1 Metodi sperimentali della fisica moderna Luca Gavioli Dipartimento di Matematica e Fisica...

1

Metodi sperimentali della fisica moderna

Luca GavioliDipartimento di Matematica e FisicaUniversità Cattolica del Sacro CuoreVia dei Musei 41, I-25121 Brescia, Italy

[email protected]://www.dmf.unicatt.it/~gavioli/corsi/MSFM/www.dmf.unicatt.it/nano

2

• Introduction

• Basic concepts of vacuum

• Vacuum Hardware (pumps, gauges)

• Mass Spectrometry

OUTLINE

•References

• Ferrario: Introduzione alla tecnologia del vuoto: Cap 1-4, 8-11• Woodruff – Delchar: Modern techniques of surface science

(Cambridge University Press) Chap 2,3• Chambers, Modern Vacuum Physics (Chapman & All)

• Published papers

3

GETTERS

Getters are stripes of material adsorbing the gas

NEED OF VACUUM

TV TUBESLCD BACKLIGHTGAS LIGHTS (NEON, HIGH POWER LAMPS)DEWAR (FOR DRINKS)

Active material: alkali (Cs, Rb), rare earths (Yb, Lu), HgSupport: Al2O3, Zr

Interaction of gas (CO2, O) with getter surface (passivation or oxidation)Role of the surface morphology: surface area/bulk

Research applications: impact on everyday life

4

Basic concepts of vacuum

•UHV Apparatus•Gas Kinetics•Vacuum concepts•Vacuum Pumps•Vacuum Gauges•Sample Preparation in UHV

•Cleaving•Sputtering&Annealing•Fracturing•Scraping•Exposure to gas/vapor•Evaporation/Sublimation

5

Ultra High Vacuum Apparatus

6

Ultra High Vacuum Apparatus

7

Tk

mv

B

B

x

eTk

m

V

Nvf 2

x

2

2

Maxwell-Boltzmann distribution 1D

kB = Boltzmann constant

n = Molecular density

N=nNA = total number of molecules

N = Total number of molecules

Gas kinetics

Tk

mv

B

BevTk

m

V

NvvfvF 22

3

2

2

2

124


Mean number of particles perunit volume between v and v+dv

Tk

mv

B

BeTk

m

V

Nvf 2

3 2

2

2

In polar coordinates

8

Gas kinetics

m

Tk

dv

vdFv B2~

Tk

mv

B

BevTk

m

V

NvF 22

3 2

2

12


m

Tkv B

8

Average

m

Tkvv B

rms

32

T (°C)

Molecular speed

Quadratic mean

Most likely

Neon @ 300 K

mNe = 20 • 1.67 x 10-27 kg

smvrms / 6101067.12

3001038.1326

23

9

Arrival rate R:number of particles landing at a surface per unit area,unit time

TNKpVmTk

v

B

B

8

Tmk

pvTkpv

VN

RBB 244

cos vdVvFdR

mTk

VN

R B

8

4

dSvdt cos

dVvF

Gas kinetics

dVvvFdRR cos

Tmk

pR

B2

Tkmv

B

BevTkm

VN

vf 22

3 2

212

volume

Mol. per unit volume

0

32

0

22/

0

2

0

2

2

2

2 )( cos sin dvve

Tk

m

V

NdvvvFddR Tk

mv

B

B

dvvdddV 2 sin

10

p = Pressure (torr)

T = Temperature (K)

m = Molecular mass (g)

21-22 s 105.3 cmmoleculemT

pR

O2 at p = 760 torr, 293 K R = 2.75 1023 molecules s-1cm2

O2 at p = 1 x 10-6 torr, 293 K R = 3.61 1014 molecules s-1cm2

kB = Boltzmann’s constant (erg/K)

