Modeling and Calibration of a MEMS Tensile Stage for ... · Modeling and Calibration of a MEMS...

Modeling and Calibration of a MEMS Tensile Stage for Elevated Temperature

Experiments on Freestanding Metallic Thin Films

by

Suhas Eswarappa Prameela

A Dissertation Presented in Partial Fulfillmentof the Requirements for the Degree

Master of Science

Approved April 2016 by theGraduate Supervisory Committee:

Jagannathan Rajagopalan, ChairLiping Wang

Yang Jiao

ARIZONA STATE UNIVERSITY

May 2016

ABSTRACT

Mechanical behavior of metallic thin films at room temperature (RT) is relatively

well characterized. However, measuring the high temperature mechanical properties

of thin films poses several challenges. These include ensuring uniformity in sample

temperature and minimizing temporal fluctuations due to ambient heat loss, in addi-

tion to difficulties involved in mechanical testing of microscale samples. To address

these issues, we designed and analyzed a MEMS-based high temperature tensile test-

ing stage made from single crystal silicon. The freestanding thin film specimens were

co-fabricated with the stage to ensure uniaxial loading. Multi-physics simulations of

Joule heating, incorporating both radiation and convection heat transfer, were carried

out using COMSOL to map the temperature distribution across the stage and the

specimen. The simulations were validated using temperature measurements from a

thermoreflectance microscope.

i

I would like to dedicate this thesis to my family.

ii

ACKNOWLEDGMENTS

I am grateful to Dr. Rajagopalan for giving me the opportunity to work in his lab.

I would like to thank him for his constant support and encouragement in carrying

out this project.

I am grateful to my lab mates, Rohit Sarkar and Ehsan Izadi for providing me with

MEMS samples for carrying out these experiments. Their constant help throughout

my stay has been instrumental in driving this project. I will always treasure the

meaningful and fun discussions we have had in the lab. It was also a great experience

to share lab space with Cole Snider and Abhinav Kowdle Prakash, both of whom

graduated during my stay.

Thanks to George Garcia from PG enterprises and Jerry Eller from ASU for

providing timely help with the gold wire bonding. I am also grateful to Hamsini

Gopalakrishna for providing chemicals used in initial stages of calibration.

I am grateful to Prof. Liping Wang and Jui-Yung Chang for their help with the

thermoreflectance microscope experiments. I have enjoyed collaborating with the

Nano-Engineered Thermal Radiation Group for the calibration studies.

Thanks to my committee members, Dr. Liping Wang and Dr. Yang Jio for taking

the time to participate in this endeavor. I would also like to thank the Center for Solid

State Electronics Research at Arizona State University for access to their facilities.

iii

TABLE OF CONTENTS

Page

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

CHAPTER

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Materials Under Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5 Structure of the Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 NUMERICAL MODEL FOR JOULE HEATING . . . . . . . . . . . . . . . . . . . . . . 8

2.1 Heat Transfer at the Micro/Nano Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 COMSOL Multiphysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 Parametric Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Parametric Study - FCC Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5.1 Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.5.2 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.5.3 Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.5.4 Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3 CALIBRATION OF THE MEMS STAGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.2 Thermoreflectance Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.3 Thermoreflectance Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Measuring Sample Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 EXPERIMENTAL TECHNIQUES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

iv

CHAPTER Page

4.1 Fabrication of the Device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 Microstructure Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3 RT Tensile Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4 High Temperature Test Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.3 Outline for Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

v

LIST OF FIGURES

Figure Page

1.1 Nanocrystalline Aluminum Films (reproduced from [11]) . . . . . . . . . . . . . . 3

1.2 In situ Thermo-mechanical Test Set up (reproduced from [12]) . . . . . . . . 4

2.1 from left : (a) Basic MEMS Test Stage for the nc Films. (b) Close up

Near the nc Thin Film Sample (reproduced from [3]) . . . . . . . . . . . . . . . . . 9

