quasi-neutrality”. It is assumed that

the number of electrons is nearly equal to the number of ions.

48

The expectation of quasi-neutrality also leads to the expectation that motion of either

electrons or ions will carry the other along through ambipolar diffusion.

By application of equation (6-3) for diffusion of electrons and ions, and assuming nearly

equal number of electrons and ions, and no external electric fields; the following

ambipolar diffusion equations may be developed (75):

(6-6)

and,

(6-7) 0

Where is the ambipolar diffusion constant; which consists of (75):

(6-8)

Where is the ion mobility, is the electron mobility, and and are the electron

and ion diffusion constants of equations (6-4) and (6-5).

6.3 Magnetic Effects in a Plasma

6.3.1 Magnetic effects on a particle

Magnetic fields have a direct effect on the capability of electrons and ions to move within

a plasma through the basic force equation:

(6-9)

49

The basics of which may be seen in equation (4-1). The magnetic field applies a force

perpendicular to both the velocity and the magnetic field. The net result is the magnetic

field creates a circular motion on top of whatever trajectory the system had initially.

Since the magnetic field is always applying a force to the perpendicular component of

velocity, this becomes basic circular motion with the magnetic field providing the inward

force that maintains an object in circular motion. The end result being:

(6-10) | |,

which develops the Larmor radius for a charged particle as:

(6-11) .

is the angular cyclotron frequency which is:

(6-12)

Key facts to note are that frequency is not velocity dependent, larger masses increase the

Larmor radius and that the Larmor radius decreases with increasing magnetic field.

6.3.2 Magnetization of a plasma

Magnetization of a plasma occurs when the geometry of the system allows the charged

particles within the plasma to successfully complete a Larmor radius. Electrons being

relatively light may be considered “magnetized” within as little as a 100 gauss field.

The Larmor radius for an electron is approximately:

50

(6-13) . √ ,

with in gauss and in electron volts. The magnetization of electrons freezes the

electrons in place within the magnetron helping to generate the higher density plasma

glow close to the cathode surface.

6.3.3 Magnetic field effects on diffusion

The magnetic torus that keeps a dense plasma close to the sputtering cathode’s surface is

a large gradient in plasma density, and therefore may also be expected to be affected by

diffusion. By applying the diffusion coefficients definitions to equation (4-1) while

including a magnetic field, the resulting flux equation is (75):

(6-14) Γ

Where and are the perpendicular mobility and diffusion coefficients, and are

defined by (75):

(6-15)

and (75),

(6-16) 2

2 2 2

51

where is the cyclotron frequency from equation (6-12), and is the time for one

collision to occur. The velocities and are the drift and diamagnetic drift

velocities where (75):

(6-17)

is the drift and (75),

(6-18) B

is the diamagnetic drift.

The end result being that the flux of the charged species perpendicular to the magnetic

field lines have the drift velocities’ contribution reduced by collisions, and mobility and

diffusion constants are increased with collisions; the exact opposite is true for flux in

nonmagnetic fluxes. The mobility and diffusion terms in the perpendicular flux equation

are also inversely proportional to the magnetic field squared.

6.3.4 Bohm diffusion

Experimental data on magnetic plasmas has developed a formula for the perpendicular

diffusion rate that is different from above equation (6-16). Bohm diffusion depends

inversely upon magnetic field only as B rather than B squared as shown (75) (22):

(6-19)

This diffusion constant does not appear to depend upon density, or collisions, and the

time constant for Bohm diffusion is approximately (22):

52

(6-20)

Where N is the total number of charge carriers in the plasma. Bohm diffusion has been

attributed to turbulent disturbances within plasma generated by instabilities within the

plasma. The instabilities occur from waves within the plasma absorbing free energy

within the system. These instabilities may be fueled by streaming ions or electrons, and

variations in temperature etc.

6.3.5 Drift velocities in a fluid

In the theory for polarization drift for a magnetized plasma with perpendicular magnetic

and changing electric fields E(t), the center of motion of an electron has a polarization

drift velocity in the same direction as the electric field due to the changing drift velocity

perpendicular to the electric and magnetic fields. The polarization current would follow

the equation (22):

(6-21) dtdE

BnmM

J p 20

0)( +=

A number of papers have been published recently discussing self polarization and other

methods for electron transport for plasmoids as they approach a magnetic barrier (37)

(38). The mechanisms are self polarization and magnetic expulsion. An oversimplified

way to define “self polarization” is to consider the ions continuing past a barrier

unattainable for the electrons. The plasmoid then develops a change in electric field as

the ions get exposed. The changing electric field now develops a polarization drift in the

53

electrons which then drives a set of electrons past the previously unattainable magnetic

barrier.

A second possibility in order to overcome the barrier is for the plasma to develop a

magnetic field counter to the field the plasma sees being applied by external forces. This

would occur through the diamagnetic current of the plasma. This current attempts to

expel lines of flux from the plasma similar to superconducting fluids.

The drifts and characteristic frequencies of a magnetized plasma can develop into

oscillations within the plasma. In order to describe these oscillations, the equations of

magnetized particles and their effects on ionized fluids will now be applied assuming a

small sinusoidal variation.

54

Chapter 7 Waves and Plasma Oscillations

7.1.1 Sinusoidal equations of particle motion

In order to look at the frequencies that occur within the plasma, it would be helpful for

the notation for the description of the plasma as a fluid to be in terms of sinusoidal

behavior. The sinusoidal behaviors are expected to be small, with an angular frequency

of oscillation “ ” and a wavenumber “ .” This results in replacing: time derivatives

with the term “ ”; and the gradients by the term “ ” for a given direction of

oscillation in the x direction. For example the oscillations of the velocity, electric field

or density may be described as sinusoidal. The result is that the force equation (4-1)

neglecting collisions and magnetic fields for the moment may be written as (75):

(7-1)

And the equation (4-2) for continuity becomes (75):

(7-2)

And for an electric field that may be described by the gradient of the electric potential

(75):

(7-3)

7.1.2 Development of the plasma frequencies

Within plasmas, especially magnetized plasmas, a whole host of various frequencies are

possible to develop. A first step in understanding that waves and oscillations will occur

55

within a plasma is to first consider a hypothetical situation of a slab of initially neutral

plasma with a plasma density of . Now imagine applying a force that pulls all the

electrons to the left just a small bit “ ,” and that “ ” is a function of time as shown in

Figure 7-1.

The jostling of the electrons uncovers the slower ions on the right hand side, and

generates a set of uncovered electrons on the left hand side. After this initial shove, the

plasma is let go and observed.

Figure 7-1. A displaced electron cloud (downward cross-hatching) is schematically drawn over a set

of stationary ions (upward cross-hatching). An enclosed surface for finding the electric field over a

region using Gauss's law is also drawn.

-

-

-

-

-

+

+

+

+

+

Q enclosed electrons

ions

both

56

The plasma now has a charge on one side, developing a field. Assuming a semi-infinite

slab of plasma, there is only an electric field inside the plasma, and apply gauss’s law to

find that electric field resulting in (22):

(7-4) ,

is the dielectric constant permittivity of free space. The electric field applies an

electric force to the electrons, and an acceleration (22):

(7-5) .

By applying these two equations, one gets (22):

(7-6) ,

which has the form of a double derivative equal to itself times a constant (indicating

simple harmonic motion), thus recognizing simple harmonic motion and the angular

frequency for the electrons as (22):

(7-7) ,

where is the mass of an electron. Similarly there is an angular frequency for the ions

(22):

(7-8) .

The base frequencies of the plasma are the plasma electron frequency and the plasma ion

frequency: ωp =2πfp, and follows the relationships described above in (7-7) and (7-8).

57

Previously, equation (6-12) (the cyclotron frequency) demonstrated an angular frequency

for charged particles in a magnetic field. There will be at a minimum two cyclotron

frequencies within a plasma as well. One for the electrons (22):

(7-9)

And one for the ions (22):

(7-10)

where q is the charge of the particle, B is the field, and M is the mass of the ion or the

electron for ωci and ωce respectively. A magnetized plasma therefore has four basic

frequencies, the electron and ion plasma frequencies (equations (7-7) and (7-8)) and the

electron and ion cyclotron frequencies (equations (7-9) and (7-10)).

There are a number of other frequencies and waves that may propagate from a

magnetized plasma. These include ion acoustic waves, lower hybrid waves, electrostatic

ion cyclotron waves, Alfvén waves, and Magnetosonic waves. To further complicate the

issue, the magnetic fields vary in strength and direction within the area of interest from

400 to 50 gauss and therefore each “base” frequency becomes a range of frequencies.

7.1.3 Electrostatic wave propagation

Initially the condition of electrostatic wave propagation may sound like a misnomer;

however this behavior is based on the behavior of a sound wave. Electrostatic waves

propagate a pressure wave that is exchanging heat energy and electric energy. The

electric fields are in the same direction as the propagation direction, which is the clue to

58

how this wave does not necessarily have a magnetic component. Imagine an electron

reacting to the changing electric field, this electron alone would clearly be generating a

magnetic field as a charged particle that is accelerating. This motion’s magnetic field

however, would be counter balanced by electrons moving toward the same position as the

first electron, but from the opposite side, thus generating pressure without a net magnetic

field that will adiabatically compress and exchange energy with the electric field setup by

the ion’s lack of mobility in comparison to the electrons.

Another way to look at the concept is that the electric field of this wave is parallel to the

propagation direction. The magnetic field is the cross product of the propagation

direction and the electric field. This results in no net magnetic field since the cross

product is zero.

The classic way to observe electrostatic behavior is through the ion acoustic wave. By

starting with the fluid equation (4-1) for ions, and assuming: sinusoidal oscillations, the

electric field is the gradient of the potential, and compressions of the ion wave are planar,

resulting in the following sinusoidal equation result (75):

(7-11)

(7-12)

Solving for in equation (7-12) and replacing in equation (7-11)

(7-13)

A linearized expansion of the Boltzmann relation is:

59

(7-14) or

and the continuity equation for from equation (7-2):

(7-15)

Using equations (7-14) and (7-15), equation (7-13) then results in: (75)

1

(7-16)

Equation (7-16) is the electrostatic wave behavior for ions in a magnetized plasma with

collisions for the ions. Ignoring collisions, the resulting equation is (75):

(7-17)

The non magnetized ion acoustic wave propagation results in the equation (75):

(7-18)

Equations (7-16), (7-17) and (7-18) therefore summarize the electrostatic wave behavior

for ions under various assumptions.

60

7.2 The plasma as a Dielectric

There are many methods to electrically describe various portions of a plasma within the

confines of the lab. A laboratory plasma without a magnetic field will be contained by a

sheath at its boundaries, which we will consider the boundaries as two plates, and

therefore two sheath regions. To a first approximation, an electrical analogy to this

system would be a capacitor for each of the two sheaths, and an inductor or a capacitor

for the plasma dependent on the waves’ frequency (77). The dielectric constant of the

plasma (εp) is described by the equation (22):

(7-19) 1

where ε0 is the permittivity of free space, ωpe is the electron frequency, ω is the

frequency of the incoming wave. This plasma dielectric equation is valid for (1) non-

magnetized plasmas and (2) electric fields parallel to magnetic field lines. Below the

plasma frequency the plasma acts as an inductor (negative dielectric constant), while

above the plasma frequency, the plasma acts as a capacitor.

7.2.1 Electromagnetic wave propagation

Generally, this shows that for frequencies less than the plasma frequency, waves should

be stopped at the plasma surface and prevented from entering. By applying the plasma

dielectric constant to the following equation (22):

61

(7-20)

it can be found that waves stop propagating when the electric field becomes zero. This

may be seen through the dispersion relation for the electromagnetic waves of the above

dielectric constant (22):

(7-21)

which will become zero at frequencies below the plasma frequency ( ).

7.2.2 Dielectric tensor

The above description works for dielectric constants that do not vary with respect to

angle or polarization within the material. The magnetized plasma however, has an

anisotropic behavior that also has off-axis dependencies due to the cross product effect

the magnetic field has on the velocity of ions and electrons. The solution is to represent

the plasma medium using a dielectric tensor where (22):

(7-22) ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ −= ⊥

⊥

||

0

0000

κκκκκ

εε x

x

p jj

Where κ is the dielectric constant for perpendicular to field lines, κx is the effect

perpendicular electric field in one direction has on the remaining perpendicular direction

and κ is the dielectric constant parallel to field lines, which are described in detail

elsewhere. (22) When including ions, and ignoring collisions the dielectric constants

become (22):

62

(7-23) 22

2

22

2

1ci

pi

ce

pe

ωωω

ωωω

κ−

−−

−=⊥

(7-24) 22

2

22

2

ci

pici

ce

pecex ωω

ωωω

ωωω

ωω

κ−

−−

=

(7-25) 2

2

|| 1ωω

κ p−=

and by letting (22):

(7-26) xl

xr

k κκκκκ

+=−=

⊥

⊥

one can apply this complex dielectric constant to an electromagnetic wave propagating

within the medium. Using N= k/k0 one can develop an equation describing the dispersion

of the waves within the plasma using (22):

(7-27) ( )( )

( )( )lr

lr

NNNN

κκκκκκκ

θ−−−−

−=⊥

2//

2

22//2tan

where θ is the angle of propagation with respect to the magnetic field lines. This

representation assumes no collisions. From equation (7-27), it is evident that there are

various frequency solutions depending on the angle of propagation.

7.2.3 Geometric oscillations

The frequencies developed in prior sections deal with resonances for an unbounded

generic plasma. This would be the equivalent of developing the propagation expectations

of a sound wave, and wondering why tubas and trumpets sound differently. The HiPIMS

and dc sputtering plasmas have a number of geometric limitations that have the

63

possibility of generating other frequencies within the plasma and any discussion of

possible oscillations would therefore need to include geometric solutions as well.

7.3 Summary

A summary of a number of possible waves within a plasma and their characteristics are

given in Table 7-1 (22) (75).

Table 7-1 Shows a set of possible waves present in a plasma, including type of propagation and

dispersion relation.

Particle

type

Wave type Relative

field

Dispersion relation Name

electron electrostatic 0 or k

3 plasma

oscillations k upper hybrid

electromagnetic 0 or k

light or “O”

k

X wave

k whistler “R”

k “L”

ion electrostatic k ion cyclotron

0 or k

acoustic

k lower hybrid

electromagnetic k

Alfven

k

Alfven

k 1 magnetosonic

64

Resonant frequencies, and other frequencies where the plasma is expected to allow the

frequencies to propagate, would provide electrons with a possible method of escape from

their magnetic electron trap if they were driven at one of these frequencies through the

polarization drift effect. The point is however, we expect to find these frequencies

naturally occurring in plasmas not necessarily driven at a certain frequency. Resonant

frequencies occur as the wave number goes to infinity, and waves are cut off as the wave

number goes to zero. The plasma, its behavior when magnetized, the sheath and

propagation of waves within plasmas have been developed to the point where we can

again take a look at magnetron sputtering.

65

Chapter 8 General Expectations for a dc Magnetized Plasma

This dissertation has now uncovered several of the underlying physical behaviors that

should be expected within HiPIMS. The current voltage characteristics should follow a

diode type curve as has been shown for other magnetron plasmas. The HiPIMS plasma

should include both a plasma region and a sheath. The plasma will behave as a fluid,

with additional electric and magnetic forces applied to it. Magnetized plasmas are known

to allow the propagation of numerous oscillating wave types. These waves include both

electrostatic and electromagnetic. The propagation of waves within the plasma depends

upon a number of plasma properties including density, magnetic field intensity, geometry

and mass of the atoms. From these expectations, a clearer picture of the magnetron

plasma develops.

8.1 Power Law and Child Law Sheath

The plasma sheath should follow the Child-Langmuir Law for the current supplied at a

given voltage as developed in equation (5-14). The expected relationship should be

approximately an “n”=1.5 as described previously in equation (2-2):

(8-1)

Experimental values for “n” in a magnetron system are typically five to nine. The Child

sheath, at first glance, develops into a discrepancy with the experimentally found power

law. Rossnagel and Kaufmann were able to fit the two equations to each other through

the dependence of the Child sheath current on the sheath thickness (78). Others have

66

shown that the plasma density increases as the current increases (33). This increase is in

large part due to the magnetic trap for the electrons. Increases in plasma density can be

expected to decrease sheath thickness as shown in equation (5-17) and repeated here:

(8-2)

The same equation relates increases in sheath voltage as a cause for the sheath thickness

to increase. These two behaviors can be seen as an electric field pushing the plasma

away from the cathode, and the increased plasma density due to magnetic confinement

pushing back, resulting in a balanced system.

8.2 Plasma Frequencies

Underneath the currents flowing within the magnetron, there is the expectation of waves

developing within plasma. These waves may be a type of ionic sound wave, or

electromagnetic. In dc magnetron plasmas using argon, the base frequencies for ion

cyclotron, plasma ion, electron cyclotron and plasma electron are in the range of:

8-20 kHz, 0.58 -1.46 GHz, 3.5 kHz, 94MHz. In comparison,

the expected frequencies for HiPIMS are in the range of: 8-20kHz, 0.58 -1.46

GHz, 11MHz, 29GHz for magnetic fields between 200 and 500 gauss which

are typical magnetic field strengths for magnetrons.

67

8.2.1 Electromagnetic wave propagation

As previously discussed, a laboratory plasma would have an electrical analogy of a

capacitor for each of the two sheaths, and an inductor or a capacitor for the plasma

dependent on the waves’ frequency. The dielectric constant of the plasma (εp) is

described by equation (7-19) and repeated here:

(8-3) ⎟⎟⎠

⎞⎜⎜⎝

⎛−= 2

2

0 1ωω

εε pep ,

This equation is graphed in Figure 8-1 for specific values representative of HiPIMS

processes (22). This plasma dielectric equation is valid for non-magnetized plasmas and

electric fields parallel to magnetic field lines. Below the plasma frequency the plasma

acts as an inductor, while above the plasma frequency, the plasma acts as a capacitor.

68

Figure 8-1. The square of the theoretical refractive index (N2) for a high density magnetized plasma

parallel to the magnetic field predicted using Equation (8-3) as a function of frequency. The value is

negative resulting in an imaginary refractive index, not allowing waves to propagate. The parameters

are 200 gauss, 1019 ions per m3, argon gas, ignoring collisions.

Waves propagating in the parallel direction are met with a large inductance as seen in

Figure 8-1. Since we are interested in the behavior of the plasma as a function of

frequency, we have the graph shown as N2 as a function of frequency. Magnetic fields

alter the course of electrons and to some degree the ions in the plasma to form helixes

about magnetic field lines. Due to the magnetization of the electrons, the plasma

dielectric constant (ε⊥) perpendicular to the magnetic field at low frequencies behaves

according to equation (7-23) and repeated here (22):

69

(8-4) ⎟⎟⎠

⎞⎜⎜⎝

⎛+=⊥ 2

00

00 1

BMnε

εε ,

which may be derived from the polarization drift current (equation (6-21)):

(8-5) dtdE

BnmM

J p 20

0)( += .

This concept may be further evaluated by applying the above equations in a dielectric

constant tensor to evaluate propagation through the plasma. The tensor results in a

relationship that may be evaluated at various angles with respect to the magnetic field

(equation (7-27) repeated here for easy reference).