Arrival rate R of atoms at a surface per unit area

Tmk

pR

B2

Gas kinetics

11

Gas kinetics: why the UHV

1 Monolayer ~ 1014 – 1015 atoms/cm2

Residual Gas H2O

CO2

CO

CH4

O2

N2Solid Surface

Bulk SolidAdsorbed Atoms & Molecules

12

Mean free path

Gas kinetics

2r

2r

The sphere with 2r is the hard volume

The surface of the sphere is the effective section or cross section for impact

The number of impacts per unit time is

mTk

VN

rvVN

rf B

844 22

13

Mean free path

Gas kineticsFor different molecules A and B

Tk

VN

rf BAB

84 2

rBrA

2BA

AB

rrr

BA

BA

mmmm

fv

224 rN

Vfv

pr

TkB 1

2 2

is so large that the collisions with walls aredominant with respect to molecular collisions

15

Sticking probability = 11 monolayer of atoms or molecules fromthe residual gas is adsorbed at the surface in:

1 sec @ p = 1 x 10-6 torr10 sec @ p = 1 x 10-7 torr100 sec @ p = 1 x 10-8 torr1,000 sec @ p = 1 x 10-9 torr10,000 sec @ p = 1 x 10-10 torr100,000 sec @ p = 1 x 10-11 torr

Utra High Vacuum (UHV): p = 10-10-10-11 torr

Why the UHVO2 at p = 1 x 10-6 torr, 293 KR = 3.61 1014

16

Plots of relevant vacuum features vs. pressure

17

Gas flux through a pipe

dtdV

pQ

d

[Q] = [p][L]3[t]-1

Qdt

dNTK

dtpVd

TKNpVTKNnRT

mNMNKRNN

n

atB

BatBat

AVAVBAV

at

)(

;

; ;

pipe

p = pressure on planedV = volume change across plane

Flux

dtdN

TKQ atB

Volumetric flux: variation of number of molecules through an area

dV/dt= Volumetric flow rate

(Throughput)

18

dtdV

pQ

mat

Bat

AVB

Bat

AV

AVat QQRTM

dtdN

TKRTM

dtdN

NKMK

dtdN

NmN

dtmNd

dtd

)(

QRTM

Qm

dtd

Qm

Mass flux

Variation of mass through an area

Volumetric flux

• Magnitude of flow rates • Pressure drop at the pipe ends• Surface and geometry of pipe• Nature of gases

Gas flux through a pipe

M=mole mass

M = total mass

AVmNM

Factors affecting the flux

19

Regimes of gas flux through a pipe

For < d viscous

For d intermediate

For > d molecular

dtdV

pQ d

Viscous

laminar

turbulent

pipeFlux

The mol-mol collisions are dominant

dydv

SF xf Friction force = viscosity

S = layer contact areadvx /dy = mol speed gradient

(Throughput)

20

dtdV

pQ Volumetric flux

Laminar: Re<1200

turbulent: Re>2200

mass fluxdtd

Qm

For a pipe with diameter d and section d2/4

Q’ mass flux per unit section 2

4'

dQ

areaQ

Q mm

Reynolds numberd

QRe ' = viscosity

d pipe


21

Laminar: Q < 8 103 (T/M)d [Pa m3/s]

Reynolds numberd

QRe '

QdRT

MddQ

R me

442

eRd

MRT

Q4

Turbulent: Q > 1.4 104 (T/M)d [Pa m3/s]


22

For < d

For d

For > d

dtdV

pQ

d viscous

intermediate

molecular

Knudsen number = d/ Only for intermediate and molecular flux

intermediate

molecular

3 d/ 80

d/ 3

pr

TkB 1

2 2

10-2 p d 0.5

p d 10-2

For air at RT


pr

TkB 1

2 2

23

Pipe conductance:0pp

QC

In parallel

N

iiCC

1

Flux across pipe

Pressures at pipe ends[C] = [L]3[t]-1

Pipe impedance:C

Z1

PCQ

PCQ

22

11

PCCQQQ 2121

21 CCCT

SI: m3s-1

cgs: lt s-1

24

In series

N

i iCC 1

11

222

111

PCQ

PCQ

T

TT C

QCQ

CQ

PPP 2

2

1

121

Q1 = Q2 = QT or gas would accumulate

T

TTTT C

QCQ

CQ

P 21

21

111CCCT

25

Pipe conductance

221

4 ppL

dC

Viscous and intermediate regime

Molecular regime

dL

dC

Ld

C

34

13

3Long cylindrical pipe

Elbow pipe

Laminar Turbulent L

dppC

522

21

The molecules must collide with walls at least once before exiting

Equivalent to a longer piper

For air at 0 C: 11,6 d3/L [lt/s]