2.2 from top left : (a) Creating Geometry (b) Setting up Model (c) Apply-

ing Boundary Conditions ; from bottom left : (d) Meshing (e) Result

:Voltage Profile (f) Temperature Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 from left : (a) TEM Model (b) Ambient Model . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Temperature Profile for Titanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 Close up of Titanium Thin Film Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.6 Plot of Sample and Stage Temperature vs Voltage . . . . . . . . . . . . . . . . . . . 14

2.7 (a) Temperature Profile for Single Crystal Silicon (b) Voltage Profile

(c) Close up of Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.8 Temperature Profile for Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.9 Close up of Aluminum Thin Film Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17


2.11 Temperature Profile for Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.12 Close up of Copper Thin Film Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19


2.14 Temperature Profile for Nickel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.15 Close up of Nickel Thin Film Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21


2.17 Temperature Profile for Gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.18 Close up of Gold Thin Film Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

vi

Figure Page


3.1 Schematic of Thermoreflectance Microscope (reproduced from [1]) . . . . . 26

3.2 Variation of Thermoreflectance Coefficient with Illumination Wave-

length (reproduced from [2]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Variation of Reflected Signal with Temperature . . . . . . . . . . . . . . . . . . . . . . 28

3.4 Thermoreflectance Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.5 Two Ends of the Sample Marked for Measuring the Temperature . . . . . . 29

3.6 Reflected Signal Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.7 Temperature Measurements at Two Ends . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.8 Position 1: Laser Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.9 Position 2: Laser Images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

4.1 Fabrication Process Flow (reproduced from [3]) . . . . . . . . . . . . . . . . . . . . . . 35

4.2 TEM Image: Ti Thin Film Microstructure (Thickness: 200 nm at RT)) 36

4.3 XRD Plots: Ti Thin Film (Thickness: 200 nm at RT) . . . . . . . . . . . . . . . . 36

4.4 MEMS Device to Perform Tensile Test at RT (reproduced from [4]) . . . . 37

4.5 RT Test Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.6 Stress Strain curve for Titanium at RT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.7 Type 1: Teflon Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.8 Type 2: Aluminum and Macor Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.9 Type 1: Gold Wire Bonding on the Device . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

vii

Chapter 1

INTRODUCTION

1.1 Background

The interest in study of nanocrystalline (nc) metals, with average and total range

of grain sizes typically less than 100 nm (1 nm = 10−9m), has increased notably over

the past few decades [5, 6, 7]. The unique advantages associated with grain refine-

ment in the nc regime, such as increased strength, hardness, resistance to tribological

damage, and the potential for enhanced super plasticity at low temperatures and

high strain rates, have primed such interest.The apparent flourish in research of these

structural nanomaterials has been accelerated by recent advancement in both fabri-

cation and characterization technologies, where thin films of nanocrystalline metals

of ultra-high purity and full density can now be processed with narrow grain size

distributions in the nc regime [8, 9]. Further, the ability to probe the grains with

high resolution (few tenths of nm/Angstroms), and the mechanical response with

nm and picoNewton (pN =10−12m) resolution, has provided unprecedented means to

systematically characterize these materials.

Presently, there are no strict conventions in place to bifurcate metals based on the

grain size.But in general, the following classification is often considered for the studies,

which will also be employed for this report. Terms used are nc : Nanocrystalline; ufc :

ultrafine crystalline; mc : micro crystalline [10]. Nanocrystalline grains of Aluminum

[11] can be seen in figure ??i1.

2

Figure 1.1: Nanocrystalline Aluminum Films (reproduced from [11])

• nc: Average and total range of grain sizes are below 100 nm.

• ufc: Average grain size is between 100 nm and 1µm, with the total range of

grain sizes below 1 µm.

• mc: Average grain size is above 1 µm.

During operation, nc metals can be subjected to elevated levels of temperature

and thermal stresses which can significantly alter their mechanical properties. Me-

chanical behavior of NC metals which have size dependent material properties at

room temperature is relatively well characterized. However, lack of adequate testing

set-up and sensitive material properties has hindered the understanding at high tem-

perature levels. Recently, MEMS (Micro-Electro-Mechanical Systems) based testing

devices are found to be good candidates to characterize thermo-mechanical behavior

of free standing NC thin films. Measuring the sample temperature in situ is difficult

due to various fabrication constraints. Further, it is challenging to accurately mea-

sure heat transfer losses from the sample and the stage surfaces at relatively high

temperature levels.