(8-6) ( )( )

( )( )lr

lr

NNNN

κκκκκκκ

θ−−−−

−=⊥

2//

2

22//2tan

By evaluating the results for the dielectric tensor, a few propagation states may occur.

Three basic waves are plotted in Figure 8-2, Figure 8-3 and Figure 8-4. Waves may

propagate when N2 is positive, and waves are cutoff where N2 is negative indicating an

imaginary optical constant; discontinuities in the graph indicate a resonance. The result

is a plasma with multitudes of wave-like phenomena which is unlike the plasma without

magnetized electrons.

70

Figure 8-2. The square of the theoretical refractive index (N2) for a high density magnetized plasma

perpendicular to the magnetic field (extraordinary wave) predicted using Equation (8-6) plotted with

respect to frequency. The parameters are 200 gauss, 1019 ions per m3, argon gas, ignoring collisions

Specialized waves having left or right hand circularly polarized propagation solutions

may propagate parallel to the magnetic field. These waves correspond to electron

cyclotron as shown in Figure 8-3 and ion cyclotron waves as shown in Figure 8-4.

71

Figure 8-3. The square of the refractive index (N2) plotted with respect to frequency for special right

handed polarization propagation parallel to the magnetic field. Resonance occurs around 108 Hz

(not shown). The parameters are 200 gauss, 1019 ions per m3, argon gas, ignoring collisions.

72

Figure 8-4. The square of the refractive index (N2) plotted with respect to frequency for special left

handed polarization propagation parallel to the magnetic field. Resonance occurs around 104 Hz.

The parameters are 200 gauss, 1019 ions per m3, argon gas, ignoring collisions.

8.2.2 Geometry based frequencies

Another frequency that may be likely to appear would be the frequency of the drift

current around the magnetron erosion track. Published drift velocities range from (0.2 to

4.0) x104 m/s for HiPIMS which would result in a drift current frequency for a 150mm

cathode (estimating a 127mm diameter erosion track) between 5 and 100 kHz (79).

It would be logical for the plasma to oscillate from the charge imbalances at one and

perhaps all of its resonant frequencies. The velocity of the plasmoid and the strength of

the magnetic field are likely factors in the resulting observed frequencies (28).

73

In order to discuss the concept of assuming the uniformity of the plasma, it is useful to

consider the circular cathode depicted in Figure 8-5. As an electric field is applied to the

cathode, containing a ring of uniform plasma, the electrons will move away from the

cathode following the magnetic field lines of the magnetron cathode. Basic magnetron

designs have field lines that go out radially from the center to the outside of the

magnetron. Consider a system that starts with a perfectly uniform ring of high density

plasma as depicted within Figure 8-5 (a). Looking at the behavior of a small angular

section of the plasma over time, electrons within this angular section will have an inner

region that will move toward the outside, and an outer region that will move toward the

inside.

Figure 8-5. The change in the configuration of the plasma from a uniform plasma density to a non-

uniform plasma density, due to circular geometry. a) The first section shows an initially uniform

plasma density, with a small region ∆ marked, and b) then the electrons move in their cyclotron

path, resulting in c) the regions subtended in part “a)” switching places, generating a plasma density

fluctuation, not previously present. The plasma density change will result in an outward pressure

gradient .

e-

c)

b)

a)

∆

74

The electron density that was originally constant must now have an imbalance as the

volume enclosed in the outer portion of the ring is greater than the volume on the inside.

The motion by the electrons as they “hop” around the cathode inevitably results in a

plasma density variation in a circular cathode. Secondarily, an increase in pressure to a

smaller radius may be expected to result in an outward force from a pressure gradient.

This force in turn should move the high density plasma to a larger radius than may be

expected without consideration of the plasma as a fluid.

The plasma drift velocity in conjunction with the magnetic field and density gradient also

result in the possibility of drift waves within the plasma. These drift waves or other

waves are expected to inevitably develop in the plasma (28) (75). A schematic of these

oscillations is shown in Figure 8-6. The magnetic field lines come out of the plane at the

center of the cathode and arc back into the cathode on the outside ring (the “x’s” in the

schematic). The plasma density “wave fronts” are represented by the shaded area. The

wave fronts would likely continue to follow the arcing field lines.

Figure 8-6. A possible oscillation that can develop alongside the pressure gradient and drift within

the magnetic trap is schematically drawn (75).

Vdrift

75

8.2.3 Frequency matching

Through a process called frequency matching, any number of wave propagation

possibilities are opened up. Frequency matching is the excitation of a pair of waves from

an original higher frequency wave (75). Provided momentum is conserved two new

waves may be generated replacing the original wave. This provides a mechanism for

developing waves at various allowed frequencies.

8.3 Summary

In order to develop tools to understand the plasma and its interactions with waves, one

needs to look at the underlying equations and physics related to the plasma. Through this

equation analysis, conceptual models have been developed to understand the plasma

behavior.

Perpendicular to the magnetic field, depictions of the plasma behavior may be developed

to include the effects of ions, collisions and geometry, and may be further described

through the two-stream instability or the modified two stream instability theories.

Regardless of the model used, the dielectric constant remains large and positive for the

perpendicular direction over a large band of frequencies, indicating a capacitive effect.

The oscillations present may be of both electromagnetic waves and ionic sound waves.

These waves have characteristic cutoff and resonance frequencies within the plasma.

Key frequencies of note are the plasma frequencies and the cyclotron frequencies.

76

In general for the analysis there are minimally two species, argon ions and electrons,

resulting in four basic frequencies within the plasma. These frequencies increase with

increasing plasma density, and increase with increasing magnetic field for both plasma

and cyclotron frequencies. The analysis of these magnetized plasma equations results in

finding that 1) there is the possibility for wave propagation perpendicular to the magnetic

field within the plasma; 2) wave frequencies depend on plasma density and magnetic

field magnitude; and 3) the dielectric constant of the plasma may be large and positive

perpendicular to the magnetic field. Thus looking at wave propagation within a plasma is

one tool that can be used to understand plasma behavior.

77

Chapter 9 Case Study: Analysis of Prior Magnetron Models

Particle in cell models (PIC), like the plasma frequencies discussed last chapter, have also

become an important tool in the development of the understanding of how a magnetron

sputtering cathode will function. Goree and Sheridan were two early adapters of this

technique and brought a new level of understanding of the plasma’s behavior (31). Their

modeling was driven by an attempt to divulge an understanding of what caused the

transport of electrons across the magnetic field boundaries within plasmas, which at the

time was considered to be the result of plasma turbulent oscillations (28) (74).

9.1 Oscillations in Magnetron Plasmas

Sheridan et al. attempted to discredit the likelihood of oscillations contributing to the

conductivity of the plasma in several ways (28) (29) (30) (33). First, Sheridan and Goree

performed experiments at low sputtering intensities and analyzed the oscillations below

1MHz, concluding that these waves could not contribute to the current carrying of the dc

supplied power as ionic sound waves (28). Second, Sheridan et al. found that any

relationship described needs to follow a dependence on the mass of the gas (29). Third

Sheridan et al. attempted to demonstrate through particle-in-cell modeling that collisions

were an important factor in electron transport, and a more likely candidate than

oscillations for the current flow (31).

Sheridan et al. provide an excellent skeptical point of view and supplies a set of logical

requirements when looking for the mechanisms involved within current transport for a dc

magnetron. Sheridan and Goree discusses the concept of “τ” (tau), a time constant,

78

defining the confinement time of an electron in a plasma per equation (9-1) “τ” is defined

as proportional to the density of a plasma and inversely proportional to the current

flowing through the circuit. According to Sheridan and Goree “τ” may be described by

the equation:

(9-1)

where “e” is charge, N is total number of carriers in the plasma and Idis is the discharge

current of the magnetron. This variation is developed by acknowledging “ ” may be

replaced with “ ”. This provides a quick look at how fast the electrons within the

plasma must be replaced in order to maintain a steady state current flow.

Sheridan and Goree, then recognize that the low frequency waves are likely to be ionic

sound waves, and assume electrostatic ionic sound waves which may be described by:

(9-2)

However, in the case of Sheridan, the ions are assumed to be cold in comparison to the

electrons, and due to geometry constraints, the forces generating the minor deflections to

the ions from the magnetic field are ignored. Provided the frequency does not begin to

approach the ion plasma frequency, the “ ” term may also be ignored. These three

developments allow the simplification to the ion acoustic wave:

(9-3) ,

79

where is the ion acoustic wave speed. By combining the expected dispersion relation

of (9-3) with: a linearization of the Boltzmann relation per equation (7-14) for

a time varying potential; and a time varying electric field per equation (7-3); Sheridan et

al. developed (28):

(9-4)

The inverse of the time constant provides a zeroth order understanding for oscillations to

contribute. In order for a single wavelength to single handedly carry all the charge, the

frequency would be required to be greater than the inverse of the confinement time “τ”.

If the current in the magnetron is to be aided by the plasma’s oscillations the total amount

of flux transferred by each frequency measured within the plasma must be summed

across all possible frequencies. Sheridan invokes Parseval’s theorem to perform this

calculation finding the contribution at each given frequency as a method to find the total

power carried by the waves. Parseval’s theorem equates the power in the time domain to

the power in the frequency domain. One caveat to this calculation is that it assumes the

integration over the entire frequency spectrum, only a portion of which is available to

Goree and Sheridan.

Goree and Sheridan used a cylindrical Langmuir probe oriented parallel to the radial axis

of the magnetron for measuring the characteristics of the plasma. Plasma densities were

found in numerous positions within the system for finding the total N of the system. The

oscillations were measured at two positions within the plasma, both at 6.8 mm from the

face of the cathode, one nearly at the point where the magnetic field is parallel to the face

80

of the cathode (r=1.6 cm), and one at a magnetic field angle of 34 degrees with respect to

the face (r=2.1 cm). Both of these probes were within field lines that started and ended

on the target. Current fluctuations were recorded at the plasma potential in an effort to

avoid disrupting the plasma. Their results are shown in Table 9-1.

Table 9-1 Shows the data provided by Goree and Sheridan (28). A corrected column of “τ” is

included.

Idis N τ τ shown place Plasma V Te Ne del ne % change E

0.0536 2.17 0.649 0.648 1 -2.38 4.49 1.49 5.12 76300.0856 4.12 0.771 0.759 1 -1.24 3.77 2.69 3.73 3700

0.127 6.52 0.822 0.826 1 -0.89 3.55 4.16 2.69 21600.168 8.77 0.836 0.836 1 -0.73 3.4 5.6 2.46 17600.227 12.1 0.854 0.856 1 -0.74 3.29 7.69 2.07 13500.303 16.2 0.857 0.854 1 -0.7 3.14 10.5 2.13 1170

0.0536 2.17 0.649 0.648 2 -1.09 3.76 0.98 4.04 56600.0856 4.12 0.771 0.759 2 -0.38 3.14 1.94 2.82 2470

0.127 6.52 0.822 0.826 2 -0.01 2.81 3.26 2.09 12700.168 8.77 0.836 0.836 2 0.03 2.72 4.16 2.04 11200.227 12.1 0.854 0.856 2 0.04 2.59 6.01 1.9 10500.303 16.2 0.857 0.854 2 -0.16 2.54 8.56 1.99 820

One issue with these measurements is that they rely on the assumptions from the

Boltzmann relation, and the Bohm velocity. One of these assumptions is that there is no

drift velocity of the electrons. The electrons with the highest likelihood of escaping the

magnetic trap are those of higher energy, just released from the cathode. Those electrons

will have a very large drift velocity resulting in a poor accounting of their contribution.

Sheridan and Goree calculate the “τ” for the low power sputtering plasma to be below 1

µs. The time constant indicates an absolute minimum time requirement for all the current

to be carried by waves to 1MHz. Any frequency lower would be incapable of carrying

81

enough current, even if every available free electron contributes. Other groups had

indicated higher frequency oscillations at higher plasma powers (26); the intent of

Sheridan and Goree’s paper however was consideration of low frequency contributions.

Sheridan and Goree removed all high frequencies above 2.5 MHz with a highpass filter to

prevent aliasing and only consider measurements below 1MHz to avoid calculations

close to the plasma ion frequency (analyzing just a portion of the frequency domain).

Sheridan and Goree, therefore, have indicated that only oscillations with frequencies

above 1MHz will significantly contribute to the current, but then go on to measure only

frequencies below 1MHz. In effect, Sheridan and Goree measured for fluctuations in a

plasma whose density is so low that oscillations containing the entire group of available

charged particles within the plasma would not be enough to carry the current at the

frequencies the system is set up to measure.

Sheridan then demonstrates that the oscillations fail to follow the expected electric field

behavior by assuming the oscillations measured within the plasma are unmagnetized

ionic sound waves and analyzing their behavior. In the true sense of the term, the ions

are unmagnetized, due to the geometry of the system. However, their data suggests a

strong resonance at the ion cyclotron frequency. The dispersion relation of (9-3) for the

ionic sound wave approximation then begins to fail right where the frequency variation is

greatest.

The original dispersion equation of (9-2) results in a reduced dependence of the wave

number on frequency. Given a reduced dependence on frequency for wave number, the

electric field will no longer be strongly dependent on frequency, making the analysis of

82

the electric field from the base ion acoustic waves not as useful. Sheridan points out that

his experimental data lacks the required dependence on electric field with respect to “τ”

for the portion of the frequency domain experimentally analyzed using the simple ion

acoustic wave approximation. Without this dependence, he concludes the oscillations

present are not contributing to the current.

This conclusion however hinges on equation (9-3) which at low frequencies approaches a

lower limit at the ion cyclotron frequency and an upper limit at the plasma ion frequency.

At these limits the frequencies’ dependence on wave number is reduced and equation (9-

3) no longer accurately describes the dispersion relation. At these limits, frequency has a

reduced impact on the electric field calculations. Further complicating matters is

Sheridan’s attempt to divulge the electric field effects from the current measurements. A

more accurate way would be to use a direct measurement of the field which is the method

used by Martines (35).

This conclusion also relies on a uniform global “τ” applicable throughout the plasma

which would only be the case if the density uniformly changes with power applied. This

may be the case for position 1, but for position 2, (see Table 9-1) there is a secondary

dependence for local plasma density vs. total density. Figure 9-1 shows the behavior of

the local density in Sheridan’s magnetron system with respect to the local density divided

by the total number of ions Sheridan calculated within the plasma. The behavior is

different in the two places Sheridan et al. measured. In the first position which had a

higher magnetic field, which was also more perpendicular to the electric field, the relative

plasma density actually decreases. For the second region that contains a less

83

perpendicular field and lower magnetic fields, the measured relative density increases

with increasing global plasma density. Experimentally this makes good physical sense.

When a magnetron is operated at lower plasma densities, the region of high density

plasma is smaller, and at higher operating powers, the region of the higher density plasma

increases. This may also be evident in the erosion of targets.

Figure 9-1. The dependence of electron density with respect to electron density divided by the total

number of charge carriers. This plot allows the establishment of variable dependence. The power

value of “-.031” indicates a small dependence, with the relative local density decreasing as the total

plasma density increases. The power value of “.0626” indicates a small dependence, with the relative

density increasing as the total plasma density increases.

Numerically this may be understood in two separate ways, first similar to basic dc diode

behavior, the dc magnetron will have a “Paschen curve” for a given gas, pressure and

material (22) (80). A second way to reason the increased high density plasma region is

through the increased cathode fall voltage needed to maintain the plasma at the higher

y = 0.68x‐0.031

y = 0.45x0.063

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0 2 4 6 8 10 12

Normalized

Den

sity

electron density

Ne/N Pos 1

Ne/N Pos 2

(ne)

84

currents. Sheridan starts at 350 V and ends at 550V for the voltage applied to the

cathode. This higher voltage results in a larger Larmor radius for the electrons emitted

from the cathode. The energetic electron gyroradius may be expected to follow the

following equation (22):

(9-1)

The Larmor radius is expected to determine the magnetic field line that the electron

becomes trapped upon, the larger the Larmor radius, the higher up the electron gets, and

the wider path the electron takes near the surface of the target.

Figure 9-2. The electrons move along lines of flux above the target. The width w of the track

followed by the electrons is in part due to the gyroradius for the electron. Higher voltage electrons

(grey) will have larger width erosion tracks. Schematic drawn after Liebermann and Lichtenberg

(22).

Finally, Sheridan’s work depends on the assumption that the waves are of the ion

acoustic type. Although possible, there are other modes available to the plasma in this

region including electromagnetic waves such as the left hand polarized electromagnetic

e- e-

w

85

wave. In fact there could be expected three separate electromagnetic waves within the

plasma, in the range of 0.1 to 1MHz.

The three possible wave types are the extraordinary, left hand polarized, and right hand

polarized waves. Previously these waves were plotted for the HiPIMS characteristics in

Chapter 8; the waves will again be plotted here with the parameters of Sheridan and

Goree. The right hand polarized wave as shown in Figure 9-3 begins to roll off near 104

Hz. Similarly, Sheridan and Goree’s data trails off as their data approaches the

megahertz region.

Figure 9-3. The the square of the refractive index (N2) vs. frequency (f) in Hz for the right hand

polarized wave, as known as the whistler mode. The values for this calculation were 1016 m-3 density,

argon gas and 132 Gauss magnetic field.

86

Sheridan and Goree also indicate a large spike near the ion cyclotron frequency, which

for the left hand polarized wave is a resonance, as may be seen in Figure 9-5.

Figure 9-4. Goree and Sheridan's observed frequency spectrum for variation in density (28). The

graph shows a normalized plot of the fluctuation in density with respect to the frequency of the

fluctuation.

The left hand polarized wave as shown in Figure 9-5 has a resonance around 8 kHz,

below which, the dielectric constant is large and positive. The LH wave is cutoff after

resonance and remains cutoff until nearly the plasma frequency well above 10 MHz.

87

Figure 9-5. The frequency (f) in Hz vs. the square of the refractive index (N2) for the left hand

polarized wave is graphed. The values for this calculation were 1016 m-3 density, argon gas and 132

Gauss magnetic field.

The extraordinary wave (defined as a wave propagating perpendicular to the magnetic

field) is shown in Figure 9-6 to have a large and positive dielectric constant over the

entire measured region until the lower hybrid resonance where the waves cuts off at just

over 106 Hz. The large positive dielectric constants for the waves in Figures 9-3, 9-5 and

9-6 indicate that the extraordinary wave may be capable of carrying power within the

plasma in the range analyzed by Sheridan and Goree.

88

Figure 9-6. The frequency (f) in Hz vs. the square of the refractive index (N2) for the extraordinary

wave is graphed. The values for this calculation were 1016 m-3 density, argon gas and 132 Gauss

magnetic field.

Although Sheridan’s own measurements tend to contradict a uniform change in plasma

density; this paper nonetheless clearly shows the difficulty lower frequencies would have

in carrying all the current. This paper thus sets forth the need for, at minimum,

contributions from other sources such as collisions or higher frequencies.