26

[S] = [L]3[t]-1

Pumping speed S = Q/p0

Q= flux through aspiration aperturep = Vessel PressureV = Vessel Volume

p0

Relevant physical parameters of a pumping system

SI: m3s-1

cgs: lt s-1In the presence of a pipe

Effective pumping speed

Q at the pump inlet is the same as Q in pipe

SSS

SS

S

pp

Sppp

Qpp

C e

e 1111

1 0

0

00

C

pSSpQ e 0

0pp

SS

e

CSSe

111

S = Volumetric flow rate

27

[S] = [L]3[t]-1

Pumping speed S = Q/p0


p0


if S = C

Effective pumping speed

the Se is halved

C

CSSe

111

CSSC

Se

28


p0


10 QQQ

Q1 = True leak rate(leaks from air,wall permeability)

Q2 = Virtual leak rate(outgas from materials, walls)

Outgas rate for stainless steel after 2 hours pumping: 10-8 mbar Ls-1 cm-2

Sources of flux (molecules)

29

QpSdtdp

V

Pump-down equation for a constant volume system

01 QQQ

True leak rateOnly the gas initially presentcontributes

Virtual leak rateOther outgassing sources contribute

Short time limit Long time limit

Q = Q0 +Q1

S = Pumping speedp = Vessel PressureV = Vessel Volume

30

QpSdtdp

V


True leak rate

Short time limit

tVS

epp

0

Q = Q0 +Q1


Constant S

Q = 0pS

dtdp

V

dtVS

pdp

pp

SV

t 0ln

Time needed to reduce p by 50 %

SV

69,0

V= 1000 LP0 = 133 PaS= 20 L/s

t = 331,6 s 7.5 L/s = 27 m3/h

Vol of 1 m3 = 103 L to be pumped down from 1000 mbar to 10 mbar in 10 min =

600 s sLpp

tV

S /5.710ln6001000

ln 20

31

QpSdtdp

V


Q = Q0 +Q1


SQpu

Ultimate pressure

QpS 0

dp/dt = 0

Virtual leak rateOther outgassing sources contribute

Long time limit

32

Example

2xp

33

Differential pumpingoperate adjacent parts of a vacuum system at distinctly different pressures

The size of the aperture depends by its function conductance C is determined.

A, B to be maintained at pressures P1 and P2, P1 >> P2

A: gas in with flux QL

gas to B with flux qQ1 = flux pumpedS1 = Q1/p1 QL/p1

B: gas in with flux qTo keep pressure p2

S2 = q/p2

q = C(p1 − p2) C p1

S2 = Cp1/p2

34

ExampleCVD coatings on panels

Antireflective coatings, p-n junction growth for solar panels

P0P1 P2 P1 P0

S1S2 S3

S1 = Cp0/p1

C CC

S2 = Cp1/p2 S3 = Cp2/p1

35

Gas-solid interaction

H2O

CO2

CO

CH4

O2

N2

HeH2

elastic inelastic trapped

physical adsorption (shortened to Physisorption): bonding with structure of the molecule unchanged

Chemisorption:bonding involves electron transferor sharing between the molecule

and atoms of the surfaceCan be thought of as a chemical reaction

36


H2O

CO2

CO

CH4

O2N2

HeH2

Origin:Van der Waals forces

The well depth is the energy of adsorption

Typical q:6 - 40 kJ/mol = 0,062 - 0,52 eV /molecule

Physisorption

612 rc

rb

zU

37


H2O

CO2

CO

CH4

O2N2

HeH2

Origin:Electron sharing or transfer between molecules and surface atoms

The well depth is the energy of adsorption

Typical q:40 - 1000 kJ/mol = 0,52 - 10 eV /molecule

612 rc

rb

zU

Chemisorption

38

Gas-solid interactionHow does this affect vacuum?

probability per second that a molecule will desorb

O2

Molecule trapped in the adsorbed state at temp. Tpotential well of depth qDilute layer (no interactions with other mol.)

How long does it stays?