Recently Wonmo Kang et.al [12] have shown that the brittle-to-ductile transition

(BDT) transition for single crystal silicon is dependent on the temperature and the

3

Figure 1.2: In situ Thermo-mechanical Test Set up (reproduced from [12])

sample size. They have employed a unique high temperature stage [13] to test the

single crystal silicon sample of different sizes as shown in figure 1.2. Their study re-

ported that at smaller scales, there is almost 31% reduction in the BDT temperature,

from 545oC to 293oC for a sample of 720 nm. In the absence of quantitative in situ

thermo-mechanical data, it is often difficult to decouple the effect of temperature and

size on the onset of plasticity. Therefore carrying out thermo-mechanical tests can

reveal interesting pattern in the material properties at the micro or nanometer level.

1.2 Objectives

Pertinent goals of the project include:

1. Simulate Joule heating for the MEMS devices in which NC thin films are co-

fabricated.

2. Study the effect of varying voltage on the temperature profile across sample.

3. Study the effects of convection and radiation heat transfer during the Joule

heating process.

4. Calibrate the stage using a contact-less thermal measurement technique

4

5. Carry out tensile test of titanium thin films at elevated temperature

1.3 Approach

To carry out the objectives stated above, it is beneficial to build a numerical model

which can predict the temperature profile of both the MEMS stage and the sample.

Finite Element Analysis (FEA) of the three dimensional solid model was carried out

using COMSOL Multiphysics package [14]. Some of the important features that ought

to be considered include that of meshing, appropriate physics package, boundary

conditions, radiative and convective effects, geometry effects and material properties.

Further, the calibration was carried out using thermoreflectance microscope which

can offer good spatial and temporal resolution.

1.4 Materials Under Study

The materials selected for the numerical model study are titanium and single

crystal silicon. Single crystal silicon is opted to verify the numerical model with

the previously carried out studies. For calibration and testing, MEMS based devices

with free standing Titanium thin films are taken up. Titanium has many applications

in the field of space and medicine. Titanium has a crystal class of hexagonal close

packing (hcp) and shows very little plasticity at room temperature under uniaxial

tension.

1.5 Structure of the Report

The first chapter gives a brief overview of Nanocrystalline metals and motivation

5

to take thermo-mechanical studies. Main objectives and the materials taken up for

study are also discussed in the same chapter.The second chapter explains the pro-

cess of simulating Joule heating of the stage and the samples.The next chapter talks

about calibration of the device using thermoreflectance microscope. The final chap-

ter provides important conclusions drawn from the study while discussing pertinent

limitations and outline for future work.

6

Chapter 2

NUMERICAL MODEL FOR JOULE HEATING

Numerical modeling has been carried out on the MEMS test stage in which the

nanocrystalline thin film is cofabricated. The results for titanium and Single Crystal

Silicon samples are provided in the current chapter. These results primarily include

voltage and temperature profile for the stage and the sample. Further, parametric

study has been carried out to study the effect of varying voltage on the temperature

profile of the sample.

2.1 Heat Transfer at the Micro/Nano Scale

The basic energy carriers in materials include mainly electrons, phonons and pho-

tons. In case of metals, electrons form the majority and dominate over other heat

carriers. Electrons in a metal are similar to that of atoms/molecules in a free gas hav-

ing a certain mean free path. The energy transport occurs through collisions which

are random in nature [15]. When the mean free path is comparable or larger than

the size of the system, quantum effects show pronounced effect. In this case, classical

heat transfer by Fourier heat conduction no longer applies and quantam mechanical

effects have to be taken into consideration. The general order for the mean free path

of the electrons is around 100 Ao. This is few orders lower than the size of our given

system (MEMS test stage as shown in figure 2.1) and nanoscale effects can essentially

be ignored [16]. However, in these micro devices the radiative and convective heat

losses/gain are enhanced as a result of the huge surface to volume ratio. Therefore it

is essential to consider these effects to accurately predict the temperature profile.