Sheridan’s discussion of low frequency waves is further narrowed to observe only self-

induced oscillations within the plasma and does not include any frequencies that may be

applied to the plasma in an attempt to drive a given frequency. Sheridan and Goree

89

indicate experiments were performed in driving the plasma at low frequencies. The data

Sheridan and Goree collected for the low frequency driven plasma was so different with

large variations in density that they concluded this behavior had to be a different

phenomenon then those oscillations present naturally and thus they did not include those

results (28).

9.2 Collisional Model and Particle in Cell

Goree and Sheridan then developed a particle-in-cell simulation of electrons escaping the

surface of a magnetron and tracked their movements (31) (32). 2-d simulations were

carried out with and without collisions. This model uses predetermined static electric and

magnetic fields. Initially electrons are released from the cathode surface to develop an

electron distribution near the cathode. This new electron distribution is then used to

formulate the probability of where to release electrons for the collision simulation. The

final result roughly represents a profile similar to the erosion track profile. The electrons

released during their model produced on average 3-4 excitation collisions, 48-49 elastic

collisions, and 20 ionization collisions. The time step for the system was 50ps and an

electron on average had a collision once every 130 time steps. The average electron

therefore was tracked for a total of 0.470 µs. This time constant is low in total time,

however, electrons were also ignored after 2.5 µs, providing an upper limit to the time

constant.

A more telling result is that the average number of ionizations was 14.26 which is larger

than the expected number of collisions. This result indicates that more electrons are

90

being generated, and confined for longer than they should. For a self consistent model,

the ionization rate of argon atoms from the electrons should equal the secondary electron

emission coefficient. Without equality, either the plasma is incapable of being sustained,

or the current should end up in runaway as the plasma density skyrockets. Sheridan and

Goree also show that for 600 electrons, about 200 electrons ionize 20 or more times.

These electrons no longer have the energy to escape the trap.

Their model also relatively well predicts the expected erosion track of the cathode. The

actual erosion track profile is slightly farther out in radial distance in comparison to the

modeled ionization events. This discrepancy is likely due to the modeling as a single

particle, in a static electric field. This model is not sensitive to pressure gradients, and

the electrons as they move inward will effectively increase in pressure, in comparison to

their maximum radial position.

9.3 Conclusions

Although the goal was to prove collisions were solely responsible for enabling electrons

to escape the magnetic field of the target, the conclusion was that most collisions are

small angle scattering events. The Sheridan and Goree model finds that significant

numbers of the electrons fully use up their energy ionizing argon, indicating the excellent

efficiency of a magnetron. Nearly one third of the electrons were tracked for the full 2.5

microsecond time allotment. If the particle-in-cell model was an accurate depiction of

events, the result would be a buildup of spent electrons within the magnetic trap.

91

A buildup in electrons within the magnetic trap would effectively screen the cathode

from the plasma and reduce/remove the cathode fall’s electric field. The potential drop

would be forced to be diverted across the whole of the plasma. Clearly this does not

occur, nor would it make sense. The other behavior that might occur is current run

away. If each electron ejected creates more ions than are needed for a balanced

magnetron, then the current will simply continue to increase. The picture thus created

would be a decreasing cathode fall voltage with increasing current. The model therefore,

does not appear to be charge/current flow balanced. Ideally each electron would be

tracked until the electron finds a wall or is otherwise neutralized. Clearly there is still a

need to describe the traversal flow of electrons across magnetic field lines beyond the

expectations derived from following single electrons. One possible method used by some

is a circuit equivalent model (21) (76).

92

Chapter 10 Plasma circuit equivalent model

In previous chapters the dielectric constants of the plasma were described in the parallel

and perpendicular direction to the magnetic field. Perpendicular, the dielectric constant is

large and positive; parallel to the magnetic field, the dielectric constant is large and

negative. So, in effect, a magnetic plasma behaves as a semi-infinite network of

inductors and capacitor;, a simplified view of the network is depicted in Figure 10-1 (81).

N N S

Figure 10-1. An illustration of the magnetron plasma represented as a series of capacitors and

inductors; resistive components have been removed for clarity.

Figure 10-1 is a sketch of an electrical analogy for a magnetron plasma and shows the

capacitive behavior perpendicular to the magnetic field lines, and the inductive behavior

along field lines. This concept may be further evaluated by applying the above equations

in a dielectric constant tensor to evaluate propagation through the plasma as developed in

chapter Chapter 1 and applied in chapter Chapter 8 (22).

93

10.1 Magnetron circuit

Noting that the plasma can act as a network of inductors and capacitors is interesting, but

more interesting is what effects this may have on the expected plasma behavior locally,

and overall on the plasma current-voltage characteristics for DC and HIPiMS processes.

In order to more easily evaluate various effects on the plasma model, a simplified version

using individual RLC components in Matlab’s Simulink software is used. The power

supply was modeled as a capacitor discharging into the plasma as shown in Figure 10-2

a); and in Figure 10-2 b) the inductor capacitor network depicted in Figure 10-1 is

schematically drawn. The number of elements used in Figure 10-2 was chosen as the

minimal number needed to accomplish the development of every possible connection that

may be expected using the inductance/capacitance relationship for a magnetized plasma.

94

Figure 10-2. The model for the power supply (a), and the model for the plasma (b) is schematically

depicted. A capacitor set is shown for both sheaths. The flux lines are modeled as inductors parallel

and capacitors perpendicular to the plasma. The flux lines that are modeled are overlaid as dotted

grey lines.

a)

b) Sheath Sheath Flux lines

95

The viability of the HiPIMS supply model was tested through a resistor first, and then

through the plasma model. Figure 10-3 shows the current (dashed lines) and the voltage

(solid lines) through both a resistor and through the plasma network.

Figure 10-3. The Current and Voltage vs. time curve for the power supply through a resistive load (

grey dashed lines) and the I and V vs. t curve for the plasma model without resistive variation (solid

lines).

The capacitance of the network absorbs some of the energy output by the supply as

illustrated by the voltage dropping quicker initially. At the end of the pulse this

capacitance slowly reduces the target voltage in comparison to the resistor. No ringing

was observed. No oscillations grew during the pulse. An initially large drop in voltage

was not observed. The magnetron model consists completely of passive elements, and

-1000

-900

-800

-700

-600

-500

-400

-300

-200

-100

0

0 0.001 0.002 0.003 0.004 0.005

time (s)

Volta

ge (V

)

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Cur

rent

(A)

96

fails to create by itself any significant ripples within the current or voltage curves. This

model is still in need of mechanisms to generate the oscillations. Possible adjustments

could be; exchanging the resistive component of the sheath for a diode, more elements

generating a 3-d picture rather than the 2-d simulation shown, and simulating the inherent

oscillations within the plasma by directly varying a passive element to simulate the

expected turbulence within the plasma. This third concept is explored next.

10.2 Turbulence effect

In order for the capacitive portion of the plasma to make a contribution to the conduction

of current, a portion of the current must be carried as a wave. dc magnetron sputtering is

known to have rf fluctuations within the plasma (27) (28) (35) (74). Since the only

power source within the magnetron plasma is the cathode we do not necessarily want to

simply add a varying power supply. We know through the body of work performed in

sputtering plasmas and discussed in chapter 9 that plasma densities will oscillate. This

model allows a variation in plasma density to be represented as a change in local

resistance within the plasma. The total resistance will be kept constant by varying

another region of the plasma out of phase with the first. A switch will be implemented

that varies the resistivity locally in the plasma network. The switch results in zero net

change in dc resistivity through timing with other switches in the network. In an effort to

analyze the current carrying capability, we will simplify the network circuit as shown in

Figure 10-4 and described below.

97

Figure 10-4. The simplified network with a pair of choppers (modulated resistivity) used to simulate

the plasma as a pair of capacitors with parallel resistors to conduct the power.

In this model the HiPIMS supply has been replaced by a simple dc supply. The plasma

has been reduced to a pair of pathways each containing a capacitor on each end

representing the sheaths, and a pair of parallel resistors for the plasma. The resistors are

modulated between a resistance of 100 and 1 Ω at the frequencies of 1 Hz and 10 kHz.

The paths through the resistors are set up such that when one switch opens, the switch on

the other path closes, and to insure there is no time spent with both on, the array is set

with a 45% duty cycle, providing a brief time with both resistors out of the circuit

resulting in an overall increase in resistance of the circuit over time. The dc resistance of

the entire circuit is about 18 Ω, and the resistance during oscillations is approximately 18

Ω 90% of the time and 60 Ω 10% of the time. The resistance, capacitance of the system

and system frequency has been arbitrarily selected for demonstration purposes.

98

Figure 10-5. The dc behavior for Voltage and RMS current supplied to the cathode as depicted by a

simplified power system model is graphed as current vs. time. The upper line operates the chopper

circuit at 10 kHz, and the lower line is at 1Hz.

Initially the system is operated with the switches alternating at a time greater than the

analysis time (1 Hz) to approximate a dc signal. As seen in Figure 10-5, after the initial

charging of the capacitors within the circuit, the current reaches a steady state value of 56

A. This is in-line with the expected current from adding up the resistances of the simple

circuit. The voltage for both cases remains nearly steady at the applied value of 1000 V.

By setting a higher frequency for the switching, the current passing through the system

increases and doubles to 112 A in the steady state, indicating the possibility of a

mechanism by which the capacitive effect of the plasma perpendicular to the target

voltage may result in a lower resistance for an applied dc input. One such mechanism

would be any changing plasma density over time at a fixed position within the plasma.

0

50

100

150

200

250

0 0.0005 0.001 0.0015 0.002

time (s)

Cur

rent

(A)

Current with chopper at 10kHz

Current with chopper at 1Hz

99

This chopper mechanism may be considered an approximation of any number of

measured waves found by other groups (27) (28) (74) for magnetron plasmas. For

example, a likely source would be a diocotron type wave developed within the E×B drift

current above the cathode as described by Thornton (23). For simplicity the network was

setup with just two branches, however, it is entirely likely that the magnetron has

multiple regions of variations of plasma density over the surface of the target providing

the system with multiple switching possibilities.

10.3 Conclusions

A model for predicting the behavior of magnetron plasmas has been described. A

mechanism by which the magnetized plasma may contribute to dc conductivity in wave

form has been introduced and demonstrated using electrical circuit equivalents. This lays

the groundwork for better modeling of the magnetron plasma through electrical

equivalents and through finite element modeling. The model shows that it is possible to

generate an improved current through the density variations known to exist within

plasmas (27) (35) (82) (83). Variations of the type developed within this model,

however, fail to show a variation or amplification of an oscillation in the applied voltage

and output current like those that have been experimentally observed in HiPIMS plasmas

(8) (71). The oscillations presented are local oscillations; their presence reduces the

effective resistivity of the system, but they do not cause global ripples. The global

oscillations, therefore, must affect an entire region of the plasma. The most logical place

left to look is at the sheath, and at our own data.

100

Chapter 11 Experimental Data

The experimental data was collected on two separate systems. One system was in

Linköping Sweden; the other system was at University of Nebraska-Lincoln (UNL).

Data was collected over a range of material targets in both systems.

11.1 Experimental Setups

The two experimental setups have slight variations in comparison to each other,

particularly in chamber geometry and magnet configuration. The UNL system is

designed for controlled unbalanced sputtering, and includes a coil behind the substrate.

11.1.1 The “Maggie” Chamber

The UNL system (as shown in Figure 11-1) consists of a 150 mm nearly balanced Sierra

Applied Sciences “high material utilization” cathode, a coil to provide greater

unbalancing and magnetic field at the target, and a 44 wavelength ellipsometer mounted

at 66 degrees relative to the substrate plane. Figure 11-2 shows the typical magnetic field

strengths and orientation inside the chamber due to the magnetron cathode. The 50mm

substrates were positioned approximately 150mm away from the target surface, and the

chamber is pumped by a turbopump to achieve a base pressure on the order of 1x10-7 torr.

A 100 turn coil is positioned 200mm away from the cathode behind the substrate and

may be supplied with up to 5 amps generating a field of 50 gauss at the substrate.

101

Substrate

Coil

Target

Ellipsometer

Figure 11-1. A schematic diagram of the magnetron sputtering system at UNL “Maggie”.

Figure 11-2. A confirmed model of the magnetic field direction, and strength of the "maggie

chamber". The contour lines represent magnetic field strength of 10 gauss increments, and the

arrows indicate magnetic field direction.

102

All runs were carried out by first setting the coil to an appropriate current (0-5 amps).

Next the chamber was backfilled to a pressure of one to five mTorr with argon gas, and

the Chemfilt Sinex 1.2 HiPIMS power supply was set to the desired voltage. The

HiPIMS power supply consisted of 10µF capacitor bank that may be charged to a

maximum of 2kV; thus generating pulses in excess of 1 MW peak power at a frequency

of 60Hz. These pulses have an initial current peak on the order of 200 microseconds

followed by a variable secondary peak whose timescale depends on the target material

and may approach 1/60 s.

A Tektronix P6015 high voltage probe measured the target voltage, while the current was

measured with a Tektronix TCP202 ac/dc current probe. At larger currents a Tektronix

CT-04 high current transformer together with a Tektronix TCP202 current probe were

used. The probe current, target voltage and target current were monitored and recorded

using a Tektronix TDS 520C oscilloscope.

11.1.2 Linköping University chamber

The Linköping University (LiU) chamber consisted of a vacuum system composed of a

cylindrical vacuum chamber (height 70cm, diameter 44cm) with a turbo-molecular pump

delivering background pressures between 10-6 and 10-8 Torr (schematic is shown in

Figure 11-3). Inert gas pressures in the range of 2 to 20 mTorr were backfilled into the

chamber; then a plasma was ignited using a HiPIMS supply as described below.

103

Figure 11-3. Schematic Diagram of the Swedish HiPIMS system. Courtesy Johan Böhlmark, Chemfilt

Ionsputtering AB

A circular planar magnetron (magnetic field schematic shown in Figure 11-4) equipped

with either a 150-mm chromium or aluminum target was used for the experiments. In

both cases short high voltage pulses were applied between the cathode/target material and

the chamber walls. The power supply used is a Sinex 1 manufactured by Chemfilt

Ionsputtering AB, Sweden. The Sinex 1 is able to deliver 2400 V and 1200 A peak values

with pulse duration lengths of approximately 100 µs with a repetition frequency of 50 Hz,

and is delivered by a 13.5 μF capacitor bank.

A Tektronix P6015 high voltage probe measured the target voltage, while the current was

measured with a Tektronix CT-04 high current transformer together with a Tektronix

TCP202 current probe. The probe current, target voltage and target current were

monitored and recorded using a Tektronix TDS 520C oscilloscope.

104

Figure 11-4. The applied magnetic field of the magnetron. The numbers are given in mT. The data

were taken using a Hall probe. The solid lines represent the direction of the magnetic field, while

dashed lines represent the magnetic field strength. Courtesy Johan Böhlmark, Chemfilt Ionsputtering

AB.

Both systems geometrically have similar targets, although much different magnet arrays,

both systems also have very similar power supplies. Minor variations are the larger depth

of the LiU system, and the LiU system’s downward sputtering arrangement vs. UNL

sideways sputtering arrangement.

11.2 Current and voltage vs. time data collection for each system

Current and Voltage behavior with respect to time were measured for both LIU and UNL

systems and repeated for various pressures, applied voltages and target materials. The

105

voltage range evaluated was between 500-1600V, since below 500V the current was low,

and above 1600V the plasma becomes unstable. A full set of data may be found in the

Appendices. Appendix A is the UNL data, and Appendix B is the LIU data.

Since HiPIMS generators, and the definition of HiPIMS covers a wide range of pulsed

systems, HiPIMS results appear to vary from system to system. These variation may

occur due to magnetic, grounding, stray inductances and capacitances as well as design

differences.

A typical discharge curve found in the UNL “Maggie” chamber is shown in Figure 11-5

with the same time scale for the Linköping system. The curves shown for the UNL

system are for an argon gas pressure of 3mTorr, at an applied voltage of 1144 Volts on a

titanium target, the UNL data may be found in Appendix A. The data in the appendix

will not look like Figure 11-5 but instead Figure 11-6.

106

0.0012 0.0013 0.0014 0.0015 0.0016

-1000

-500

0

Volta

ge (V

olts

)

time (s)

0.0012 0.0013 0.0014 0.0015 0.0016

0

5

10

15

Cur

rent

(Am

ps)

Figure 11-5. Typical discharge for UNL HiPIMS system, current and voltage for titanium at 3mTorr

of argon and 1144 Volts, scaled to a similar time frame to LiU data.

The data looks like Figure 11-6 because, in the process of taking the data in Linköping,

an improved data compression method was found and later used in the data collection at

UNL. This allowed for significantly more data points to be saved and transferred for a

single pulse. Figure 11-5 is a subset of the data presented in Figure 11-6 zooming in at

the large initial pulse.

107

0.000 0.005 0.010

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.000 0.005 0.010

0

5

10

15C

urre

nt (A

mps

)

Figure 11-6. Typical discharge for UNL HiPIMS system, current and voltage for titanium at 3mTorr

of argon, and 1144 Volts applied discharging to about 500 V.

A typical discharge curve acquired in a system in Linköping is shown in Figure 11-7, the

LIU data may be found in Appendix B.

108

0.0000 0.0001 0.0002-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.0000 0.0001 0.00020

20

40

60

80

100

Cur

rent

(Am

ps)

Figure 11-7. Typical discharge for Linköping system. Voltage applied to aluminum at 22.5 mTorr

starting at about 832 Volts initially applied, discharging to about 500 volts.

11.3 Physical data range

The characteristics of the HiPIMS plasmas have been collected on 2 systems, 5 elements,

several pressures, and one working gas, and a range of applied voltages. Table 11-1

indicates the expanse of experimental space reviewed.

109

Table 11-1. Materials and conditions selected for observing oscillations in HiPIMS.

Chamber Material AMU Gases (AMU)

Pressure (mTorr)

Applied Voltage

UNL copper 63.6 Ar(40) 3 750-1300V

titanium 47.9 Ar(40) 3 435-1330V

silver 108 Ar(40) 3, 5 300-1000V

LiU aluminum 27 Ar(40) 5-22.5 400-1700 V

chromium 52 Ar (40) 2-22.5 400-1700V

Each run has a number of characteristics that help describe the behavior of the system. In

order to further refine the analysis, the current vs. time and the voltage vs. time are also

important characteristics to further define the system.

110

11.4 Current and voltage vs. time for each element

The following curves (Figure 11-8 through Figure 11-11 are for various experiments run

on the UNL system. The first figure (Figure 11-8) is the current and voltage vs. time

graph trends for copper at 3 mTorr and 800 volts. A complete set of graphs may be

found within the appendix A.1 .

0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

0

4

8

Cur

rent

(Am

ps)

Figure 11-8. Current and voltage curves for copper at 3mTorr and 830 Volts initially applied.

111

The current and voltage vs. time graph trends for titanium at 3 mTorr and 800 volts are

shown in Figure 11-9 and no coil current. A complete set of graphs may be found within

the Appendix A.2

0.0003 0.0004 0.0005 0.0006 0.0007

-800

-600

-400

-200

0

Targ

et V

olta

ge (V

)

time (s)

0.0003 0.0004 0.0005 0.0006 0.0007

-20

-15

-10

-5

0

Targ

et C

urre

nt (A

)

Figure 11-9. Current and voltage characteristics for titanium at 820 Volts initially applied and

3mtorr with the coil off.