Surface atoms have Evib = h = KBT = KBT/h

At RT = 0.025/(6.63 × 10−34 ÷ 1.6 × 10−19) = 6 × 1012 s−1 1013 s−1

= number of attempts per second to overcome the potential barrier and break free of the

surface.

Boltzmann factor

TKq

Beprobability that fluctuations in the energy

sharing will result in an energy q

TKq

Be

39


probability per second that a molecule will desorb

O2

TKq

Be

p(t) = probability that it is still adsorbed after elapsed t

p(t+dt) = p(t) x (1-dt)

probability of not beingdesorbed after dt

dp = p(t+dt) - p(t) = - dt p(t)

pdtdp

tetp

average time of stayTKq

aBe

11

40


O2

average time of stay TKq

aBe

11

At RT 1013 s−1

TKq

aBe1310

97 kJ / mol = 1 eV / molecule

Temperature dependance

Molecule dependance

Note: Simple modelNeglects all other interactions, surface diffusion, adsorption sites so a can change

41

DesorptionP = 1000 mbar P = 10-7 mbar

Equilibrium

pumping

Far from equilibrium till….

tq

qG1Experimental

relation Gas flux /area

hGqq11

ht

t1

= 1 for metals = 0.5 for elastomers

= 0.5

= 1

q1 5x10−8 mbar L s−1cm-2

TKNpV Bat1 mbar L Nat 2.46x1019 Outgassing rate 1012 molec s−1cm-2

42

Desorption

How important is the molecule/surface interaction energy? H2O

N2TKq

aBe1310

Rate of desorption

aa

des

a ndtdn

1

TKq

des

a Bedtdn

1310

Simple model calculationidealized UHV system RT, V= 1 L, A = 100 cm2

S = 1 L/sonly gas source: initially complete ML of specified binding energy adsorbed at the wall

fall of pressure at RT

q

43

Outgassing

Origin of fluxes:

Permeation

Adsorption

Solubility

Desorption

Gas is continuously released, (at relatively small rates) from wallsPrincipally water vapor

Limit to attainable vacuum achievable in reasonable times (hours) ∼10−6 mbar

44

Gas-solid permeation

p1 = 1000 mbar

Residual Gas

H2O

CO2

CO

CH4

O2

N2

p2 = 1x10-8 mbar

HeH2

45

Gas-solid permeationp1 = 1000 mbar

Residual Gas

p2 = 1x10-9 mbar

Permeation is acomplex process Adsorption

Dissociation

Solution into the solid

Diffusion

Recombination

Desorption

46

Gas-solid permeationp1 = 1000 mbar p2 = 1x10-9 mbar

Permeation processcan be quantified troughPhenomenologicalquantities

permeability

=Q/(p1-p2)A

Q=flux trough wallA= unit area

[Q] = [p][L]3[t]-1

=[L]3[t]-1[L]-2

m3s-1m-2 ls-1cm-2

Residual Gas

47


Kp = Permeability coefficient

For a given gasA = wall area d = wall thickness

dA

pfpfKQ pp 21

m3s-1m-1Pa-1

He

cm3s-

1cm

-2 P

a-1

p = 13 mbard = 1 mm

pppf ,

depending on diffusionmechanisms

48


Metal – gas Kp

Glass Metals Polymers

He, H2, Ne, Ar, O2

No rare gas All gases

p p p

Table of gas permeability

49

Solubility

Is the quantity of substance A that can be dissolved in B at given T and p

For a gas

Gas quantity dissolved in solid volume unit at standard conditions

For undissociated molecular gas (interstitial)

c = gas concentration Henry’s law

Valid for low concentrations and for glass and plastic materials

No formation of alloys

psc

50

Solubility

For dissociated gas

Sievert’s law

Valid for low concentrations and for metals

Interstitial or substitutional

psc

H2 on metals

Note the high solubility of H2 in Ti,Zr

51

Vacuum Pumps

Capture pumps

• Pistons• Gears• Turbines• Jet stream

• Cold traps• Ionization• Getters

Throughput pumps

Differences: pressure range, speed, gas selectivity

52

Pressure Ranges Spanned by Different Vacuum Pumps

More than one pump to HV and UHV

53

What pump to use?