8

Figure 2.1: from left : (a) Basic MEMS Test Stage for the nc Films. (b) Close upNear the nc Thin Film Sample (reproduced from [3])

2.2 COMSOL Multiphysics

The numerical simulation for the different metal samples was carried out by Com-

sol Multiphysics package[17]. Comsol Multiphysics is a finite element analysis solver,

based on advanced numerical methods, which is used for modeling and simulating

physics based problems. The basic procedure followed to obtain the solution is illus-

trated in figure 2.2. In the first step, a 2D geometry is created which is then scaled to

a model. This is followed by applying appropriate boundary conditions, mesh (free

triangular) and physics module to yield the final result.

Figure 2.2: from top left : (a) Creating Geometry (b) Setting up Model (c) ApplyingBoundary Conditions ; from bottom left : (d) Meshing (e) Result :Voltage Profile (f)Temperature Profile

9

2.3 Mathematical Model

In order to simulate Joule heating Comsol couples the heat transfer in solids model

with the electric currents model. For heat transfer in solids the heat equation is given

by [18]

∂(ρcpT )

∂t= ∇ · (k∇T ) = div(k∇T ) +Qj(x, y, z, t) (2.1)

where ρ is the density, cp is the specific heat and Qj(x, y, z, t) is the Joule heating

term.k is some positive scalar quantity which may depend on the medium and is

called the thermal conductivity. The convection (with h: heat transfer coefficient,

T∞: Ambient temperature) and radiation (with σ′

: Stefan constant, ε: emissivity,

A: Area) boundary conditions applied in the current module are:

k∇T = h(T − T∞) + σ′εA(T 4 − T 4

∞) (2.2)

The sample is subjected to both a convective and radiative boundary condition at

the surface. The value Qj(x, y, z, t) depends upon the resistivity of the material, the

geometry of the structure and the current flowing through the device. Joule heating

involves the conversion of electrical energy to heat energy due to the resistance of the

element. This term is obtained with the help of the electric currents model in which

:

J = σE + Je (2.3)

E = −∇(V ) (2.4)

10

Figure 2.3: from left : (a) TEM Model (b) Ambient Model

Qj = ∇.(J) (2.5)

Where σ is the electrical conductivity, E the electric field, V the potential differ-

ence and J the current density. The above coupled equations would be trivial to solve

if there is homogeneous material with uniform current density and consistent material

properties.However, this is not the case in the current model where there are different

materials and properties that are temperature sensitive. The geometry was created in

Comsol based on the preexisting Autocad drawing. The model was created through

a series of Bezier Polygons in a work plane followed by an extrusion.Two different

geometries were considered : Ambient Model and TEM Model. Ambient model refers

to the one without backbeam and is meant for testing inside the lab as opposed to

a TEM model which has a back beam and is meant for study in situ in a TEM.The

figures for the Ambient and TEM model are shown in figure 2.3. The properties

for the materials were obtained from existing literature [19, 20] and care was taken

to select the most suitable values for our model. Most material properties such as

emissivity, heat capacity, thermal conductivity, and resistivity are a function of tem-

perature. Some of the properties can be entered as temperature dependent functions

in Comsol by making using of interpolation function. However, having the material

properties a function of temperature uses a lot of computing power while running the

11

simulation. The temperature dependence for all metal thin film samples was ignored.