112

The current and voltage vs. time graph trends for titanium at 3 mTorr and 800 volts with

the coil on are shown in Figure 11-10 with a coil current of 5 amps. A complete set of

graphs may be found within the appendix A.2 .

0.0002 0.0004 0.0006 0.0008-900-800-700-600-500-400-300-200-100

0100

Targ

et V

olta

ge (V

)

time (s)

0.0002 0.0004 0.0006 0.0008

-16-14-12-10-8-6-4-202

Targ

et C

urre

nt (A

)

Figure 11-10. Current and voltage characteristics for titanium at an initially 820 Volts and 3mtorr

and a coil current of 5 amps.

113

The current and voltage vs. time graph trends for silver at 5 mTorr and 800 volts are

shown in Figure 11-11. A complete set of graphs may be found within the appendix A.3 .

The silver target failed to ignite at 3 mTorr without the coil on at 5 Amps.

0.004 0.006 0.008 0.010

-800

-600

-400

-200

0

Targ

et V

olta

ge (V

)

time (s)

0.004 0.006 0.008 0.010

-2

-1

0

Targ

et C

urre

nt (A

)

Figure 11-11. Current and voltage characteristics for silver at an initially applied 820 Volts and

5mtorr.

114

A characteristic current and voltage vs. time graph trend for aluminum (run on the LiU

system) at 5 mTorr is shown in Figure 11-12. A complete set of graphs may be found in

Appendix B.1

0.0000 0.0001 0.00020

20

40

60

80

100

Cur

rent

(Am

ps)

time (s)

0.0000 0.0001 0.0002

-800

-600

-400

-200

0

Volta

ge (V

otls

)

time (s)

Figure 11-12. Current and voltage curves for aluminum at 5 mTorr and 830 Volts initially applied.

115

A characteristic current and voltage vs. time graph for chromium (run on the LiU system)

at 5 mTorr and 800 volts is shown in Figure 11-13. A complete set of graphs for the

range of applied voltages and pressures may be found within Appendix B.2 .

0.0000 0.0001 0.0002-1000

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

0.0000 0.0001 0.00020

20

40

60

80

100

Cur

rent

(Am

ps)

time (s)

Figure 11-13. Current and voltage curves for chromium at 5 mTorr and 830 Volts initially applied.

116

Chapter 12 Results and Discussion

The intent of this dissertation is to provide a better understanding of the HiPIMS process

by first analyzing the underlying physics, second developing a model of the process, and

third experimentally confirming the results and analyzing the differences between the

model and the experimental results. Within this dissertation, the previous chapters:

• provided motivation for using and understanding the HiPIMS process;

• outlined core plasma behaviors pertinent to magnetron sputtering;

• reviewed prior developments in magnetron sputtering; developed a basic circuit

equivalent model for the magnetron plasma; and

• experimentally generated current and voltage characteristic curves for materials of

aluminum, chromium, copper, silver, and titanium.

The unifying purpose for these sections was to identify the fluctuations that appear in

many HiPIMS processes. From this identification we hope to improve HiPIMS processes

in the future through industry acceptance and introducing other fields of study and their

body of work to HiPIMS processes.

First, the current and voltage characteristics for HiPIMS plasmas need to be discussed,

and the oscillations of interest identified. One particular point of interest is that the

oscillations may be present in either the voltage curve and/or the current curves. The

Linköping system tended to have the oscillations appear in the voltage, and the UNL

system tends to have the oscillations in the current (see Figure 12-1 and Figure 12-2 vs.

Figure 12-3). Variations in impedance from system to system due to any number of

117

variables, including length of power cable could contribute to where the oscillations

appear.

12.1 Current and Voltage Characteristics

A HiPIMS process starts with a high voltage pulse applied to a magnetron, and after a

small time delay, current begins to flow (See Figure 12-1, Figure 12-4, and Figure 12-5).

The delay time shortens slightly with increasing applied voltage.

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-600

-400

-200

0

Targ

et V

olta

ge (V

)

time (s)

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-4

-3

-2

-1

0

Targ

et C

urre

nt (A

)

Figure 12-1. Titanium at 3mTorr with 550V applied. A clear lag (shaded region) between current

flow and voltage applied may be seen.

118

Once current begins to flow, the voltage drops and the current increases. An initially

sharp current spike is visible in Figure 12-2. The current develops into a sharp peak, and

then declines. After this sharp initial current spike, the current gradually increases a

second time. The second peak begins to overtake the initial peak in maximum current

with larger initially applied voltages. The larger voltage also indicates more total charge

available for the pulse. The second peak contains a number of small oscillations in the

current. These oscillations match up with the region of large voltage oscillations from

Linköping University’s HiPIMS system shown in Figure 12-3. The second peak is often

attributed to the metal ion dominated plasma (73). The oscillations do not occur for all

metals or all initial applied voltages.

0.000 0.002 0.004

-1000

-500

0

Vol

tage

(V)

time (s)

Ar ionvoltage drop

metal ion voltage drop

0.000 0.002 0.004

-10

-8

-6

-4

-2

Cur

rent

(A)

metal ion peakAr ionpeak

Figure 12-2. Titanium current and voltage curves at 1200V, a clear second region is present in the

current curve after the initial peak. Typically there is an initial current from the argon ions, and

119

then a second peak from the metal ions is detected. The current peaks have corresponding voltage

drops.

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1800-1600-1400-1200-1000-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

metal ion voltage drop

Ar ion volt drop

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1000

100200300400500600700

Cur

rent

(Am

ps)

time (s)

Figure 12-3. 5 mTorr aluminum at 1700V applied voltage indicating several behaviors present in

HiPIMS current and voltage curves. An initial voltage drop again is followed by a second voltage

drop. A periodic oscillation increases in frequency and amplitude during the discharge of the supply

overlaying the region of the second voltage drop.

Figure 12-3 does not have the corresponding peaks for the argon and metal ions in the

current. This is likely due to the method of acquiring the current (measuring the

magnetic field), and that the current occurs on a much more compressed timescale on the

Linköping University system which may contribute to the peaks overlapping.

120

12.1.1 Current and voltage curves for selected pulses

In order to provide an in-depth analysis of the voltage curves, chromium and aluminum

current and voltage graphs are compared. Figure 12-4 shows a series of the voltage

curves for chromium at 5mtorr and for initial voltages of approximately -1500V, -1250V,

-900V and -620V. Figure 12-5 for aluminum shows a series of curves similar to that of

Figure 12-4 for chromium. These graphs show higher starting voltages resulting in lower

final voltages in nearly the same discharge time. The graphs indicate the aluminum tends

to have higher current (through larger total voltage drops) and larger fluctuations than the

chromium.

Figure 12-4. Shows voltage vs. time for chromium at 5 mTorr for 600 through 1700 starting voltages.

(a) is 600 volts initially applied, (b) is 800 Volts initially applied (c) is 1100 Volts initially applied (d) is

1300 Volts initially applied and (e) is 1700 Volts initially applied.

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04time (s)

targ

et v

olta

ge (V

)

Cr 5mTorr

a

b

c

d

e

a,b

cd

e

121

Figure 12-5. Shows voltage vs. time for aluminum at 5 mTorr for 600 through 1500 starting voltages.

(a) is 600 volts initially applied, (b) is 900 Volts initially applied (c) is 1050 Volts initially applied (d) is

1250 Volts initially applied and (e) is 1500 Volts initially applied.

In the case of the present process for the Linköping system, higher initial voltages were

met with larger currents and faster discharge times. The resistance of the system drops

with applied voltage. The drop in the resistance of the system is expected as the HiPIMS

process attempts to follow the behavior of equation (8-1) since, the equation is non-linear

between current and voltage. In looking at the oscillations in the current voltage curves,

the oscillations get bigger with higher applied voltages. The oscillations also are material

-1800

-1600

-1400

-1200

-1000

-800

-600

-400

-200

0

0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04time (s)

Vol

tage

(V)

Al 5mTorr

a

b

c

d

e

ab

cd

e

122

dependent. The largest oscillations occur for aluminum, which also has the highest

current of all the metals tested.

12.1.2 Maximum current vs. maximum voltage

The maximum current developed by the system varied with applied voltage and argon

pressure. A plot of the maximum current for chromium as a function of initial applied

voltage is shown in Figure 12-6.

Figure 12-6. A graph of peak applied voltage vs. peak developed current is plotted for various

pressures of argon. Error in the applied voltage measurement is +/- 10 Volts.

0

200

400

600

800

1000

1200

1400

1600

1800

1 10 100 1000

Current (A)

Volta

ge (V

)

2 mTorr5 mTorr10 mTorr15 mTorr20 mTorr

Cr

123

One interesting note is the apparent decreasing dependence of the current on pressure at

high voltages. The semi-log plot of the data helps accentuate the shift to an n=1

behavior; and the set of chromium curves appear to be approaching the same final

limiting value. The approach changes however, dependent upon the strength of the

trapping magnetic (B) field. In Figure 12-7 two separate magnet arrays are compared for

their peak maximum currents. The peak maximum currents are larger for the stronger

magnet array.

Figure 12-7. Chromium graphs of voltage applied vs. the maximum current. The two sets are

different magnet arrays used in the same cathode body. The weaker magnet set (diamonds)

generated voltages in the 100’s of amps. The stronger magnetic field (squares) generated larger peak

maximum currents.

0200400600800

100012001400160018002000

1 10 100 1000 10000

Current (A)

Volta

ge (V

)

2mTorr Cr

2 mTorr Crincreased B field

124

The pressure independence is not solely a behavior of chromium as the Figure 12-8

shows for aluminum at pressures of 2 and 20 mTorr. The transition in the current-voltage

curve is also not as pronounced for the aluminum.

Figure 12-8. Current maximum vs. maximum applied voltage for aluminum at both 5 and 20 mTorr.

The values appear to converge toward a single value.

12.2 Average Resistance vs. Applied Voltage

By using the Voltage vs. time curves and approximating the discharge time, as well as

initial and final voltages, an average resistance and current of the plasma may be obtained

0

200

400

600

800

1000

1200

1400

1600

1800

1 10 100 1000 10000

Current (A)

Volta

ge (V

)

5mTorr20 mTorr

Al

125

through fitting the data. An average resistance is developed through the following

capacitance discharge equation:

(12-1) ⎟⎠⎞

⎜⎝⎛ −

= RCt

c EeV or ⎟⎠⎞

⎜⎝⎛ −=⎟

⎠⎞

⎜⎝⎛

RCt

EVcln

where Vc is the current voltage of the capacitor, E is the initial voltage of the capacitor, t

is the elapsed time since discharging started, and R and C are the resistance and

capacitance of the system respectively. Using equation (12-1), and the 13.5 μF

capacitance of the power supply, the resistance for a -1500V pulse is determined to be 1-

2 ohms, and the resistance for a -700V pulse is about 45 ohms for aluminum. By finding

the average resistivity of the system over a number of applied voltages, the trends

illustrated in Figure 12-9 and Figure 12-10 are developed.

126

Figure 12-9. The resistance as a function of applied voltage for chromium at a range of pressures.

All the pressures appear to converge to one resistance at high applied voltages.

0

50

100

150

200

250

0 500 1000 1500 2000Voltage (V)

Res

ista

nce

(Ω)

2 mTorr5 mTorr10 mTorr15 mTorr20 mTorr

Cr

127

Figure 12-10. The resistance as a function of applied voltage for aluminum at 5 and 20 mTorr.

Similar to the chromium, the different pressures appear to converge to one resistance.

From Figure 12-9 and Figure 12-10, it is clear that increasing voltage reduces the overall

resistance of the system for all pressures, and begins to approach a lower limit on the

order of a few ohms. In the chromium case, the lower limit is around 4-5 Ohms; and for

aluminum the limit is around 1 Ohm. At higher voltages, the contribution from pressure

appears to decrease and the curves appear to converge. However, as illustrated in Figure

12-11, the resistivity of the plasma has not leveled off, and continues to drop when

viewed at a reduced scale. Figure 12-11 indicates that the various pressures still have a

0

5

10

15

20

25

30

35

40

45

0 500 1000 1500 2000

Voltage (V)

5 mTorr

20 mTorr

Al R

esis

tanc

e (Ω

)

128

small influence near the end of the explored voltage range indicating not a change in

behavior, but an approach to a non-zero asymptote.

Figure 12-11. The pressure and material dependence of the resistance from the plasma may be

observed through the voltage vs. resistance curve. The chromium data is in gray (triangles, asterisks,

bullets and plusses), and aluminum data is black (diamonds and squares). The scale of this graph has

been adjusted to have a non zero lower limit in order to see that the curve continues at the small

resistance values.

To test whether the magnetic trapping still has an affect at these high voltages, a newer

magnet array was installed. Figure 12-12 indicates the effect of an increased magnetic

field on the chromium target resistance behavior at 2mTorr. Increasing the magnetic

3

4

5

6

7

8

9

10

0 500 1000 1500 2000

Voltage (V)

Res

ista

nce

(Ω)

5 mTorr20 mTorr2 mTorr5 mTorr10 mTorr15 mTorr20 mTorr

Al

Cr

129

field extends the region where the current-voltage relationship follows the Equation (8-1)

power relationship until reaching a minimum resistance of approximately 1 ohm.

Figure 12-12. A new asymptotic approach for the minimum resistance in comparison to the original

magnet array for the same pressure may be seen in the figure. The lower magnetic field data set is

black squares. The larger magnetic field data set are dark circles. The increased B field achieves a

lower minimum resistance.

12.3 Modified magnetron I-V fit

In order to compare this data to the voltage-current relationship for magnetron sputtering,

the average current for each pulse was calculated from the change in target voltage. The

0

10

20

30

40

50

60

70

80

90

100

0 500 1000 1500 2000 Voltage (V)

Res

ista

nce

(Ω)

Increased B

standard B

Cr

130

initial voltage values for the pulse were then plotted with respect to the resulting average

current, as illustrated in Figure 12-6. As reported by others (84) (85) (86), the I-V

characteristics initially follow an “n” value for equation (8-1) between five and six. At

higher voltages, the curve transitions to an “n” value of approximately one. A single fit

may be made over the entire voltage regime by adding a second term to the voltage

characteristics of the magnetron. Thus, modifying the equation as:

(12-2) IRk

IVn

n+= 1

1

Where R is the resistance, and the IR term accounts for the n=1 contribution. The IR

term also accounts for the non-zero asymptote clearly visible when the data is plotted

with respect to resistivity in Figure 12-9 through Figure 12-12. The IR term may be

caused by several phenomena. First, the resistance and their associated voltage drops

between the measurement point and the target face may become significant at currents in

the range of hundreds of amps. Second, the system is not dc, and the cabling, and any

inductors included in the setup will oppose the rapidly increasing current. Finally, the IR

behavior can also result from the magnetron beginning to lose magnetic confinement as

proven by others previously (74).

Equation (12-2) fits the data over the entire measured voltage range. For example, in

Figure 12-13 the voltage is plotted with respect to current for chromium along with the fit

of equation (12-2) with n=6 and R=2 ohms; the individual terms are also graphed to

illustrate their contribution to the whole equation. Two ohms is much greater than the

expected resistance and resulting voltage drop across the cathode and target for chrome

131

and therefore this resistance is likely plasma based, such as an indication of a magnetic

field too weak to provide confinement. Figure 12-14 shows the I-V curve for the

aluminum fit using equation (12-2) with n=6 and R=0.5 ohms.

Figure 12-13. A fit to the current maximum vs.-applied voltage maximum curve by adding an "n=1"

term to the system for 15 mTorr chromium. The graph also helps demonstrate that at large

currents, the "n=1" term will become dominant.

0

200

400

600

800

1000

1200

1400

1600

1800

1 10 100 1000

Volta

ge (V

)

Current (A)

15 mTorr Chromium

n=6 Fit

n=1 Fit

Fit total

132

Figure 12-14. A fit to the current maximum vs.-applied voltage maximum curve by adding an "n=1"

term to the system for 5 mTorr aluminum. This helps demonstrate the broad application of this fit

through demonstration on separate material and pressure.

The modified equation demonstrates that a small change in system resistance can make a

significant impact on the expected behavior of the magnetron’s current voltage curve, and

shows the effect to be largely dependent on magnetic field, and weakly dependent on

pressure at high currents.

0

200

400

600

800

1000

1200

1400

1600

1 10 100 1000

Volta

ge (V

)

Current (A)

5 mTorr Aluminum

Fit total

n=6 Fit

n=1 Fit

133

12.4 Fluctuations

The fluctuations in the curves are analyzed with respect to amplitude and frequency. The

frequencies tended to start at low frequencies at the beginning of the pulse, and slowly

increase in frequency as seen in Figure 12-15.

Figure 12-15. The derivative of the voltage vs. time (left axis) and the current vs. time (right axis)

graphs. The voltage oscillations decrease in frequency during the length of the pulse.

Figure 12-16 b) and d) show a derivative of the voltage vs. time and the current vs. time

during a HiPIMS pulse from the Linköping system. The derivative of the voltage curve

had been taken in order to isolate oscillations from the dc component shown in a) and c)

-200

-100

0

100

200

300

400

500

600

700

-1.00E+09

-8.00E+08

-6.00E+08

-4.00E+08

-2.00E+08

0.00E+00

2.00E+08

4.00E+08

6.00E+08

8.00E+08

1.00E+09

0.00E+00 5.00E-05 1.00E-04 1.50E-04 2.00E-04C

urre

nt (A

)

Volta

ge s

lope

(dV/

dt)

time (s)

increasing frequency

134

of Figure 12-16. There are large fluctuations in the applied voltage during the peak

current of the plasma. The fluctuations however, are not consistent in frequency or

amplitude. The waves increase in frequency and amplitude during the discharge, unlike

the expected behavior for a ringing effect similar to when the voltage is initially applied.

These oscillations increase in amplitude, an increasing amplitude tends to indicate a

negative resistance. Another way to look at these oscillations is a positive imaginary

component in the relationship between wave propagation and angular frequency. The

positive component instead of a negative component allows the waves to build and get

larger, rather than dampening out. These oscillations have initially been found to be

proportional to the current developed in any given pulse similar to the expected behavior

from polarization drift (equation (8-5)) repeated here:

(12-3) dtdE

BnmM

J p 20

0)( +=

Plasma densities are known to be very large and decrease over the life of the HiPIMS

pulse (87) (88) (89), which could provide an explanation for the variation in the

amplitude and frequency of the voltage fluctuations from the beginning to the end of the

pulse. This may be due to the current flow from polarization drift being linearly

dependent on both plasma density and frequency of the changing electric field. The

plasma density increases and the frequency should also increase. Looking at polarization

drift however, does not give us a clear causation, but we do have approximate correlation.

Increased current results in larger oscillations; this behavior may be expected if

polarization drift was the enabling behavior.

135

Figure 12-16. The correlation between current flow and fluctuations on the I-V curves has been

highlighted. a) and b) show the behavior for an applied voltage of -1500 dv/dt is appr 1e9 and the

current approaches 800 amps for aluminum. c) and d) show the behavior for an applied voltage of -

700V, dV/dt is almost 1e8, and the current approaches 60 amps also for aluminum.