S = [L]3[t]-1Pumping speed S = Q/p

pSdtdp

Vfrom

p = inlet pressure

dtdp

ppV

Su

For a pressure range where S does not depend on p, i.e. the pumping speed is constant

dppp

VSdt

u )log( uppVSt

10lnV)log( S

tpp u

Compression ratio: inlet

out

pp

CR

This can be used to measure Sor to estimate the time to reach pu

• Depends on the gas type• S varies with p

54

• Ultimate pressure

• Time to reach the u.p.

• Residual gas composition

• Other (absence of magnetic fields)

What pump to use?

55

Rotary Roughing Pump

Pu: 10-2 mbar

Rotor blade

Eccentric rotor

inlet

Exhaust valve

Spring

Cylindricbody

Oil

S: 2,5 ÷ 102 m3/h 0.7 ÷ 28 l/s

1 m3/h = 0.28 l/s

CR: 105

Starting operating pressure: 103 mbar

56

Dual stage Rotary Roughing Pump

Pu: 10-3 ÷ 10-4 mbar

Advantages

• No saturation• Heavy duty• Low cost (2500 €)

Disadvantages

• Oil backstreaming• Need traps for oil vapor• Noisy

Rotor blade

Eccentric rotor

inlet

Exhaust valve

Spring

57

Rotary Roughing Pump: gas ballast

CR=105

Op. tempT 70 °C

Pump water vapor at 70 °Cwhen P reaches 3.3 104 Pa

The vapor liquefies and does not reach P > 1 105 PaSo the exhaust valve does not open

The vapor remains inside the pump and is mixed with oil

Decrease pump speed, and can damage the rotor by increasing the friction

The gas can liquefyinside the rotation chamber

Vapor pressure

58

Rotary Roughing Pump: gas ballast

Ballast valve

Solution: gas ballast

NO gas ballast Gas ballast

liquid

The valve is set to decrease the CR to 10

The vapor does notliquefy

59

Diaphragm Pump

HousingValvesHead coverDiaph. clamping discDiaphragmDiaphragm supp. discConnecting rodEccentric bushing

Pu: ~ 1 mbar

CR: 102 103

Starting operating pressure: 103 mbar

60

Diaphragm Pump

Advantages

Oil-freeNo saturation

Low cost

Disadvantages

High ult.pressure (4 mbar)Low pump speed

Noisy

61

Root Pump

Advantages

Oil-freeNo saturation

High throughput

Disadvantages

Need prevacuumMedium cost

delicate

Eight-shaped rotor turningin opposite direction

•Clearance between rotors ~ 0.3 mm•No lubricants •CR depends on clearance

62

Root Pump

S and CR of a root pump dependon the preliminary pumpinstalled ahead

The gas flux is the same for both pumps

root palette

prpp

patm

SpSr

pprr PSPS

r

pr P

PCR

rpr CRSS

Palette: 60 m3/h = 16,8 l/s Sr = 16,8 x 40 = 672 l/s

63

Turbomolecular Pump

Pu: 10-10 mbar

S: 50 ÷ 5000 l/s

CR: 105 109

Starting operatingpressure: 10-2 mbar

64

Turbomolecular PumpPrinciple of operation

High pressure side

Low pressure side

The pumping action is provided by the collisionsbetween blades and molecules

Molecular regime

The speed distribution (ellipse) depends on the angle betweenV and blade

65

Turbomolecular Pump

Pumping speed: depends on gas type

Residual gas: H2After bake out

66

Compression Ratio of a Turbomolecular Pump

67

Turbomolecular Pump

Advantages

No saturationClean (magnetic)

UHVAny orientation

Disadvantages

CostDelicate

Quite noisy

70 l/s ~5000 €250 l/s ~10000 €

2000 l/s ~23000 €

Rotor suspension

Ball bearings (lubricant required)

Magnetic (lubricant absent)

68

Molecular drag pump

Turbo disk

Threaded stator

Cylindrical Rotor

Forevacuum flange(outlet)