For the silicon carbide sample the temperature dependence of resistivity was taken

into account since it varies significantly. The resistivity as a function of temperature

can be expressed using the linear relationship :

σ = σo(1 + (T − To)) (2.6)

where σ is the resistivity at temperature T, σo is the resistivity at temperatureTo.When

carrying out the experiment in an ambient environment we need to consider natural

convection. The convective heat transfer coefficient depends upon the temperature of

the film and the geometry. However we assumed a constant value for the convective

heat transfer coefficient of 5W/m2K. When carrying out the experiment in-situ we

can ignore heat transfer due to convection. The heat transfer due to radiation be-

comes then becomes dominant at elevated temperatures which can be evaluated using

by Stefan-Boltzmann law.A standard free triangular mesh was used for each surface

followed by a swept mesh. The use of a swept mesh is justified as the length of the

device is much larger than the thickness of the substrate and thin film . This reduces

our temperature distribution to two dimensions (namely the x and y).These simpli-

fications in the simulation may result in a certain level of inaccuracy in temperature

predictions. However, the trend followed during Joule heating follows a characteristic

parabolic rise.

2.4 Parametric Study

For device with titanium thin film, parametric study was carried out where the

voltage was varied from 0.1 V to 2.5 V. The temperature profile of the sample and the

stage was mapped taking into consideration radiation and convective heat transfer

12

Figure 2.4: Temperature Profile for Titanium

Figure 2.5: Close up of Titanium Thin Film Sample

(See figure 2.4, 2.5 and 2.6).

13

Figure 2.6: Plot of Sample and Stage Temperature vs Voltage

Further, this study was extended to Silicon Carbide stage with single crystal

silicon sample as shown in figure 2.7. The main reason for carrying out this test

was that the temperature profile of the sample and stage has been modeled and

validated experimentally by Wonmo Kang et. al[21] . Similar exercise when carried

out in COMSOL with temperature dependent material properties yielded temperature

values that are in the same order for our samples. This validates the approach adopted

towards modeling in the current study to determine the temperature profile of the nc

films co-fabricated on a MEMS testing stage.

14

Figure 2.7: (a) Temperature Profile for Single Crystal Silicon (b) Voltage Profile (c)Close up of Sample

2.5 Parametric Study - FCC Thin Films

In addition to Single Crystal Silicon and Titanium, parametric study was taken up

for various metal films such as Aluminum, Gold, Copper and Nickel. These metals

are fcc and have wide range of applications. Some of the main results from these

metals is tabulated below.

2.5.1 Aluminum

Aluminum is an abundantly available metal which is know for low density and

high resistance to corrosion. The thermal conductivity of Aluminum is around 237

W/(m.K) and the electrical resistivity is around 30 nΩ.m at 20 C. The main ap-

15

Figure 2.8: Temperature Profile for Aluminum

plications are in transportation, packaging, construction etc. Parametric study was

carried out on free standing Aluminum thin films and the MEMS device as shown in

figure 2.8, 2.9 and 2.10.

16

Figure 2.9: Close up of Aluminum Thin Film Sample


17

2.5.2 Copper

Copper is well know FCC metal with very high thermal and electrical conduc-

tivity. It is used both a building material and for electrical wirings. It has high

ductility with Young’s modulus varying from 110-128 GPa. The thermal conductiv-

ity of Copper is around 401 W/(m.K) and the electrical resistivity is around 17 nΩ.m

at 20 C.Parametric study was carried out on free standing Copper thin films and the

MEMS device as shown in figure 2.11, 2.12 and 2.13.

It can be observed that the temperature rise as a function of voltage is lower with

both convection and radiation effects considered. At higher temperature levels, the

difference is more significantly and cannot be ignored.

Figure 2.11: Temperature Profile for Copper

18

Figure 2.12: Close up of Copper Thin Film Sample


19

2.5.3 Nickel

Nickel is transition metal that is ductile and shows significant chemical activity

in the powdered state. At high temperature, Nickel is found to be ferromagnetic. It

has high Young’s modulus of around 200 GPa and is also anisotropic. The thermal

conductivity of Nickel is around 90.9 W/(m.K) and the electrical resistivity is around

69.3 nΩ.m at 20 C. Parametric study was carried out on free standing Nickel thin

films and the MEMS device as shown in 2.14, 2.15 and 2.16.

Nickel is currently being used in many applications including in making nickel

steels, nonferrous alloys and super alloys. It is in general an excellent alloying candi-

date for precious metals and bulk Nickel is found to be resistive to corrosion.