12.5 Plasma immersion ion implantation matrix sheath model

Plasma immersion ion implantation (PIII) is a useful technique used to implant ions in

semiconductor and metallurgical processes, and has been suggested as a technical

information source for HiPIMS (90) (91) (92). The plasma immersion process involves

-200-1000100200300400500600700

-2000-1750-1500-1250-1000-750-500-250

0

0.00E+00 1.00E-04 2.00E-04

Cur

rent

(A)

Vol

tage

(V)

time (s)

a)

-200-1000100200300400500600700

-1.00E+09

-5.00E+08

0.00E+00

5.00E+08

1.00E+09

0.00E+00 1.00E-04 2.00E-04

Cur

rent

(A)

Vol

tage

slo

pe(d

V/d

t)

time (s)

b)

-20-10010203040506070

-900-800-700-600-500-400-300-200-100

0

0.00E+00 2.00E-04 4.00E-04

Cur

rent

(A)

Vol

tage

(V)

time (s)

c)

-2.00E+08

-1.50E+08

-1.00E+08

-5.00E+07

0.00E+00

5.00E+07

1.00E+08

1.50E+08

2.00E+08

-20-10

010203040506070

0.00E+00 2.00E-04 4.00E-04

Vol

tage

slo

pe (d

V/d

t)

Cur

rent

(A)

time (s)

d)

136

immersing an item/workpiece into a plasma and instantly applying a large bias to the

work piece/substrate. The application of a large bias causes the electrons to move away

from the workpiece/cathode on the order of the electron plasma frequency (GHz

timeframe). This motion uncovers the slower moving ions to create what is called a

“matrix” sheath “s0” illustrated in Figure 12-17 (93). The region of uncovered ions

accelerates and collides with the substrate. The loss of ions reduces the shielding for the

electrons, and the electrons retreat further from the substrate. The net result is eventually

the plasma regains its Child law sheath at a larger distance “s” which is greater than the

initial Child law sheath prior to the applied voltage “s0”.

Figure 12-17. Illustrated is the sheath moving away from the cathode exposing a matrix sheath of

ions. The large group of initially exposed ions creates a spike in current.

n0

x

n

cathode

initial sheath

plasma

s

pre-sheath

ne ni

+ + + + + +

matrix sheath

s0

137

Typically the peak PIII current density will follow the normalized equation (22):

(12-4)

Where is normalized through the equation:

(12-5) with

(12-6) where is the initial applied voltage.

The normalized time t is normalized through the equation:

(12-7) t ω · t,

where “t” is time; and ω is the plasma ion frequency previously defined in equation (7-

8) and repeated here for convenience:

(12-8)

The result of the matrix sheath current equation is a current behavior similar to the one

shown in Figure 12-18. The theory indicates the position of the peak accurately, but

provides only a ball park figure on current, typically being off by about 10% (90).

138

Figure 12-18. The normalized current vs. normalized time for the plasma immersion effect from

Lieberman (90). The dashed line is the theoretical values, the solid line is the experimental (22).

The maximum current is expected to be 0.55 at the normalized time of t 0.95. The

matrix sheath current assumptions begin to fail at t 2.7 . The PIII ion matrix model

may be extended to HiPIMS by making the cathode the target instead of the work piece.

Shown in Figure 12-19 are typical current and voltage curves for titanium sputtered using

HiPIMS. The initial current spike compares well in shape to the ion matrix sheath

expectations, but deviates from the expectations at longer normalized times.

139

0.000 0.001 0.002 0.003 0.004

-1200

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge (V

olts

)

time (s)

0.000 0.001 0.002 0.003 0.0040

5

10

15

20

Targ

et C

urre

nt (A

mps

)

Figure 12-19. The current vs. time and voltage vs. time for titanium at 1245 volts initially applied

and 3mTorr. The initial peak has strong similarities to the matrix sheath model.

Given that the HiPIMS system contains a magnetic field acting against the electrons in

the plasma, the behavior cannot be expected to follow that of a PIII plasma exactly. For

example, both the secondary electrons and those initially present within the plasma will

begin to generate a higher plasma density once the pulse is initiated due to magnetic

trapping. Also, the PIII model is based on the dc sheath model and ignores any effect the

140

magnetic field would have on the mobility of the electrons to create the matrix sheath. It

is still informative to apply the PIII matrix sheath model to the HIPIMS data.

The above pulse shown in Figure 12-19 would suggest from its width, a plasma density

on the order of 109 m-3, and the current generated in the cathode would suggest a plasma

density on the order of 1017 m-3.

Compared to PIII, HiPIMS has a higher ionization that increases the current over the PIII

predictions, and a magnetic field that will reduce the distance the electrons can move

away from the cathode. The reduction in electron motion results in a smaller sheath

distance traveled and therefore reduces the expected normalized time in comparison to

the prediction for PIII. However, the PIII model provides trends to look for within the

HiPIMS data. The application of the PIII model to HiPIMS suggests that a moving

sheath may be part of the behavior seen in HiPIMS. Key PIII behaviors to look for are:

1) The initial spike in current will depend on the plasma density; therefore process

parameters with lower overall plasma densities will not clearly exhibit this

behavior. The literature has shown that lower pressure, and lower voltage

HiPIMS processes have lower densities (88).

2) Oscillations and current should be dependent upon the square root of the mass of

the gas.

3) The current should drop to a more sustainable current as the approximate Child

law sheath is reached.

As may be seen in the data provided in the previous chapter, and the curves included in

the appendices, higher voltages, and higher pressures result in larger initial spikes of

current that die off. The PIII ion matrix sheath model does not account for the continuous

141

oscillations that are especially prevalent in the aluminum data at high applied voltages as

seen in Figure 12-3 and Figure 12-16. The oscillations in the case for aluminum are more

periodic in structure than the single initial spike in current predicted by the PIII ion

matrix sheath model. The frequency of the observed oscillations in the aluminum

HiPIMS pulse is low which infers a wave of ionic origin rather than electron origin. One

region that ions develop unstable oscillations is within the sheath (94).

12.6 Plasma sheath instability

The plasma sheath may become unstable, if the velocity of the ions coming into the

sheath is too high. If the ions have too high of an initial velocity, the assumed balance

between electrons and ions at the sheath boundary is violated as shown in Figure 5-4.

The expectation for the onset of the plasma sheath instability is the equation (94):

(12-9) 2π ω · t 3π

Where “t” is the time for an ion to traverse the sheath. Within the literature, oscillations

in the plasma sheath are found to occur under the following conditions:

1) Large applied currents; when very large current/voltage requirements are applied

to the plasma the sheath can become unstable. An experimental example from the

literature of a large applied current generating an instability is shown in Figure

12-20 for a hollow cathode and a pulse generator (95). A similar behavior in a

HiPIMS plasma from aluminum is shown in Figure 12-21. Large currents also

affect the time in equation (12-9). Larger currents require shorter transit times in

order to maintain the current. If the transit time falls within the range of equation

(12-9), the sheath collapses (94) (96).

142

2) Large changes in plasma density; if the plasma density is high and the pre-sheath

voltage drop is too steep, the plasma can become unstable. The plasma frequency

is dependent upon the plasma density as noted in equation (12-8). The plasma

may become unstable if the plasma density becomes great enough to place the

system within the range outlined in equation (12-9) (96).

3) Multiple species; if there are multiple species of ions within the plasma, the

velocities of the individual species are different. The velocities will be different

due to the same potential all the ions traverse. Ions of different velocities are also

known to result in instabilities developing within the plasma sheath (97) (98) (99).

Figure 12-20. A graph of 3 separate current vs. time graphs from Arbel et al. (95). The time scale is

200 ns/div. a) shows the behavior of a stable discharge with 10 mA/div; (b) shows an oscillation

slightly above discharge threshold for instability with 20mA/div; and (c) shows a current well above

the threshold current at 40 mA/div.

143

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2000

-1500

-1000

-500

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

0

200

400

600

800

Cur

rent

(Am

ps)

time (s)

Figure 12-21. The oscillations in the current and voltage for aluminum at 22.5 mTorr and 1800 V

maximum applied voltage. After the intial ringing dies down, a set of oscillations develops during the

discharge.

HiPIMS plasmas have all of the above: large currents and high voltages, high plasma

densities, and multiple ion species. The multiple species are the result of metal ions that

are ionized in transit from the target surface, in addition to the inert gas ions that form as

the plasma is ignited.

144

The plasma sheath oscillations are expected to be strongly damped by collisions due to

their low frequency. The plasma sheath instabilities therefore will only appear when

significant currents are applied. Collisional dampening also explains the lack of

oscillations for the heavier metals as slower oscillations are more strongly damped in

comparison to the lighter elements such as aluminum such as the chromium pulses shown

in Figure 12-4.

12.7 HiPIMS plasma analysis

The magnetron sputtering plasma is a dense plasma close to the cathode (78). The

plasma is confined through magnetic fields intersecting the surface of the cathode at two

points. These magnetic fields trap electrons close to the target/cathode and through

ambipolar diffusion maintain a quasi-neutral dense plasma near the cathode. The plasma

varies in density within the chamber, and especially near the cathode (18). The plasma

density gradient results in a pressure gradient. As discussed in chapter 5, the plasma

density plays a role in the sheath thickness and the resulting sheath currents.

In HiPIMS, the previous pulse’s plasma is dissipating as the next pulse is initiated. As

the plasma is initiated, the HiPIMS pulse, utilizing the remaining plasma, will generate an

intense current spike as the ionized gas accelerates toward the target across the expanding

sheath indicative of a matrix ion sheath. The ions that just accelerated across the sheath,

sputter the target and eject secondary electrons.

The sputtered material then traverses back across the sheath in its journey toward the

substrate. The emitted electrons are accelerated across the sheath, providing a large

145

number of electrons with high ionization capability, and traverse the sheath faster than

the sputtered material due to their charge and mass.

The sheath begins collapsing to develop a new steady state sheath dependent upon the

decreasing applied voltage while the trapped electrons begin increasing the plasma

density. Due to the large number of electrons, and the lower ionization energy for metals,

the sputtered flux is ionized maintaining the quasi-neutrality of the high density HiPIMS

plasma near the cathode.

The HiPIMS plasma now becomes primarily a metallic ion plasma. The plasma sheath

now has at least two ionic species accelerating across the sheath. The multiple species

means that there will be different velocities within the sheath (98). The plasma density

is also higher than required for steady state maintenance of the sheath due to the large

number of secondary electrons emitted from the cathode. The high plasma density and

high currents begin to match the criteria for an unstable sheath (96). When this is

combined with lighter elements such as aluminum comprising the ion species, the

collisional damping of the instability will be reduced, and the likelihood for oscillations

improves even further. The collapsing sheath of the PIII model also provides an

explanation for the shift in frequency of the aluminum oscillations shown in Figure 12-15

and Figure 12-21. The time to traverse the sheath may be expected to become reduced as

the sheath shrinks to its steady state thickness. The sheath will also collapse due to the

increased pressure developed through the increased plasma density as in equation (5-17)

discussed again in Chapter 8 section 8.1 and repeated here:

146

(12-10)

After the sheath begins to collapse, self-sputtering begins to occur with the metallic ion

species (100).

As the metallic ions are used for sputtering, and the voltage begins to decrease, the

current in the cathode also drops. The HiPIMS current pulse ends in a small flow of

current that maintains the cathode voltage in the range of 0 to 500V until the pulse is

completed. At this point, there is a decaying residual plasma in the chamber with which

to initiate the next HiPIMS pulse.

The PIII model and plasma ion sheath instabilities fit well into the experimental data for

HiPIMS processes. The two concepts also help with the related process patented by

Chistyakov. A figure from the patent of Chistyakov describing the I-V characteristics is

shown in Figure 12-22 (20). The patent describes applying the voltage to a cathode in a

way to develop more power than would be expected. The power is generated by making

a step increase in the voltage, which in turn steps up the current. The voltage that

generates the large current is seen to have a small oscillation associated with the larger

current. The exact amplitude of this oscillation is not necessarily known, as the data

acquired are close to the Nyquist rate. This may be seen by the drawn in peaks earlier in

the pulse.

147

Figure 12-22. Current and voltage are graphed with respect to time from Chistyakov's patent Figure

5C. The figure shows a dramatic increase in current being generated by a quick change in the

applied voltage. As may be seen by the drawn in peaks, the frequencies are close to the Nyquist rate

of the measurement.

The PIII model in conjunction with an instability in the sheath, fits the effect of the

increased current seen by Chistyakov. The oscillating sheath exposes a large number of

ions to the accelerating voltage of the sheath at one time, and the sheath instability may

be pumped by the oscillation in the power supply. Thus the modified PIII behavior

appears to be a good fit for HiPIMS and related processes.

148

12.8 Sheath and PIII Implications

There are several implications of applying the plasma sheath instability and PIII behavior

to the HiPIMS field. For instance, during reactive sputtering with nitrogen, or at the

beginning of a run after venting, the target voltage will likely oscillate (even for higher

mass targets) as the targets have the surface oxides and nitrides removed. These

oscillations would be due to multiple ion species in the plasma sheath. This in turn

provides the operator with a method to determine the cleanliness of the target.

Another implication of the matrix sheath is in the timing and length of the pulse. Shorter

pulses should provide better sputter yields as they consume the local argon plasma

without switching to a metallic sputtering process. Another key implication is in the

necessity for a high initial plasma density.

The lower resistivity curve for the higher strength magnetic fields discussed earlier this

chapter also connects back to the sheath behavior. The sheath increases in current

density through increased plasma density, and a smaller sheath thickness which directly

affects the current flow per equation (12-10).

The fields of PIII and sheath instability research have a wealth of information for

understanding the HiPIMS plasma well beyond the oscillations (101). Within the PIII

field of study, there are predictions for the expected ion energy distributions, which will

further help characterize the HiPIMS process, and the exact nature of this moving

magnetized sheath. Overall this dissertation has found a key piece to the HiPIMS plasma

puzzle in the work of Plasma Immersion Ion Implantation (PIII) and sheath instabilities.

149

Chapter 13 Summary and future work

13.1 Summary

The goal of this dissertation was to explore causes of the oscillations found in the current

and voltage vs. time curves for HiPIMS processes. This dissertation found that a

combination of sheath instabilities and a moving matrix sheath similar to the behavior of

plasma immersion ion implantation help explain the behaviors observed experimentally.

This goal was achieved through a combination of analyzing the underlying mathematical

relationships, developing computer simulations, comparing the results to the

experimental data, and analyzing the data with respect to known behaviors in plasma

physics.

The underlying plasma physics was developed in the early chapters by establishing: the

sheath behavior, the effects of electric and magnetic fields; and the frequencies expected

in magnetized and nonmagnetized plasmas. In later chapters, this information was used

to: understand the work of Goree and Sheridan; infer a magnetized plasma model; and

establish a basis for the plasma immersion ion implantation field of study, and sheath

instabilities. This leads to the conclusion that the HiPIMS plasma has a behavior similar

to plasma immersion ion implantation, in particular a moving matrix sheath.

Rossnagel and Kaufmann were able to experimentally relate the thickness of the sheath

through the Child law sheath to the overall plasma impedance for a magnetron. The

sheath thickness decreases with increasing voltage satisfying both the child law sheath

150

equation, and the magnetron power law. The experimental data of this dissertation was

fit to a modified power law equation (12-2) throughout the voltage regime explored

(800V -1800 V). In the past others used two independent fit results of an n=6 regime and

an n=1 regime. A modification to explain results across the entire spectrum of this basic

magnetron power law equation of (2-2), is the addition of a basic resistive term. This n=1

term shows little dependence on the pressure, but is largely dependent on magnetic field

as the current of the magnetron increases. The currents in HiPIMS plasmas become

relatively large, and become a topic of discussion as their current flow exceeds that

predicted by Bohm diffusion (79). The excessive current flow has been outlined by

others and was discussed in the introductory chapters. Analysis of Bohm diffusion lead

to an investigation of how the current is carried in the discharge, and how oscillations

could contribute to this current.

In order to explore the role the oscillations can play in directly contributing to the current

of the system, a conceptual circuit design for a magnetron was included. The conceptual

circuit design for the plasma included a chopper circuit to account for the non-uniform,

time varying plasma and serve as a source for the oscillations. This model demonstrated

how oscillations can improve current flow within the magnetron by taking advantage of

cross field transport in a wave. The model failed however, to include the observed

voltage oscillations present on the cathode. One method for improving electron transport

from the sheath region would be to provide an oscillating frequency to the plasma for

example from an rf bias applied to the substrate or another region within the plasma. The

oscillations induced by the chopper circuit is a local variation and did not generate

151

oscillations in the modeled current and voltage curves, a more global effect is needed to

explain oscillations observed on the target current and target voltage curves. One region

that can globally affect the potential at the target is the sheath. The fluctuations at the

focus of this dissertation are in the cathode’s voltage and current, indicating a time

varying fluctuation averaged across the cathode surface.

The experimentally observed target oscillations have been analyzed by frequency,

amplitude and the derivative of the curves vs. time. Some of the target oscillations do not

dampen over time, but rather they appear to increase in amplitude. In particular for the

aluminum, the oscillations increase in frequency and amplitude. The increase is

indicative of a negative resistance or positive imaginary component in the relationship

between wave propagation and angular frequency. These oscillations appear similar to

sheath instabilities observed in other fields of plasma research (95).

The initially large spike in current occurring at the beginning of the HiPIMS pulse is

predicted by looking at sheath dynamics described in plasma immersion ion implantation

(PIII). PIII experiments and analysis by others have developed the concept of a dynamic

sheath which transitions from a matrix sheath to a Child law sheath (90). The expected

behavior of the sheath and its oscillations compares well to that of the initial current peak

within the HiPIMS system discussed within this dissertation.

152

13.2 Future work

There are some promising areas for future work that develop from this dissertation for

example, linear cathode arc reduction through active variation of an electric field and

improvement of HiPIMS currents by increasing the residual plasma.

Linear cathodes do not have the same density gradient with the oscillations of the

electrons in the linear portion of the linear cathode as described in Section 8.2.2. Linear

cathodes therefore could be improved in arc suppression by applying an alternating

current (ac) bias to the substrate or nearby ground to artificially generate plasma density

oscillations. A superimposed ac bias could potentially improve the high frequency

conductivity of the plasma, which electrons could take advantage of, in order to maintain

the positive space charge column associated with magnetron sputtering.

Second, alternative HiPIMS supply designs could be explored. In light of the plasma

immersion similarities, HiPIMS power supplies should maintain a small negative voltage

on the cathode. The small negative voltage would provide the cathode with a larger

initial plasma density with which to generate the initial burst of sputtering ions.

Third, the magnetron’s transition from the n=6 term to a resistive n=1 term should be

revisited. The resistive term makes physical sense as wires and connections should

contribute some base resistance to the overall system. However, the experimentally

determined resistance is higher than expected. The resistive term’s dependence on

magnetic field also calls into question the base resistance concept. A better candidate for

the origin of the n=1 term is the force balance between the plasma density and the applied

153

electric field that develop the sheath thickness. The sheath cannot shrink forever; it must

hit a limit; or transition to a different plasma behavior. The plasma density will also

begin to lose confinement as the pressure gradient begins to win out over the magnetic

trap, and therefore would be affected by a change in the magnet array. This force balance

likely forces the sheath to approach an asymptotic minimum sheath thickness. A sheath

limited current voltage curve should approach a limit of n=1.5 rather than n=1. As

previously described in the child law sheath current density equation, the sheath current is

dependent on voltage to the three halves power. The primary challenge in exploring this

concept is the shear number of variables in the model makes it easier to achieve a fit

regardless of their individual physical meaning.