Threaded stator

Safety ball bearing

Gas entry

Magnetic bearing

Lubricant reservoirElectrical socket

Operating principle:Same as turbo but different geometry

No blades but threads

69

Molecular drag pump

Pu: 10-7 mbar

S: 40 ÷ 100 l/s CR:H2: 102 109

He: 103 104

N2: 107 109


They are use in combination with turboin a single mounting so

Use a low CR backing pump(i.e. membrane for clean

operation)

Higher backing vacuum pressure

70

baffle

vapor diffusion pump

Fluid is heated and ejected from nozzles at high speeddue to the nozzle shape and pressure difference betweeninside and pump cylinder.Fluid speed up to Mach 3-5The gas molecules are compressed to the pump base through collisions with oil vapor

71

vapor diffusion pump

Advantages

No saturationHeavy duty

Low cost

Disadvantages

gas reactionLiquid vapor tension

ContaminationNeeds water cooling

Pu: 10-9 mbarS: 20 ÷ 600 l/sStarting operatingpressure: 10-2 mbar

The pumping speed and the pressure strongly depends on oil type

72

Getter pumps

The active material is sublimatedby thermal heating

Sublimation getters

- Gas-surface chemical interaction- Chemisorption- Solution of gas inside material

Pumping mechanism

Non evaporable getters

The active material is constituted by porous medium

73

Sublimation getter pumps

Sublimation getters


Ti or Ti – Mo filaments

Pumping mechanism

The material form a thin filmon the pump walls that becomesthe active layer

The molecules are chemisorbed on the film

74

Non evaporable getter pumps

Cartridge of porous material (Zr-16%Al)

Pumping operation

Problem: saturation of getter material requires cartridge change

Activated by heating (750 °C) and keptat operating T 300 °C to increasemolecule diffusion

75

sublimation

S strongly depends on gas

> 103 l/s

Zr-Al

Getter pumpsPum

pin

g s

peed (

l/s)

A’= sublimation, A=non evaporable

Non evaporable

800- 2x103 l/s

S depends on active surface saturation

AmT

S

mass

area

Adsorptionprobability

76

Gas-surface weak interactionPhysisorption anddiffusion into the bulk

Plus: Wall cooling

Pressure limit:10-10 ÷ 10-12 mbar

Advantages

Pump H2

Heavy dutyLow cost

No contamination

Disadvantages

SaturationMetal vapours

No rare gas pumping

Stripes of active material

Getter pumps

With a number of panelsone can obtain S > 1x104 l/s

But if warmed it releases the gas

77

Ion-getter pump

7 KV

~1 Tesla

Ti


Pumping mechanism

- Ionization of gas molecules- Burying inside the active material

Ion-getter with cathodic grinding

78

Basic processes occurring within a single cell

• e- ionize molecules• Secondary e- ionize molecules

Ions are accelerated to cathodes

• produce secondary e-

• grind up cathode material• make craters

Ions buried intocathode material

Produce cathode vaporsDepositing also on anodesto work as getters

H2: accumulates into the cathodes Need regeneration by annealing

79

Ion-getter pump

Advantages

Heavy dutyNo traps

No contaminationAny mounting position

Silent

Disadvantages

High magnetic fieldsLow pump S for H2

Medium - high cost


S: 4 ÷ 1000 l/s Starting operatingpressure: 10-3 10-4 mbar

80

Adsorbing pumps

Liquid N2 cooledAdsorbing material

- Gas – cold surface interaction- Physisorption

Pumping mechanism

Adsorbing porous materialHigh surface/volume ratio

ZeolitesAl2O3, SiO2

H2O and N2 pumping

Liquid He cooledCold walls- Gas – cold surface interaction

- Physisorption, condensationPumping mechanism

Cryogenic pumps

81

Cryopump

- Gas – cold surface interaction- Physisorption and condensation

Pumping mechanism

Metal wall

82

Cryopump


Advantages

Heavy dutyNo contamination

Low cost

Disadvantages

SaturationNoisy

Needs other UHV pumps

The gas condensationif gas pressure > vapor pressureat wall T

S: 4 ÷ 100 l/s


vapor pressure

83

Ionization in gases

Type of collisions:- neutral Molecule – electron - neutral Molecule – ions- neutral molecule – neutral molecule (Penning)- radiation absorption- neutral Molecule – hot metal surface