Figure 2.14: Temperature Profile for Nickel

20

Figure 2.15: Close up of Nickel Thin Film Sample


21

2.5.4 Gold

Gold is a ductile metal and is a group 11 transition element. It is least reactive to

the chemicals and is to provide contacts in electronic packages. The Young’s modulus

is found to be around 79 GPa and is a good conductor of heat and electricity. The

thermal conductivity of Gold is around 318 W/(m.K) and the electrical resistivity is

around 22.14 nΩ.m at 20 C. Parametric study was carried out on free standing Gold

thin films and the MEMS device as shown in 2.17, 2.18 and 2.19.

Gold has numerous applications including in microelectronics industry and can

be found in biomedical applications, chemical synthesis of compounds etc. Further,

several MEMS devices have patterned gold lines for circuits and other electrical com-

ponents.

Figure 2.17: Temperature Profile for Gold

22

Figure 2.18: Close up of Gold Thin Film Sample


23

Chapter 3

CALIBRATION OF THE MEMS STAGE

3.1 Motivation

Measuring temperature accurately becomes non trivial when devices are scaled

down to the micro/nano scale [22]. Conventional techniques employing resistance

thermometer, thermocouple and thermistor often fail because of relatively larger size,

poor spatial and thermal resolution [23]. While contact techniques involving micro

thermocouples and mini thermistor sensors can be used to certain extent, they are

not suitable to measure temperature profile of features in the range of sub-micron

or nm range[24]. It is crucial to develop methods that can help in precise calibra-

tion and measurement of temperature profiles since they can have a strong impact

on device performance assessment and reliability. For example, space agencies of-

ten heavily use miniaturized devices to adhere to mass budget. The design of these

devices is often influenced by their thermal performance as per relevant MIL STD

regulations. It is therefore important to know what temperature distribution is across

the device during operation. Along with the above mentioned contact methods, there

are several contact-less techniques[25] such as IR (Infrared Thermography), near field

scanning optical microscopy (NSOM), scanning thermal microscopy (SThM), Raman

Measurements, thermoreflectance microscopy etc.[26, 27] that are being used for ther-

mal characterization of these devices. During Joule heating of the MEMS Stage, it is

important to know the temperature distribution across the device and the sample for

varying voltage. This helps in knowing the average temperature of the free standing

25

thin film being subjected to uniaxial tensile test. In particular, it is required to know

the general relationship interlinking the voltage and temperature for a set of devices

obtained from the same Silicon wafer. This ensures that calibration before each ten-

sile test is avoided by building a reliable model calibrated by input from experimental

measurements. To implement this goal, a scanning thermoreflectance microscope was

employed in this study.

3.2 Thermoreflectance Microscopy

Thermoreflectance microscope is a non-contact optical approach which relies on

change in reflectively for a given surface with change in temperature [28, 29] . This

technique offers high spatial and temporal resolution that can be very useful in pro-

ducing thermal maps of devices with resolved features being in the sub-micron regime.

The general set up of thermoreflectance microscope is shown in figure 3.1.

Figure 3.1: Schematic of Thermoreflectance Microscope (reproduced from [1])

26

The set up mainly comprises of laser source being focused on the sample after

passing through a 50:50 beam splitter with the reflected sample being captured by a

camera. In general the microscope arrangement consists of a laser diode driver, laser

diode controller, temperature controller and lock in amplifier. The goal is obtain a

reflected signal with a good signal to noise ratio. The simple form of the governing

equation [30, 31] is given below:

∆R

R=

1

R

∂R

∂T∆T = Ctr∆T (3.1)

In the above equation, ∆R is the change in reflectivity, T is the temperature

and Ctr is the thermoreflectance coefficient. This term depends strongly on the illu-

mination wavelength as seen in figure 3.2. From the figure, it can be seen that for

Titanium both Yellow (585 nm) and Red (660 nm) can be easily employed to measure

the sample temperature.