154

13.3 Conclusion

This dissertation has identified the source of the current and voltage fluctuations found on

HiPIMS sputtering systems as a combination of a moving matrix sheath and sheath

instabilities. This identification is the first step in improving the HiPIMS process. Given

this knowledge, we now have a better understanding of the Chistyakov power supply

behavior (20), and given the knowledge of the transition from argon atoms to metal ions,

we can recognize that oscillation frequencies found in the current and voltage curves will

be dependent upon the process material sputtered, and other gases present. We can also

begin to predict how this process should behave in other processes such as reactive

sputtering. Oxygen and especially nitrogen should be expected to generate instability in

the sheath, and could even possibly be used as a measure of target, and system

cleanliness in a multilayer process. Through the better understanding of the nature of the

HiPIMS process developed within this dissertation, the building blocks to improving the

HiPIMS process have been laid.

155

References

1. B. Goranchev, V. Orlinov, and V. Popova. D.C. cathode sputtering: influence of the

oxygen content in the gas flow on the discharge current. Thin Solid Films. 1976, Vol. 33,

pp. 173-183.

2. J. A. Thornton. Influence of substrate temperature and deposition rate on structure of

thick sputtered Cu coatings. Journal of Vacuum Science and Technology. 1975, Vol. 12,

p. 830.

3. R. Messier, A. P. Giri, and R. A. Roy. Revised structure zone model for thin film

physical structure. Journal of Vacuum Science and Technology A. 1984, Vol. 2, p. 500.

4. S. R. Kirkpatrick, S. L. Rohde, D. M. Mihut, M. L. Kuruppu, J. R. Swanson III,

D. Thomson, and J. A. Woollam. Process monitoring and control of low temperature

reactively sputtered AlN . Thin Solid Films. 1998, Vol. 332, 1-2, p. 16.

5. S. M. Rossnagel, and J. Hopwood. Metal ion deposition from ionized mangetron

sputtering discharge. Journal of Vacuum Science and Technology B. 1994, Vol. 12, 1, p.

449.

6. R. K. Waits. Planar Magnetron Sputtering. [book auth.] J. L. Vossen and W. Kern.

Thin Film Processes. s.l. : Academic Press, 1978, p. 157.

7. S. Sevvana, S. Chennadi, R. K. Lakkaraju, J. Li, D. M. Mihut, and S. L. Rohde.

Rate enhancement in HIPIMS growth using secondary discharge confinement. 48th

156

Annual Technical Conference Proceedings of the Society of Vacuum Coaters. 2005, p.

720.

8. D. J. Christie, F. Tomasel, W. D. Sproul, and D. C. Carter. A novel pulsed supply

with arc handling and leading edge control as enabling technology for high power pulsed

magnetron sputtering (HPPMS). Journal of Vacuum Science and Technology A. 2004,

Vol. 22, 4, p. 1415.

9. V. Kouznetsov, K. Macák, J. M. Schneider, U. Helmersson, and I. Petrov. A novel

pulsed magnetron sputter technique utilizing very high target power densities. Surface

and Coatings Technology. 1999, Vol. 122, p. 290.

10. J. Alami, P. O. Å. Persson, D. Music, J. T. Gudmundsson, J. Bohlmark, and U.

Helmersson. Ion assisted physical vapor deposition for enhanced film properties on

nonflat surfaces. Journal of Vacuum Science and Technology A. 2005, Vol. 23, 2, p. 278.

11. U. Helmersson, M. Lattemann, J. Alami, J. Bohlmark,A.P. Ehiasarian, and J.T.

Gudmundsson. High power impulse magnetron sputtering discharges and thin films

growth: A brief review. 48th Annual Technical Conference Proceedings of the Society of

Vacuum Coaters. 2005, p. 458.

12. U. Helmersson, Z. S. Khan, and J. Alami. Ionized-PVD by pulsed sputtering of Ta

for metallization of high aspect ratio structures in VLSI. Proceedings of the 3rd

International EuroConference on Advanced SemiconductorDevices and Microsystems.

October 2000, pp. 191-195.

157

13. M. Lattemann, A. P. Ehiasarian, J. Bohlmark, P. Å. O. Persson, and U.

Helmersson. Investigation of high power impulse magnetron sputtering pretreated

interfaces for adhesion enhancement of hard coatings on steel. Surface and Coatings

Technology. 2006, Vol. 200, p. 6495.

14. D. V. Mozgrin, I. K. Fetisov, and G. V. Khodachenko. High current low-pressure

quasi-stationary discharge in a magnetic field. Plasma Physics Reports. 1995, Vol. 21, p.

400.

15. J. Musil, J. Leština, J. Vlcek, and T. Tölg. Pulsed dc magnetron discharges for

high-rate sputtering of thin films. Journal of Vacuum Science and Technology A. 2001,

Vol. 19, 2, p. 420.

16. J. Vlcek, P. Kudlacek, K. Burcalova, and J. Musil,. High-power pulsed sputtering

using a magnetron with enhanced plasma confinement. Journal of Vacuum Science and

Technology A. 2007, Vol. 25, 1, p. 42.

17. J. Bohlmark, M. Ostbye, M. Lattemann, H. Ljungcrantz, T. Rosell, and U.

Helmersson. Guiding the deposition flux in an ionized magnetron discharge. Thin Solid

Films. December 5, 2006, Vol. 515, 4, pp. 1928-1931.

18. J. W. Bradley, S. Thompson, and Y. Aranda Gonzalvo. Measurement of the

plasma potential in a magnetron discharge and the prediction of the electron drift speeds.

Plasma Sources Science and Technology. 2001, Vol. 10, p. 490.

158

19. K. Sarakinos, J. Alami, and M. Wuttig. Process characteristics and film properties

upon growth of TiOx films by high power pulse sputtering. Journal of Physics D:

Applied Physics. 2007, Vol. 40, p. 2108.

20. R. Chistyakov. Methods and apparatus for generating strongly-ionized plasmas with

ionizational instabilities. US 2005/0184669 USA, August 25, 2005.

21. G. Lin, Z. Ding, D. Qi, Y. Zhao, N. Wang, and C. Dong. Plasma load characteristic

of pulsed-bias arc ion plating. Journal of Vacuum Science and Technology A. 2003, Vol.

21, 5, p. 1675.

22. M. A. Lieberman, and A. J. Lichtenberg. Principles of Plasma Discharges and

Materials. New York : John Wiley & Sons, 1994.

23. J. A. Thornton. Magnetron sputtering: basic physics and application to cylindrical

magnetrons. Journal of Vacuum Science and Technology. 1978, Vol. 15, p. 171.

24. S. L. Rohde. Unbalanced Magnetron Sputtering. [book auth.] M. Francombe and J.

Vossen. Physics of Thin Films Advances in Research and Development Vol.18: Plasma

Sources for Thin Film Deposition and Etching. New York : Academic Press, 1994.

25. J. H. Boo, M. J. Jung, H. K. Park, K. H. Nam, and J. G. Han. High-rate

deposition of copper thin films usingnewly designed high-power magnetron sputtering

source. Surface and Coatings Technology. 2004, Vols. 188-189, p. 721.

26. A. G. Spencer, and R. P. Howson. Rf Oscillations in dc planar sputtering

magnetrons. Vacuum. 1988, Vol. 38, 6, p. 497.

159

27. E. Martines, M. Zuin, V. Antoni, R. Cavazzana, G. Serianni, M. Spolaore, and

C. Nakashima. Experimental investigation of low-frequency waves propagating in a

direct current planar magnetron plasma. Physics of Plasmas. 2004, Vol. 11, 5, p. 1938.

28. T. E. Sheridan, and J. Goree. Low frequency turbulent transport in magnetron

plasmas. Journal of Vacuum Science and Technology A. 1989, Vol. 7, 3, pp. 1014-1018.

29. T. E. Sheridan, M. J. Goeckner, and J. Goree. Electron and ion transport in

magnetron plasmas. Journal of Vacuum Science and Technology A. 1990, Vol. 8, 3, p.

1623.

30. J. Goree, and T. E. Sheridan. Magnetic field dependence of sputtering magnetron

efficiency. Applied Physics Letters. 1991, Vol. 59, 9, p. 1052.

31. T. E. Sheridan, M. J. Goeckner, and J. Goree. Model of energetic electron

transport in magnetron discharges. Journal of Vacuum Science and Technology A. 1990,

Vol. 8, 1, p. 30.

32. J. E. Miranda, M. J. Goeckner, J. Goree, and T. E. Sheridan. Monte Carlo

simulation of ionization in a magnetron plasma. Journal of Vacuum Science and

Technology A. 1990, Vol. 8, 3, p. 1627.

33. T. E. Sheridan, M. J. Goeckner, and J. Goree. Pressure dependence of ionization

efficiency in sputtering magnetrons. Applied Physics Letters. 1990, Vol. 57, 20, pp. 2080-

2082.

160

34. P. Kudrna, M. Holik, O. Bilyk, O. Marek, A. Behnke, E. Martines, and M.

Tichy. Langmuir probe study of the floating potential fluctuations in the dc cylindrical

magnetron discharge. [ed.] J. Meichsner and D. Loffhagen. Proceeding of the XXVI

International Conference on Phenomena in Ionized Gases. 2003, Vol. 4, p. 157.

35. E. Martines, R. Cavazzana, G. Serianni, M. Spolaore, L. Tramontin, M. Zuin,

and V. Antoni. Electrostatic fluctuations in a direct current magnetron sputtering plasma.

Physics of Plasmas. 2001, Vol. 8, 6, p. 3042.

36. T. A. van der Straaten, N. F. Cramer, I. S. Falconer, and B. W. James. The

cylindrical dc magnetron discharge: I. Particle-in-cell simulation. Journal of Physics D:

Applied Physics. 1998, 31, p. 177.

37. T. Hurtig, N. Brenning, and M. Raadu. The penetration of plasma clouds across

magnetic boundaries:The role of high frequency oscillations. Physics of Plasmas. 2004,

Vol. 11, 7, p. 33.

38. D. Lundin, U. Helmersson, S. Kirkpatrick, S. L. Rohde, and N. Brenning.

Anamalous electron transport in high power impulse magnetron sputtering. Plasma

Sources Science and Technology. 2008, Vol. 17, 2.

39. R. Sobbia, P. K. Browning, and J. W. Bradley. Numerical investigation via three-

dimensional Monte Carlo modeling of sputtering and deposition processes in a direct

current unbalanced magnetron discharge. Journal of Vacuum Science and Technology A.

2008, Vol. 26, 1, p. 103.

161

40. J. E. Greene. Epitaxial crysal growth by sputter deposition: Applications to

semiconductors. Part I. Critical Reviews in Solid State and Materials Science. 1983, Vol.

11, 1, pp. 47-97.

41. R. Glang, and L. I. Maissel, [ed.]. Handbook of Thin Film Technology. New York :

Mcgraw-Hill Book Company, 1970.

42. M. Ohring. The Materials Science of Thin Films. San Diego : Academic Press Inc.,

1992. pp. 104-114.

43. —. The Materials Science of Thin Films. San Diego : Academic Press Inc., 1992. pp.

203-208.

44. —. The Materials Science of Thin Films. San Diego : Academic Press Inc., 1992. pp.

147-198.

45. W. Kern, and J. L. Vossen. Thin Film Processes. San Diego : Academic Press Inc.,

1978. p. 11.

46. A. J. Lichtenberg, and M. A. Lieberman. Principles of Plasma Discharges and

Materials Processing. New York : John Wiley & Sons, Inc., 1994. pp. 451-453.

47. R. Messier, A. P. Giri, and R. A. Roy. Revised structure zone model for thin film

physical structure. Journal of Vacuum Science and Technology A. 1984, Vol. 2, p. 500.

48. M. Ohring. The Materials Science of Thin Films. San Diego : Academic Press Inc.,

1992. pp. 129-131.

162

49. W. Kern, and J. L. Vossen. Thin Film Processes. San Diego : Academic Press, Inc.,

1978. p. 157.

50. —. Thin Film Processes. San Diego : Academic Press, Inc., 1978. p. 27.

51. W.-D. Munz, S. L. Rohde, and W. D. Sproul. [ed.] D. S. Rickerby and A.

Matthews. Advanced Surface Coatings. New York : Chapman and Hall, 1991.

52. S. Berg, H. O. Blom, T. Larsson, and C. Nender. Modeling of reactive sputtering

of compound materials. Journal of Vacuum Science and Technology A. March 1987, Vol.

5, 2, pp. 202-207.

53. B. Chapman. Glow Discharge Processes. New York : John Wiley & Sons, Inc.,

1980.

54. S. L. Rohde, I. Petrov, W. D. Sproul, S. A. Barnett, P. J. Rudnik, and M. E.

Graham. Effects of an unbalanced magnetron in a unique dual-cathode, high rate

reactive sputtering system. Thin Solid Films. 1990, Vols. 193-194, pp. 117-126.

55. Clarke, P. J. Journal of Vacuum Science and Technology. Magnetron dc reactive

sputtering of titanium nitride and indium–tin oxide, 1977, Vol. 14, 1, pp. 141-142.

56. W. Kern, and J. L. Vossen. Thin Film Processes. San Diego : Academic Press, Inc,

1978. pp. 14-18.

163

57. W. D. Sproul, M. E. Graham, M. S. Wong, S. Lopez, D. Li, and R. A. Scholl.

Reactive direct current magnetron sputtering of aluminum oxide coatings. Journal of

Vacuum Science and Technolgoy A. May 1995, Vol. 13, 3, pp. 1188-1191.

58. K. Koski, J. Holsa, and P. Juliet. Voltage controlled reactive sputtering process for

aluminium oxide thin films. Thin Solid Films. August 4, 1998, Vol. 326, 1-2, pp. 189-

193.

59. B. Goranchev, V. Orlinov, V. Tsaneva, and I. Petrov. Direct current reactive

sputtering of aluminium. Thin Solid Films. August 1978, Vol. 52, 3, pp. 365-371.

60. S. R. Kirkpatrick, S. L. Rohde, D. M. Mihut, M. L. Kuruppu, J. R. Swanson III,

D. Thomson, and J. A. Woollam. Process monitoring and control of low temperature

reactively sputtered AlN. Thin Solid Films. 1998, Vol. 332, p. 16.

61. J. M. Schneider, W. D. Sproul, R. W. J. Chia, M.-S. Wong, and A. Matthews.

Very-high-rate reactive sputtering of alumina hard coatings. Surface and Coatings

Technology. November 25, 1997, Vol. 96, 2-3, pp. 262-266.

62. J. M. Schneider, W. D. Sproul, and A. Matthews. Phase formation and mechanical

properties of alumina coatings prepared at substrate temperatures less than 500°C by

ionized and conventional sputtering. Surface and Coatings Technology . October 1997,

Vols. 94-95, pp. 179-183.

164

63. J. P. Lehan, R. B. Sargent, and R. E. Klinger. High-rate aluminum oxide

deposition by MetaMode reactive sputtering. Journal of Vacuum Science and Technology

A. November 1992, Vol. 10, 6, pp. 3401-3406.

64. I. Ivanov, L. Hultman, K. Jarrendahl, P. Martensson, J.-E. Sundgren, B.

Hjorvarsson, and J. E. Greene. Growth of epitaxial AlN(0001) on Si(111) by reactive

magnetron sputter deposition. Journal of Applied Physics. November 1, 1995, Vol. 78, 9,

pp. 5721-5726.

65. W. Otano-Rivera, L. J. Pilione, J. A. Zapien, and R Messier. Cubic boron nitride

thin film deposition by unbalanced magnetron sputtering and dc pulsed substrate biasing.

Journal of Vacuum Science and Technology A. May 1998, Vol. 16, 3, pp. 1331-1335.

66. W. Kern, and J. L. Vossen. Thin Film Processes. San Diego : Academic Press, Inc.,

1978. p. 131.

67. U. Helmersson, Z. S. Khan, and J. Alami. Ionized-PVD by pulsed sputtering of Ta

for metallization of high aspect ratio structures in VLSI. Proceedings of the 3rd

International EuroConference on Advanced Semiconductor Devices and Microsystems.

October 2000, pp. 191-195.

68. S. Chennadi, D. J. Christie, S. Sevvana, R. K. Lakkaraju, J. Li, D. M. Mihut,

and S. L. Rohde. HIPIMS deposition of copper films: Correlation of experiments to

model predictions. 48th Annual Technical Conference Proceedings of the Society of

Vacuum Coaters. 2005, p. 474.

165

69. N. Saviddes, and B. Window. Diamond-like amorphous carbon film prepared by

magnetron sputtering. Journal of Vacuum Science and Technology A. November 1985,

Vol. 3, 6, pp. 2386-2390.

70. D. J. Christie, W. D. Sproul, D. C. Carter, and F. Tomasel. A novel pulsed supply

wiith arc handling and leading edge control as enabling technology for High Power

Pulsed Magnetron Sputtering (HPPMS). Society of Vacuum Coaters 47th Annual

Technical Conference Proceedings. 2004, pp. 113-118.

71. J. Bohlmark, J. Alami, C. Christou, A. P. Ehiasarian, and U. Helmersson.

Ionization of sputtered metals in high power pulsed magnetron sputtering. Journal of

Vacuum Science and Technology A . Jan/Feb 2005, Vol. 23, 1, pp. 18-22.

72. U. Helmersson, M. Lattemann, J. Bohlmark, A. P. Ehiasarian, and J. T.

Gudmundsson. Ionized physical vapor deposition (IPVD): A review of technology and

applications. Thin Solid Films. 2006, Vol. 513, pp. 1-24.

73. K. Macak, V. Kouznetsov, J. Schneider, and U. Helmersson. Ionized sputter

deposition using an extremely high plasma density pulsed magnetron discharge. Journal

of Vacuum Science and Technology A. July/August 2000, Vol. 18, 4, p. 1533.

74. J. A. Thornton, and A. S. Penfold. Cylindrical Magnetron Sputtering. [book auth.]

J. L. Vossen and W. Kern. Thin Film Processes. New York : Academic Press, 1978, p.

76.

75. F. F. Chen. Introduction to Plasma Physics. New York : Plenum Press, 1974.

166

76. D. D. Blackwell, D. N. Walker, S. J. Messer, and W. E. Amatucci. Characteristics

of the plasma impedance probe with constant bias. Physics of Plasmas. 2005, Vol. 12, 9.

77. R. T. Hilbish, R. M. Montgomery, and R. A. Holmes. Frequency conversion in the

sheath capacitance of a glow discharge plasma. Journal of Applied Physics. 1968, Vol.

39, 12, p. 5782.

78. S. M. Rossnagel, and H. R. Kaufman. Charge transport in magnetrons. Journal of

Vacuum Science and Technology A. 1987, Vol. 5, 4, p. 2276.