-

+

-

Ionization of a molecule (atom) from collisions with e-

Ion - Ion +

--

84

Ionization in gases Ionization energy

eV

Ion +Electron affinityIon -

-

+

-

-

-

Less probableMore probable

85

Collision type:- elastic- atom excitation- molecule dissociation- Ionising ( e)

Relative energy loss

Atom or neutral molecule – electron collision

collision after 2

collision before 2

22

21

2

1

vmE

vmE

ek

ek

ek

kk KE

EE

1

21

2

2vm

Egask

21

1mmmm

E

EK

e

e

k

k

egas

mm

K ee

e

kk

mm

EEgas

1

64 1010 mme

Very small energy losses

Elastic collision

for gas molecules

86

Total energy lossik

L

ieEK

/

e- suffers very small energy loss for each elastic collision

e- mean free path e = average space between two elastic collisions

e- collision rate e = collisions number per unit time

eetL

number of collisions tL

ee

Elastic collision

L

87

Apply external electric field E

e

ek K

eEE

2

prTkB

e

12

Maximum kinetic energy of an e-

moving in a gas

pE

rTk

K

eE B

ek 22 Depends on electric field

and pressure

Elastic collision

eemeE

v

maxIf e- has vin~ 0

88

Ionization

Ionization energyie

eB

ek W

K

eEpE

rTk

K

eE

22 2

e- can ionize an atom

if

But it can also

- Increase the atom kinetic energy- Excite an e- to unoccupied bound states

Ionization probability i = ionizing collisions/total collisions

-

-

+

89

Ionization

Long path to produce more ions

But it can also- e- trapped inside atomwith formation of negative ions -

pe

ii

-

e- with Ek --- constant pressure --- unit lenght

electron incidention) (e of number -

i

Specific ionization coefficient

collisions number tl

ee

Due to practical measurements

e- can ionize an atom

90

Vacuum measurement

Different types of vacuometers depending on pressure range

Mechanical, thermal, ionization

91

Vacuum measurement

MechanicalBourdon

To vacuum

Membrane

Pin wheel

tube

index

105 102 Pa(103 1 mbar)

The tube curvature changeswith pressure

Needs calibrationPrecision: 1-2% fsr

105 102 Pa(103 1 mbar)

The membrane or bellow bendswith pressure

Needs calibrationPrecision: 1-2% fsr

pR

x T4

2

0

92

Thermal conductivity vacuometers

Pirani

heated filament

The filament temperature, and hence the resistancedepends on heat dissipation in the gas,

i.e. on the gas pressure

Pressure variation means T variation i.e.resistance variation.

This is measured through the W. bridge V variation

TKTTKpRR

RRV

W fgasf

4

2

32

32

93

Thermal conductivity vacuometers

unbalanced

Hence

Thermaldissipation

radiativedissipation

contactdissipation

For small p, the reference bridge is

TKTRR

RRV

W ff

4

2

32

32

00

TKpRR

RR

VVWW gas

f

2

32

32

02

0

The pressure is obtained by measuring the Wheatstone voltage

)(cos 20

2 VVtp

In general it dependson the gas type

= cost Stephan-Boltzmann=wire emissivity

Kgas= gas thermal conductivityKf= wire thermal conductivity=coefficient

TKTTKpRR

RRV

W fgasf

4

2

32

32

94

Ionization vacuum gaugesHot cathode Cold cathode

Based on gas ionization and current measurements

95

Ionization vacuum gauge

I+ = I- i e p

Sensitivity K = σi · λe

Directly proportional to pressure Sensitivity K = i e

I+ = ion current i = specific ionization coefficient

I- = electron currentfrom filament

e = electron mean free path

The gauge measure the total pressure

Range: 10-4 – 10-12 mbar

K depends on gas, gauge geometry,gauge potential

Usually one increases by designing the gometry

96

Ionization vacuum gauge

electrons from gas or field emissionsimilar to the behavior inside the ion getter pumps