Figure 3.2: Variation of Thermoreflectance Coefficient with Illumination Wave-length (reproduced from [2])

27

3.3 Thermoreflectance Coefficient

The first step in utilizing the microscope to measure the sample and device temper-

ature is to determine the thermoreflectance coefficient. A small wafer piece (reference

sample) with 200 nm of titanium layer deposited on top was placed on a heater. The

reflected signal was captured by varying the temperature from 30 C to 100 C in steps

of 10 C. The laser source used for this purpose was a red laser with a wavelength

of 635 nm. The reflected signal continuously drops as the temperature is steadily

increased. The device was allowed to reach steady state before recording the mea-

surement. The thermoreflectance coefficient calculated from the slope was found to

be around 0.0043 as shown in figure 3.3 and 3.4. At each point, the microscope is

programmed to record 100 data points.

Figure 3.3: Variation of Reflected Signal with Temperature

28

Figure 3.4: Thermoreflectance Coefficient

3.4 Measuring Sample Temperature

Thermoreflectance microscope was then used to measure the temperate of the free

standing titanium thin film. Since there was ambiguity over the tilt of the sample with

respect to the horizontal, the temperature was found at the ends of the sample. The

thermoreflectance coefficient measured for the reference sample was used to determine

the temperature of the sample heated using thin gold wires attached to the end of the

device. figure 3.5 describes the two positions marked for measuring the temperature.

The voltage was varied from 0 to 16 V and the corresponding reflected signal was

Figure 3.5: Two Ends of the Sample Marked for Measuring the Temperature

29

Figure 3.6: Reflected Signal Measurement

Figure 3.7: Temperature Measurements at Two Ends

30

Figure 3.8: Position 1: Laser Images

recorded for every 1V. The corresponding variation can be seen in figure 3.6 and 3.7.

Further, laser images were taken at both positions 1 and 2. It can clearly seen

than at lower voltages, the temperature induced due to Joule heating on the surface

is quite less. The incident laser is bright and thus there is good amount of normal

reflection and very little diffusion. With the increase in temperature, voltage signal

drops since there is high diffusion leading to very less normal reflection back to the

microscope. Thus, the shape of laser image thus becomes conformal to that of the

sample. This phenomenon is very clear in figure 3.8 and 3.9.

It is important to note that it is not possible to calibrate each sample that is

to be tested since calibration takes long time and it is quite tedious to move live

samples in between tensile stage and calibration stage. Using contacts such as silver

paste results in unique contact resistance that complicates the calibration process.

Therefore the idea is to employ a method such as wire bonding, which is discussed

in the next chapter to ensure uniform heating for all devices from the same parent

wafer.

31

Figure 3.9: Position 2: Laser Images

32

Chapter 4

EXPERIMENTAL TECHNIQUES

Experimentally realizing the high temperature tensile test is quite difficult. Num-

ber of significant challenges that crop up are making reliable contacts, measuring the

sample temperature accurately and preventing oxidation at higher temperature levels

etc. Further, this chapter also describes the process to fabricate the MEMS devices

and the micro structure characterization of the sputtered thin films.

4.1 Fabrication of the Device

The basic fabrication process flow used to fabricate the MEMS devices is show

in figure 4.1 . The device is designed to ensure uniaxial criterion during tensile test.

The basic steps involve:

• a) Deposition of the metal film on the wafer

• b) Spin coating of photo resist

• c) Removal of photo resist and etching silicon oxide layer

• d) photo resist deposition on both sides

• e) patterning both sides by lithography

• f) dry etching of the silicon oxide and removal of photo-resist

• g) DRIE etching of Si

• h) removal of oxide layer at the bottom of thin film

34

Figure 4.1: Fabrication Process Flow (reproduced from [3])

4.2 Microstructure Characterization

X-ray diffraction (XRD) and Transmission Electron Microscopy (TEM) studies

were carried out to reveal the thin film microstructure. Different sized grains were

grown using a DC sputtering machine. The XRD and TEM plots of the thin film can

be seen in figure 4.2 and 4.3 respectively.