79. J. Bohlmark, U. Helmersson, M. VanZeeland, I. Axnas, J. Alami, and N.

Brenning. Measurement of the magnetic field change in a pulsed high current magnetron

discharge. Plasma Sources Science and Technology. 2004, Vol. 13, 4, p. 654.

80. J. D. Cobine. Gaseous Conductors: Theory and Engineering Applications. New

York : Dover, 1958.

81. S. R. Kirkpatrick, D. Lundin, U. Helmersson, and S. L. Rohde. Magnetized

magnetron plasma modeling. 50th Annual Technical Conference Proceedings. 2007, p.

135.

82. D. A. Glocker, M. M. Romach, D. J. Christie, and W. D. Sproul. High power

pulsed reactive sputtering of zirconium oxide and tantalum oxide. 47th Annual Technical

Conference Proceedings. April 2004, p. 183.

83. B. M. DeKoven, P. R. Ward, R. E. Weiss, D. J. Christie, R. A. Scholl, W. D.

Sproul, F. Tomasel, and A. Anders. Carbon thin film deposition using high power

167

pulsed magnetron sputtering. 46th Annual Technical Conference Proceedings. 2003, p.

158.

84. J. A. Thorton, and A. S. Penfold. Cylindrical Magnetron Sputtering. [book auth.]

W. Kern and J. L. Vossen. Thin Film Processes. New York : Academic Press, 1978, p.

76.

85. A. P. Ehiasarian, R. New, W.-D. Munz, L. Hultman, U. Helmersson, and V.

Kouznetsov. Influence of high power densities on the composition of pulsed magnetron

plasmas. Vacuum. 2004, Vol. 65, 2, pp. 147-154.

86. S. M. Rossnagel. Magnetron plasma diagnostic and processing implications. Journal

of Vacuum Science and Technology A. May/June 1988, Vol. 6, 3, pp. 1821-1826.

87. J. Bohlmark, M. Lattemann, J. T. Gudmundsson, A. P. Ehiasarian, Y. A.

Gonzalvo, N. Brenning, and U. Helmersson. The ion energy distributions and ion flux

composition from a high power impulse magnetron sputtering discharge. Thin Solid

Films. 2006, Vol. 515, p. 1522.

88. J. T. Gudmnundsson, J. Alami, and U. Helmersson. Spatial and temporal behavior

of the plasma parameters in a pulsed magnetron discharge. Surface and Coatings

Technology. 2002, Vol. 161, p. 249.

89. J. Bohlmark, J. T. Gudmundsson, J. Alami, M. Lattemann, and U. Helmersson.

Spatial electron density distribution in a high-power pulsed magnetron discharge. IEEE

Transactions on Plasma Science. 2005, Vol. 33, 2, p. 346.

168

90. M. A. Lieberman. Model of plasma immersion ion implantation. Journal of Applied

Physics. October 1989, Vol. 66, 7, pp. 2926-2929.

91. J. T. Scheuer, M. Shamim, and J. R. Conrad. Model of plasma source ion

implantation in planar, cylindrical, and spherical geometries. Journal of Applied Physics.

1990, Vol. 67, 3, p. 1241.

92. A. Anders. Physics of plasma-based ion implantation & deposition (PBIID) and high

power impulse magnetron sputtering (HIPIMS): A comparison. Physica status solidi. A,

Applications and materials science. 2008, Vol. 205, 4, pp. 965-970.

93. M. M. Widner, I. Alexeff, W. D. Jones, and K. E. Lonngren. Ion acoustic wave

excitation and ion sheath evolution. Physics of Fluids. 1970, Vol. 13, 10, p. 2352.

94. Yu. P. Bliokh, J. Felsteiner, and Ya. Z. Slutsker. Existence and stability of the

plasma sheath resonance near the ion plasma frequency. Europhysics Letters. 1999, Vol.

46, 6, p. 735.

95. D. Arbel, Z. Bar-Lev, J. Felsteiner, A. Rosenburg, and Ya. Z. Slutsker.

Collisionless instablility of the cathode sheath in a hollow-cathode discharge. Physical

Review Letters. November 1, 1993, Vol. 71, 18, pp. 2919-2922.

96. B. P. Pandey, and S. Roy. An explanation of the sheath instability. Physics of

Plasmas. January 2003, Vol. 10, 1.

169

97. N. Hershkowitz, E. Ko, W. Xu, and A. M. A. Hala. Presheath environment in

weakly ionized single and multipsecies plasmas. IEEE Transactions on Plasma Science.

April 2005, Vol. 33, 2, pp. 631-636.

98. R. N. Franklin. The plasma-sheath and its stability in a quiescent plasma containing

two species of positive ion. [ed.] Institute of Physics Publishing. Journal of Physics D:

Applied Physics. 2003, Vol. 36, p. 1806.

99. M. M. Widner, and T. P. Wright. Laminar interaction of counterstreaming

magnetized plasmas. Physical Review Letters. 1972, Vol. 28, 18, p. 1179.

100. Z. J. Radzimski, and W. M. Posadowski. Self sputtering with dc magnetron

source: Target material consideration. 37th Annual Technical Conference Proceedings.

1994, pp. 389-393.

101. D. Vender, G. M. W. Kroesen, and F. J. de Hoog. Signatures of the Bohm and

sheath velocities in minority-light-ion energy distributions. Physical Review E. 1995,

Vol. 51, 4, pp. 3480-3483.

102. D. J. Christie, F. Tomasel, W. D. Sproul, and D. C. Carter. Power supply with

arc handling for high peak power magnetron sputtering. Journal of Vacuum Science and

Technology A. 2004, Vol. 22, 4, p. 1415.

103. J. A. Thornton. Influence of substrate temperature and deposition rate on structure

of thick sputtered Cu coatings. Journal of Vacuum Science and Technology. 1975, Vol.

12, 4, p. 830.

170

104. V. Kouznetsov, K. Macak, J. M. Schneider, U. Helmersson, and I. Petrov. A

novel pulsed magnetron sputter technique utilizing very high target power densities.

Surface and Coatings Technology. 1999, Vol. 122, p. 290.

171

Appendix A Current and Voltage Curves vs. time for select

elemental Targets at UNL

A.1 Current and voltage vs. time curves for copper

Copper run 3mTorr, no inductor

0.000 0.005 0.010 0.015 0.020

-800

-600

-400

-200

0

200

Targ

et V

olta

ge

tim e

0.000 0.005 0.010 0.015 0.020-10

-8

-6

-4

-2

0

Targ

et C

urre

nt

V767

172

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-10

-8

-6

-4

-2

0

Targ

et C

urre

nt

V827

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-1200

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-22-20-18-16-14-12-10

-8-6-4-202

Targ

et C

urre

nt

1199V

173

0.000 0.005 0.010 0.015 0.020

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.005 0.010 0.015 0.020-22-20-18-16-14-12-10

-8-6-4-202

Targ

et C

urre

nt

1015V

0.000 0.005 0.010 0.015 0.020

-1200

-1000-800-600

-400-200

0200

Targ

et V

olta

ge

time

0.000 0.005 0.010 0.015 0.020

-22-20-18-16-14-12-10

-8-6-4-202

Targ

et C

urre

nt

1151V

174

0.0000 0.0005 0.0010 0.0015 0.0020-1200

-1000

-800

-600

-400

-200

0

200

Targ

et V

olta

ge

time

0.0000 0.0005 0.0010 0.0015 0.0020

-20-18-16-14-12-10

-8-6-4-202

Targ

et C

urre

nt

1107V

0.0000 0.0005 0.0010 0.0015 0.0020-1200

-1000

-800

-600

-400

-200

0

200

Targ

et V

olta

ge

time

0.0000 0.0005 0.0010 0.0015 0.0020-20-18-16-14-12-10

-8-6-4-202

Targ

et C

urre

nt

1283

175

0.0001 0.0002 0.0003 0.0004 0.0005-1200

-1000

-800

-600

-400

-200

0

time

1.0x10-4 2.0x10-4 3.0x10-4 4.0x10-4-20

-15

-10

-5

0

Targ

et C

urre

nt

1283V

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010-1400

-1200

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010-14-12-10

-8-6-4-202

Targ

et C

urre

nt

1303V

176

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-1400-1200-1000

-800-600-400-200

0200

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-100

-80

-60

-40

-20

0

20

Targ

et C

urre

nt

0.00015 0.00020 0.00025 0.00030 0.00035-1400-1200-1000

-800-600-400-200

0200

time

0.00015 0.00020 0.00025 0.00030 0.00035-100

-80

-60

-40

-20

0

20

Targ

et C

urre

nt

1350 V Arcing data

177

A.2 Current and Voltage Curves for titanium 3mTorr titanium no inductor

0.000 0.002 0.004 0.006 0.008 0.010

-400

-300

-200

-100

0

Targ

et V

olta

ge

time

0.000 0.002 0.004 0.006 0.008 0.010

-0.04

-0.03

-0.02

-0.01

0.00

0.01Ta

rget

Cur

rent

435V

0.000 0.002 0.004 0.006 0.008 0.010

-400

-200

0

Targ

et V

olta

ge

tim e

0.000 0.002 0.004 0.006 0.008 0.010

-0.03

-0.02

-0.01

0.00

Targ

et C

urre

nt

465V

178

0.000 0.002 0.004 0.006 0.008 0.010

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.002 0.004 0.006 0.008 0.010-0.06

-0.04

-0.02

0.00

Targ

et C

urre

nt

475V

0.000 0.002 0.004 0.006 0.008 0.010

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.002 0.004 0.006 0.008 0.010

-0.10

-0.05

0.00

Targ

et C

urre

nt

485V

179

0.000 0.002 0.004 0.006 0.008 0.010-600

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.002 0.004 0.006 0.008 0.010

-0.3

-0.2

-0.1

0.0

Targ

et C

urre

nt

538V

0.000 0.002 0.004 0.006 0.008 0.010-600

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.002 0.004 0.006 0.008 0.010

-0.20

-0.15

-0.10

-0.05

0.00

Targ

et C

urre

nt

542V

180

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-0.20

-0.15

-0.10

-0.05

0.00

Targ

et C

urre

nt

550V

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-0.4

-0.3

-0.2

-0.1

0.0

Targ

et C

urre

nt

555V

181

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

636V

0.0000 0.0005 0.0010 0.0015 0.0020

-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0005 0.0010 0.0015 0.0020

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

665V

182

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

810V

0.000 0.001 0.002 0.003 0.004

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.001 0.002 0.003 0.004

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1060V

183

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-1200

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1135V

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-1000

-500

0

Targ

et V

olta

ge

tim e

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-1.0

-0.5

0.0

Targ

et C

urre

nt

1170V

184

0.000 0.001 0.002 0.003 0.004

-1200

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.001 0.002 0.003 0.004-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1245V

0.000 0.001 0.002 0.003 0.004-1200

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.000 0.001 0.002 0.003 0.004

-0.8

-0.6

-0.4

-0.2

Targ

et C

urre

nt

1285V

185

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-1000

-500

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1330V 3mTorr titanium Coil at 5 Amps

0.000 0.005 0.010-700-600-500-400-300-200-100

0100

Targ

et V

olta

ge

tim e

0.000 0.002 0.004 0.006 0.008 0.010-0.35-0.30-0.25-0.20-0.15-0.10-0.050.000.05

Targ

et C

urre

nt

618V

186

0.000 0.001 0.002-700-600-500-400-300-200-100

0100

Targ

et V

olta

ge

tim e

0.0000 0.0005 0.0010 0.0015 0.0020

-0.30

-0.25-0.20-0.15

-0.10-0.05

0.000.05

Targ

et C

urre

nt

632V

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-800-700-600-500-400-300-200-100

0

Targ

et V

olta

ge

tim e

0.0000 0.0002 0.0004 0.0006 0.0008 0.0010

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

788V

187

0.000 0.002 0.004 0.006 0.008 0.010-800-700-600-500-400-300-200-100

0100

Targ

et V

olta

ge

tim e

0.000 0.002 0.004 0.006 0.008 0.010

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

790V

0.0000 0.0005 0.0010 0.0015 0.0020-900-800-700-600-500-400-300-200-100

0100

Targ

et V

olta

ge

tim e

0.0000 0.0005 0.0010 0.0015 0.0020

-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

880V

188

0.00000 0.00005 0.00010 0.00015 0.00020

-1000

-500

0

Targ

et V

olta

ge

time

0.00000 0.00005 0.00010 0.00015 0.00020

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1196V

0.000 0.002 0.004 0.006 0.008 0.010-1400-1200-1000

-800-600-400-200

0200

Targ

et V

olta

ge

time

0.000 0.002 0.004 0.006 0.008 0.010

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1268V

189

0.0000 0.0005 0.0010 0.0015 0.0020-1400-1200-1000

-800-600-400-200

0200

Targ

et V

olta

ge

time

0.0000 0.0005 0.0010 0.0015 0.0020

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1268V zoom

0.000 0.001 0.002 0.003 0.004

-1200

-1000-800-600

-400-200

0200

Targ

et V

olta

ge

time

0.000 0.001 0.002 0.003 0.004-0.45-0.40-0.35-0.30-0.25-0.20-0.15-0.10-0.05

Targ

et C

urre

nt

1272V

190

0.000 0.001 0.002 0.003 0.004

-1400-1200-1000

-800-600-400-200

0200

Targ

et V

olta

ge

time

0.000 0.001 0.002 0.003 0.004-0.35-0.30-0.25-0.20-0.15-0.10-0.050.000.05

Targ

et C

urre

nt

1412V

0.0000 0.0005 0.0010 0.0015 0.0020-1400-1200-1000

-800-600-400-200

0200

Targ

et V

olta

ge

time

0.0000 0.0005 0.0010 0.0015 0.0020

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1448

191

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010-1600-1400

-1200-1000

-800-600-400

-200

Targ

et V

olta

ge

time

0.00000 0.00002 0.00004 0.00006 0.00008 0.00010

-0.4

-0.2

0.0

Targ

et C

urre

nt

1464V (zoom) 3mTorr Titanium no coil current

0.000 0.005 0.010

-400

-200

0

Targ

et V

olta

ge

tim e

0.000 0.005 0.010

-0.08

-0.06

-0.04

-0.02

0.00

Targ

et C

urre

nt

436V

192

0.0000 0.0005 0.0010

-400

-200

0

Targ

et V

olta

ge

tim e

0.0000 0.0005 0.0010

-0.15

-0.10

-0.05

0.00

0.05

Targ

et C

urre

nt

482V

0.0000 0.0005 0.0010

-600

-400

-200

0

Targ

et V

olta

ge

tim e

0.0000 0.0005 0.0010

-0.6

-0.5-0.4-0.3

-0.2-0.1

0.00.1

Targ

et C

urre

nt

630V

193

0.0000 0.0005 0.0010

-600

-400

-200

0

Targ

et V

olta

ge

tim e

0.0000 0.0005 0.0010

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0Ta

rget

Cur

rent

634V

0.0000 0.0005 0.0010

-600

-400

-200

0

Targ

et V

olta

ge

tim e

0.0000 0.0005 0.0010

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

Targ

et C

urre

nt

634V take 2 showing variation

194

0.0000 0.0005 0.0010

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.0000 0.0005 0.0010-1.0

-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

758V

0.0000 0.0005 0.0010-1000

-500

0

Targ

et V

olta

ge

time

0.0000 0.0005 0.0010

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Targ

et C

urre

nt

900V

195

0.000 0.005 0.010

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.005 0.010

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1080V

0.000 0.005 0.010

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.005 0.010

-0.6

-0.5-0.4-0.3

-0.2-0.1

0.00.1

Targ

et C

urre

nt

1144V

196

0.0000 0.0002 0.0004

-1000

-500

0

Targ

et V

olta

ge

time

0.0000 0.0002 0.0004

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1276V

0.000 0.001 0.002

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.001 0.002-0.8

-0.6

-0.4

-0.2

0.0

Targ

et C

urre

nt

1288V

197

0.000 0.005 0.010

-1500

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.005 0.010

-0.5

-0.4

-0.3

-0.2

-0.1

Targ

et C

urre

nt

1344

0.0006 0.0008 0.0010 0.0012 0.0014

-1000

-500

0

Targ

et V

olta

ge

time

0.0006 0.0008 0.0010 0.0012 0.0014

-0.5

-0.4

-0.3

-0.2

-0.1

Targ

et C

urre

nt

1344V

198

0.000 0.002 0.004

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.002 0.004

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

Targ

et C

urre

nt

1488V

0.000 0.005 0.010

-1500

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.005 0.010

-0.5

-0.4

-0.3

-0.2

-0.1

Targ

et C

urre

nt

1500V

199

0.000 0.002 0.004

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.002 0.004

-0.5

-0.4

-0.3

-0.2

-0.1

Targ

et C

urre

nt

1532V

0.000 0.001 0.002

-1000

-500

0

Targ

et V

olta

ge

time

0.000 0.001 0.002

-0.5

-0.4

-0.3

-0.2

-0.1

Targ

et C

urre

nt

1556V

200

A.3 Current and Voltage Curves for silver Silver 5mt coil off (silver failed to ignite at 3mtorr)

0.00 0.01 0.02 0.03 0.04

-400

-300

-200

-100

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04

-0.2

0.0

0.2

0.4

Targ

et C

urre

nt

360V

0.00 0.01 0.02 0.03 0.04

-400

-300

-200

-100

0

100

Targ

et V

olta

ge

tim e

0.00 0.01 0.02 0.03 0.04

-0.15

-0.10

-0.05

0.00

0.05

0.10

Targ

et C

urre

nt

400V

201

0.00 0.01 0.02 0.03 0.04-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04

-0.5

0.0

0.5

Targ

et C

urre

nt

515

0.00 0.01 0.02 0.03 0.04-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04

-0.6

-0.4

-0.2

0.0

0.2

Targ

et C

urre

nt

525

202

0.00 0.01 0.02 0.03 0.04-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04-3