Less precise due to problem ofdischarge current at low pressure

1 tesla

Range: 10-4 – 5 x10-10 mbar

Cold cathode

No filament so less subject toFilament faults

Note: discharge starts only by mag fieldto avoid high E field - induced currents

97

Mass Spectrometry

Need to distinguish the intensity of specific gas molecules

Collect molecules

Molecule ionizationSeparation of different molecules

Current measurement

Specific mass = ion mass (a.u.)/ion charge =

n = ion ionization multiplicity

nem

Specific mass of Ar+ = 40

Specific mass of Ar++ = 20

For a single molecule there aremany peaks, depending on n

98

Mass Spectrometry

Specific mass table

99

Mass Spectrometry

detector

Faraday cupAll ions measured

No filamentsLow sensitivity

sturdy

Channeltron - electron multiplyerHigh sensitivity

Delicate

Fast response

To remove secondary electrons

Amplifier time constant large

100

Quadrupole Mass Spectrometry (QMS)

VacuumChamber

Ion source(filament)

Analyser(Quadrupole field)

Detector(Channeltron)

Storing system

Quadrupole field between the rodsIons of varying mass are shot axially into the

rodThe applied quadrupole field deflects the ions

in the X and Y directions, causing them to describe helical trajectories through the mass

filter.

101


r0 = rod separation

U+Vcos(t)

-U-Vcos(t)

20

22 )(r

yxU

Superimpose an oscillating field Vcos(t)

The forces are uncoupled along x,y,z axis

Quadrupole potential

102


ion equation of motion2

0

22 ))(cos(r

yxtVU

Constant speed along z0

0)cos(2

0)cos(2

20

20

zm

ry

tVUeym

rx

tVUexm

Stability parameters

20

2

20

2

4

8

rmeV

q

rmeU

a

2t

0

zm

yeym

xexm

103


Solved numerically for different a and q

0)2cos2(

0)2cos2(

2

2

2

2

yqad

yd

xqad

xd

All solutions outside are imaginaryand give increasing oscillation amplitudes

Neutralization of the ions on the rods

Ions oscillate in the xy planeOnly some e/m values reach detector

Solutions inside are real (stable trajectory)

104


Zoom to region I

0)2cos2(

0)2cos2(

2

2

2

2

yqad

yd

xqad

xd

The line shrink to one pointOnly one ion with m/e ratio can reach detector

336,02

qa

VU

Stable solutions

20

2

4rq

Vem

fixed U, V and the overall ion motion can (depending on the values of a and q)

result in a stable trajectorycausing ions of a certain m/z value

to pass the quadrupole

20

220

2

4

8rm

eVq

rmeU

a

V=V0cos(t)for

qa

105


Zoom to region I

The line enter the stable solutions region

336,02

qa

VU

Work line

All the ions with a/q on the line will reach detector

20

220

2

4

8rm

eVq

rmeU

a

V=V0cos(t)

for

Reducing U relative toV, an increasingly wider m/z

range can be transmitted simultaneously.

q

the width q of the stable region determines the resolution.By varying the magnitude of U and V at constant U/V ratio

an U/V = constant scan is obtained ions of increasingly higher m/e values to travel through the quadrupole

106

Quadrupole Mass Spectroscopy (QMS) profiles of the residual gas

p ≈ 3x10-7 mbarBefore bake-out

p ≈ 5x10-11 mbarAfter bake-out

H2O

CO+N2

CO2

H2OH2

107

VACUUM SEALING

Clamps

Low Vacuum

No bake at high temperatures

Reusable

Viton rings

108

UHV

VACUUM SEALING

HV

Bake at high temperatures

Reusable (maybe once)

Plastic deformationand shear

109

VALVES

Diaphragm

Butterfly

110

VALVES

Dynamometric sealing

StemAll metal

111

VALVES

Gate

Leak

High conductanceUHV to air compatible

Large clearance for instrumentsBakeable

112

FEEDTHROUGH

Multi-pin for signal or

Low currents

Multi-pin for high currents

113

MANIPULATION

Rotation

1 Metodi sperimentali della fisica moderna Luca Gavioli Dipartimento di Matematica e Fisica...

Documents

Transcript of 1 Metodi sperimentali della fisica moderna Luca Gavioli Dipartimento di Matematica e Fisica...