4.3 RT Tensile Experiments

Several RT experiments were carried out on free standing Titanium thin films

35

Figure 4.2: TEM Image: Ti Thin Film Microstructure (Thickness: 200 nm at RT))

Figure 4.3: XRD Plots: Ti Thin Film (Thickness: 200 nm at RT)

36

Figure 4.4: MEMS Device to Perform Tensile Test at RT (reproduced from [4])

Figure 4.5: RT Test Stage

using the MEMS stage shown in figure 4.4 . The test stage set-up employed to test

this device is shown in figure 4.5 . The device is placed in between A and B pins

during the tensile testing. The load cell called the futek measures the amount of

force and optical microscope placed at the top tracks the gages to measure the strain.

Knowing the sample dimensions, it is possible to convert the force into stress and

thus one can obtain the stress strain curve for the free standing Titanium thin film.

Thus, the tensile test of the film at RT yields a stress strain plot shown in figure 4.6.

37

Figure 4.6: Stress Strain curve for Titanium at RT

4.4 High Temperature Test Stage

In order to carry out tests at elevated temperature, two types of stages were

fabricated. The first type consisted of a stage made of Teflon to carry out tests until

250 C as shown in figure 4.7. The second stage was a hybrid stage made of Aluminum

and macor ends that could withstand 1000 C for long duration as shown in figure 4.8

.

But the main challenge here is to build a strong wire connection to the device with

minimum contact resistance as possible. Towards this end, unique adapter stages were

built to carry out gold wire bonding on the device. Gold wire bonding requires an

38

Figure 4.7: Type 1: Teflon Stage

Aluminum contact pad that was deposited at the ends of the devices. Wire bonding

refers to making a weld using combination of heat, pressure, and ultrasonic energy.

The ends of the sample wire bonded can be seen in figure 4.9.

39

Figure 4.8: Type 2: Aluminum and Macor Stage

Figure 4.9: Type 1: Gold Wire Bonding on the Device

40

Chapter 5

CONCLUSION

The major objective of this study was to carry out modeling and calibration of

the MEMS Stage. Particularly, the goal was to determine the temperature profile of

the free standing nanocrystalline thin film sample co-fabricated with the MEMS test

stage. Towards this end numerical model involving Titanium with Silicon based stage

and Single Crystal Silicon(SCS) with Silicon Carbide was taken up. Further, calibra-

tion was carried out using thermoreflectance microscope on devices with titanium

thin films.

5.1 Conclusions

Some of the important conclusions that can be drawn from the study are :

1. Parametric modeling of the device and the sample has yielded a characteristic

temperature profile titanium and the Single Crystal Silicon(SCS) sample.The

temperature characteristic that is similar in all these cases is that of a parabolic

rise.

2. The temperature order and methodology followed to obtain Joule heating of the

MEMS stage is confirmed by the high temperature test on the Silicon Carbide

stage previously discussed in Wonmo Kang et.al

3. Titanium has very low conductivity and thus relatively high voltage is required

to heat up the sample compared to other metals.

42

4. Thermoreflectance microscope can be successfully employed to map the tem-

perature profile of the titanium sample

5.2 Limitations

There are some limitations in the numerical model that are worth mentioning.

These arise from the inability to account for all influence parameters at a single time

into the model. Some of the possible causes for the temperature offset are elucidated

below.

1. Meshing issues

(a) Difficulty in meshing small features

(b) Mesh misalignment

(c) Convergence issues

2. Material Properties

(a) Sensitive Material Properties

(b) Unavailability of data regarding temperature dependent properties

3. Oxide Thickness

(a) Thin layer of oxide layer may form at elevated temperature

(b) Incorporating such small layers into the model is difficult

4. Coupling Mechanical Behavior

(a) Coupling with multiple physics features leads very slow / no convergence

43

5.3 Outline for Further Work

The numerical model built for studying the Joule Heating can be improved with

adapting more factors influencing the temperature off set such as oxide layer thickness

etc. Further, tensile tests can be carried out at different temperatures for the titanium

sample to see the effect of temperature on plasticity.

44

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