-2

-1

0Ta

rget

Cur

rent

700V

0.00 0.01 0.02

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02

-2

-1

0

Targ

et C

urre

nt

820

203

0.00 0.01 0.02 0.03 0.04

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04-4

-2

0Ta

rget

Cur

rent

870V

0.00 0.01 0.02 0.03 0.04-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04

-3

-2

-1

0

Targ

et C

urre

nt

950V

204

0.00 0.01 0.02 0.03 0.04

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04

-1

0

1

Targ

et C

urre

nt

-975V

0.00 0.01 0.02 0.03 0.04-1200

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04

-1.0

-0.5

0.0

0.5

Targ

et C

urre

nt

1100V

205

0.00 0.01 0.02 0.03 0.04

-1000

-500

0

Targ

et V

olta

ge

time

0.00 0.01 0.02 0.03 0.04-3.0

-2.5

-2.0

-1.5

Targ

et C

urre

nt

1160V Silver 3mTorr coil on at 5 amps

0.000 0.005 0.010 0.015 0.020

-500

-400

-300

-200

-100

0

100

Targ

et V

olta

ge

T ime

0.000 0.005 0.010 0.015 0.020

-1.0

-0.5

0.0

Targ

et C

urre

nt

515V

206

0.000 0.005 0.010 0.015 0.020-600

-500

-400

-300

-200

-100

0

100

Targ

et V

olta

ge

tim e

0.000 0.005 0.010 0.015 0.020

-0.5-0.4-0.3-0.2-0.10.00.10.20.30.4

Targ

et C

urre

nt

560V

0.000 0.005 0.010 0.015 0.020

-600

-400

-200

0

Targ

et V

olta

ge

T ime

0.000 0.005 0.010 0.015 0.020-2

-1

0

1

Targ

et C

urre

nt

680V

207

0.000 0.005 0.010 0.015 0.020

-800

-600

-400

-200

0

Targ

et V

olta

ge

T ime

0.000 0.005 0.010 0.015 0.020

-1.0

-0.5

0.0

0.5

Targ

et C

urre

nt

775V

0.000 0.005 0.010 0.015 0.020

-800

-600

-400

-200

0

Targ

et V

olta

ge

T ime

0.000 0.005 0.010 0.015 0.020

-1.5

-1.0

-0.5

Targ

et C

urre

nt

800V

208

-0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045

-1000

-800

-600

-400

-200

0

Targ

et V

olta

ge

Time

-0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045

-1.5

-1.0

-0.5

Targ

et C

urre

nt

985V

209

Appendix B Current and Voltage characteristic curves for

Aluminum and Chromium at a range of pressures from LIU

system

B.1 Current and Voltage Curves for aluminum 22.5mTorr

0.00000 0.00008 0.00016

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

Cur

rent

(Am

ps)

614 V

210

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-700

-600

-500-400

-300

-200-100

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-10

010203040506070

Cur

rent

(Am

ps)

670 V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-800-700-600-500-400-300-200-100

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

102030405060708090

Cur

rent

(Am

ps)

718V

211

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-900-800-700-600-500-400-300-200-100

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-20

020

40

6080

100

120

Cur

rent

(Am

ps)

822V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

tim e (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-40-20

020406080

100120140160

Cur

rent

(Am

ps)

832V

212

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-50

0

50

100

150

200

Cur

rent

(Am

ps)

960V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-50

0

50

100

150

200

Cur

rent

(Am

ps)

1048V

213

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100-50

050

100150200

250

Cur

rent

(Am

ps)

1056V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1200

-1000

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100-50

050

100150200250300

Cur

rent

(Am

ps)

1064V

214

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-50

0

50100

150

200250

300

Cur

rent

(Am

ps)

1152V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

tim e (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-500

50100150200250300

Cur

rent

(Am

ps)

1176

215

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-100

-500

50100150200250300350

Cur

rent

(Am

ps)

1300V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-200

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1400V

216

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-100

0

100

200

300

400

Cur

rent

(Am

ps)

1540V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1460V

217

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-200

-100

0

100

200

300

400C

urre

nt (A

mps

)

1300V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1340

218

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1420V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1440V

219

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-300-200-100

0100200300400500

Cur

rent

(Am

ps)

1440V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2000

-1500

-1000

-500

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-300-200-100

0100200300400500600

Cur

rent

(Am

ps)

1820V

220

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100200

300

400500

600

Cur

rent

(Am

ps)

1520V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200-100

0100200300400500600

Cur

rent

(Am

ps)

1560V

221

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1000

100200300400500600

Cur

rent

(Am

ps)

1620V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

0

200

400

600

Cur

rent

(Am

ps)

1720V

222

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

0

200

400

600

Cur

rent

(Am

ps)

1660V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1000

100200300400500600700

Cur

rent

(Am

ps)

1700V

223

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2000

-1500

-1000

-500

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

0

200

400

600

800

Cur

rent

(Am

ps)

1800V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2000-1800-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1000

100200300400500600700

Cur

rent

(Am

ps)

1760V

224

15mtorr

0.00000 0.00008 0.00016-800-700-600-500-400-300-200-100

00.00000 0.00008 0.00016

0

20

40

60V

olta

ge (V

olts

)

time (s)

Cur

rent

(Am

ps)

574V

0.00000 0.00008 0.00016-700

-600

-500

-400

-300

-200

-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

80

Cur

rent

(Am

ps)

650V

225

0.00000 0.00008 0.00016-800-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-20

0

20

40

60

80

Cur

rent

(Am

ps)

738V

0.00000 0.00008 0.00016-900-800-700-600-500-400-300-200-100

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016-20

0

20

40

60

80

100

Cur

rent

(Am

ps)

822V

226

0.00000 0.00008 0.00016-1000

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-40-20

020406080

100120140

Cur

rent

(Am

ps)

900V

0.00000 0.00008 0.00016-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-40-20

020406080

100120140160

Cur

rent

(Am

ps)

884V

227

0.00000 0.00008 0.00016

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-50

0

50

100

150

200

Cur

rent

(Am

ps)

1148V

0.00000 0.00008 0.00016-1400

-1200-1000

-800-600

-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100-50

050

100150200250300

Cur

rent

(Am

ps)

1276V

228

0.00000 0.00008 0.00016

-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

100

200

300

Cur

rent

(Am

ps)

1372V

0.00000 0.00008 0.00016-1800-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-200

-1000

100200

300400

500

Cur

rent

(Am

ps)

1660V

229

0.00000 0.00008 0.00016-2000

-1500

-1000

-500

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1820V

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1900V

230

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-200-100

0100200300400500600

Cur

rent

(Am

ps)

2080V 10 mTorr aluminum

0.00000 0.00008 0.00016

-700

-600-500

-400-300

-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-20

0

20

40

60

Cur

rent

(Am

ps)

680V

231

0.00000 0.00008 0.00016-800-700-600-500-400-300-200-100

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-20

0

20

40

60C

urre

nt (A

mps

)

732V

0.00000 0.00008 0.00016-900-800-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-20

0

20

40

60

80

Cur

rent

(Am

ps)

816V

232

0.00000 0.00008 0.00016-1000

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016-40

-20

0

20

40

60

80

100

Cur

rent

(Am

ps)

876V

0.00000 0.00008 0.00016

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-40-20

020406080

100120

Cur

rent

(Am

ps)

964V

233

0.00000 0.00008 0.00016

-1200

-1000

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1124V

0.00000 0.00008 0.00016

-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1372V

234

0.00000 0.00008 0.00016-1600-1400-1200-1000-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-100-50

050

100150200250300350

Cur

rent

(Am

ps)

1476V

0.00000 0.00008 0.00016

-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-100

0

100

200

300

400

Cur

rent

(Am

ps)

235

1564V

0.00000 0.00008 0.00016-1400

-1200-1000

-800-600

-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-200

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1620V

0.00000 0.00008 0.00016-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1668V

236

0.00000 0.00008 0.00016

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1720V

0.00000 0.00008 0.00016-2000-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1780V

237

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1920V

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-200-100

0100200300400500600

Cur

rent

(Am

ps)

2050V

238

0.00000 0.00008 0.00016-2500

-2000

-1500

-1000

-500

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016-200-100

0100200300400500600

Cur

rent

(Am

ps)

2090V

0.00000 0.00008 0.00016-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-200-100

0100200300400500600

Cur

rent

(Am

ps)

2150V

239

5mTorr aluminum

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-10

0

10

20

30

40

Cur

rent

(Am

ps)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-800-700-600-500-400-300-200-100

0

Volta

ge (V

otls

)

time (s) 732V

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

-10

0

10

20

30

40

50

Cur

rent

(Am

ps)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

-800-700-600-500-400-300-200-100

0

Vol

tage

(Vot

ls)

time (s) 754V

240

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

0

100

Cur

rent

(Am

ps)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

-800-700-600-500-400-300-200-100

0

Volta

ge (V

otls

)

time (s) 780V

0.0000 0.0001 0.0002-100

0

100

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002

-1000

-800

-600

-400

-200

0

Vol

tage

(Vot

ls)

time (s) 988V

241

0.0000 0.0001 0.0002

0

100C

urre

nt (A

mps

)

0.0000 0.0001 0.0002

-1200

-1000

-800

-600

-400

-200

0

Volta

ge (V

otls

)

time (s) 1132V

0.0000 0.0001 0.0002

0

100

200

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vot

ls)

time (s) 1204V

242

0.0000 0.0001 0.0002-100

0

100

200

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1400

-1200-1000

-800-600

-400-200

0

Vol

tage

(Vot

ls)

time (s) 1244V

0.0000 0.0001 0.0002

-100

0

100

200

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1400

-1200-1000

-800-600

-400-200

0

Volta

ge (V

otls

)

time (s) 1236

243

0.0000 0.0001 0.0002-100

0

100

200C

urre

nt (A

mps

)

0.0000 0.0001 0.0002

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vot

ls)

time (s) 1180V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-100

-500

50100150200250300

Vol

tage

(Vol

ts)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1600-1400-1200-1000

-800-600-400-200

0

Cur

rent

(Am

ps)

time (s) 1460

244

0.0000 0.0001 0.0002-100

0

100

200

300

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vot

ls)

time (s) 1240

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-200

-100

0

100

200

300

Vol

tage

(Vol

ts)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1800-1600-1400-1200-1000

-800-600-400-200

0200

Cur

rent

(Am

ps)

time (s) 1620V

245

0.0000 0.0001 0.0002-200

-100

0

100

200

300

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1400

-1200-1000

-800-600

-400-200

0

Vol

tage

(Vot

ls)

time (s)

1320V

0.0000 0.0001 0.0002-200

-100

0

100

200

300

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s)

1660

246

0.0000 0.0001 0.0002-200

-100

0

100

200

300

400

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002

-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s) 1360V

0.0000 0.0001 0.0002-200

-100

0

100

200

300

400

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s) 1500V

247

0.0000 0.0001 0.0002-300

-200-100

0100

200300

400C

urre

nt (A

mps

)

0.0000 0.0001 0.0002-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s) 1680

0.0000 0.0001 0.0002

-200

-1000

100200

300400

500

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s) 1530V

248

0.0000 0.0001 0.0002

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s) 1610

0.0000 0.0001 0.0002-300-200-100

0100200300400500

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002

-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s) 1730V

249

0.0000 0.0001 0.0002-200

-1000

100200

300400

500

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1800-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

otls

)

time (s)

1610 V

0.0000 0.0001 0.0002

-200-100

0100200300400500

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vot

ls)

time (s) 1730V

250

0.0000 0.0001 0.0002

-100

0100

200300

400500

600

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-1800-1600-1400-1200-1000-800-600-400-200

0200

Volta

ge (V

otls

)

time (s) 1610V

0.0000 0.0001 0.0002-200-100

0100200300400500600

Cur

rent

(Am

ps)

0.0000 0.0001 0.0002-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vot

ls)

time (s) 2170V

251

B.2 Current and Voltage curves over a range of pressures for chromium 5 mtorr chromium target

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-700

-600-500

-400

-300-200

-100

0

Vol

tage

(Vol

ts)

time (s)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.000506

12182430364248

Cur

rent

(Am

ps)

600V

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-606

121824303642485460

Cur

rent

(Am

ps)

646V

252

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

-800-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.000506

12182430364248546066

Cur

rent

(Am

ps)

690V

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

-800-700-600-500-400-300-200-100

0

Volta

ge (V

olts

)

time (s)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-40

-20

0

20

40

60

80

Cur

rent

(Am

ps)

744V

253

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005

01020304050607080

Cur

rent

(Am

ps)

792V

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.0001 0.0000 0.0001 0.0002 0.0003 0.0004 0.0005-40

-20

0

20

40

60

80

100

Cur

rent

(Am

ps)

840V

254

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1200

-1000

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

20406080

100120

Cur

rent

(Am

ps)

880V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-40-20

020406080

100120140160

Cur

rent

(Am

ps)

936V

255

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1400

-1200-1000

-800

-600-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-50

0

50

100

150

200

Cur

rent

(Am

ps)

976V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-50

0

50

100

150

200

Cur

rent

(Am

ps)

1024V

256

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

-50

050

100

150200

250

Cur

rent

(Am

ps)

1072V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1120V

257

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1400

-1200-1000

-800

-600-400

-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-150-100

-500

50100150200250300

Cur

rent

(Am

ps)

1160V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-100

-500

50100150200250300

Cur

rent

(Am

ps)

1192V

258

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-100

-500

50100150200250300

Cur

rent

(Am

ps)

1224V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1280V

259

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1300V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1600-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1340V

260

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1380V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-2000

-1500

-1000

-500

0

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1400V

261

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1440V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1460V

262

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

-100

0100

200

300400

500

Cur

rent

(Am

ps)

1500V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200

-100

0100

200

300400

500

Cur

rent

(Am

ps)

1520V

263

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1540V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1580V

264

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1600V

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-200-100

0100200300400500

Cur

rent

(Am

ps)

1620V

265

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

-0.00005 0.00000 0.00005 0.00010 0.00015 0.00020

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

1640V 10mTorr Chromium target

0.00000 0.00008 0.00016-700

-600-500

-400-300

-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

Cur

rent

(Am

ps)

646V

266

0.00000 0.00008 0.00016

-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

Cur

rent

(Am

ps)

662V

0.00000 0.00008 0.00016

-800-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

Cur

rent

(Am

ps)

772V

267

0.00000 0.00008 0.00016

-800-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-40

-20

0

20

40

60

80

Cur

rent

(Am

ps)

784V

0.00000 0.00008 0.00016-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

80

Cur

rent

(Am

ps)

912V

268

0.00000 0.00008 0.00016-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-40

-20

0

20

40

60

80

100

Cur

rent

(Am

ps)

880V

0.00000 0.00008 0.00016-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-200

20406080

100120

Cur

rent

(Am

ps)

1032V

269

0.00000 0.00008 0.00016

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-40-20

020406080

100120140160

Cur

rent

(Am

ps)

1176V

0.00000 0.00008 0.00016-1400

-1200-1000

-800-600

-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-40-20

020406080

100120140160180

Cur

rent

(Am

ps)

1264V

270

0.00000 0.00008 0.00016

-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

Cur

rent

(Am

ps)

1376V

0 00000 0 00008 0 00016-1600-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

0.00000 0.00008 0.00016

-100

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1464V

271

0.00000 0.00008 0.00016

-1600-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1536V

0.00000 0.00008 0.00016-1400

-1200-1000

-800-600

-400-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016-150-100

-500

50100150200250300

Cur

rent

(Am

ps)

1368

272

0.00000 0.00008 0.00016-1600-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1416V

0.00000 0.00008 0.00016

-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

Cur

rent

(Am

ps)

1500V

273

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

Cur

rent

(Am

ps)

2040V

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

Cur

rent

(Am

ps)

2080V

274

0.00000 0.00008 0.00016

-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

2340V 15mTorr Aluminum

0.00000 0.00008 0.00016-700

-600

-500

-400

-300

-200

-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

Cur

rent

(Am

ps)

624V

275

0.00000 0.00008 0.00016-700

-600

-500

-400

-300

-200

-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

0

20

40

60

Cur

rent

(Am

ps)

648V

0.00000 0.00008 0.00016-800-700-600-500-400-300-200-100

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-20

0

20

40

60

80

Cur

rent

(Am

ps)

704V

276

0.00000 0.00008 0.00016

-800-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-20

0

20

40

60

80

100

Cur

rent

(Am

ps)

776V

0.00000 0.00008 0.00016

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-60-40-20

020406080

100120

Cur

rent

(Am

ps)

832V

277

0.00000 0.00008 0.00016-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-80-60-40-20

020406080

100120140160

Cur

rent

(Am

ps)

920V

0.00000 0.00008 0.00016-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-200

20406080

100120140160

Cur

rent

(Am

ps)

1032V

278

0.00000 0.00008 0.00016

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-40-20

020406080

100120140160180200

Cur

rent

(Am

ps)

980V

0.00000 0.00008 0.00016-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1064

279

0.00000 0.00008 0.00016

-1200

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-100

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1120V

0.00000 0.00008 0.00016-1400

-1200-1000

-800-600

-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1224V

280

0.00000 0.00008 0.00016-1400

-1200-1000

-800-600

-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

300

Cur

rent

(Am

ps)

1256V

0.00000 0.00008 0.00016

-1600-1400-1200-1000

-800-600-400-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-100

-500

50100150200250300350

Cur

rent

(Am

ps)

1520V

281

0.00000 0.00008 0.00016-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-300

-200-100

0100

200300

400

Cur

rent

(Am

ps)

1600V

0.00000 0.00008 0.00016

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-400-300-200-100

0100200300400

Cur

rent

(Am

ps)

1740V

282

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016-100

0

100

200

300

400

Cur

rent

(Am

ps)

2060V

0.00000 0.00008 0.00016-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

2240V

283

0.00000 0.00008 0.00016-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

2260V 20 mTorr chromium target

0.00000 0.00008 0.00016-700

-600

-500

-400

-300

-200

-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-20

0

20

40

60

Cur

rent

(Am

ps)

620V

284

0.00000 0.00008 0.00016-700

-600

-500

-400

-300

-200

-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-20

0

20

40

60

80

Cur

rent

(Am

ps)

652V

0.00000 0.00008 0.00016-800-700-600-500-400-300-200-100

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-20

0

20

40

60

80

100

Cur

rent

(Am

ps)

704V

285

0.00000 0.00008 0.00016

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016-40

-200

2040

6080

100

Cur

rent

(Am

ps)

832V

0.00000 0.00008 0.00016-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-20

020406080

100120140

Cur

rent

(Am

ps)

904V

286

0.00000 0.00008 0.00016

-1000

-800

-600

-400

-200

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-40-20

020406080

100120140160180

Cur

rent

(Am

ps)

936

0.00000 0.00008 0.00016

-1000

-800

-600

-400

-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

Cur

rent

(Am

ps)

960V

287

0.00000 0.00008 0.00016-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016-50

0

50

100

150

200

Cur

rent

(Am

ps)

1232V

0.00000 0.00008 0.00016

-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1312V

288

0.00000 0.00008 0.00016

-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-50

0

50

100

150

200

250

Cur

rent

(Am

ps)

1340

0.00000 0.00008 0.00016

-1400-1200-1000

-800-600-400-200

0

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

0

100

200

300

Cur

rent

(Am

ps)

1373V

289

0.00000 0.00008 0.00016

-1800-1600-1400-1200-1000

-800-600-400-200

0200

Volta

ge (V

olts

)

time (s)

0.00000 0.00008 0.00016

-500

50100150200250300350

Cur

rent

(Am

ps)

1670V

0.00000 0.00008 0.00016-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-100

0

100

200

300

400

Cur

rent

(Am

ps)

1830V

290

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-100

0

100

200

300

400

Cur

rent

(Am

ps)

2010V

0.00000 0.00008 0.00016

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-200

-100

0

100

200

300

400

Cur

rent

(Am

ps)

2050V

291

0.00000 0.00008 0.00016-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0

100

200

300

400

500

Cur

rent

(Am

ps)

2310V

0.00000 0.00008 0.00016

-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016-200

-1000

100200

300400

500

Cur

rent

(Am

ps)

2460V

292

0.00000 0.00008 0.00016

-2500

-2000

-1500

-1000

-500

0

Vol

tage

(Vol

ts)

time (s)

0.00000 0.00008 0.00016

-100

0100

200300

400500

600

Cur

rent

(Am

ps)

2520V