3 Vacuum Basic Concepts

Dr. G. Mirjalili, Physics Dept. Yazd University

Vacuum Techniques

Basic vacuum concepts


Vapor Pressure

• Terminology:– Evaporation: when a liquid becomes a gas

– Sublimation: when a solid becomes a gas

– Vapor: the gas produced when a liquid or solid is evaporated

– Condensation: when the vapor becomes a liquid or solid again (condensed phases)

– Equilibrium: the state of any system in which opposing forces balance each other

– Volatile: liquids that are easily vaporized - have high vapor pressure


Vapor Pressure

• Evaporation occurs when:– the temperature of the material is increased, OR

– the pressure at the surface of the material is decreased

• Vapor Pressure: the pressure at which a liquid or solid becomes a vapor at a given temperature– what happens to the vapor pressure as the temperature is

decreased?

• Outgassing: when a material in its condensed phase becomes a vapor in a vacuum system at low pressure.– Extremely small quantities of water, solvents, or fingerprints left in

a chamber can outgas and increase the time it takes to pump a system down.


Vapor Pressure

• Liquids in a closed container will evaporate until:– partial pressure in the air above

the liquid = vapor pressure of the liquid


Vapor Pressure


Vapor pressure of water at various temperatures

T (O C)

100

25

0

-40

-78.5

-196

P (mbar)

1013

32

6.4

0.13

6.6 x 10 -4

10 -24

(BOILING)

(FREEZING)

(DRY ICE)

(LIQUID NITROGEN)


Vapor Pressure• Phase Diagrams:

– determine what state a substance will exist in at a given temperature and pressure

– example: water


Vapor Pressure• Phase Diagrams:

– water metals

http://www.lsbu.ac.uk/water/phase.html


Vapor Pressure

• Examples:– At what temperature does water boil when the pressure is

reduced to 1 torr?– Are the condensed phases to the left or right of the lines?– If a CVD system runs at 500C and 1 mT, which metals

would be a poor choice to build the chamber out of?• The Moral of the Story:

– Vapor pressure must be considered when selecting EVERYTHING that goes into a vacuum system.

– This includes seals, oil, chamber materials, valves, the wafer, etc.


Gas Density (n)Ideal Gas Law

PV = NkT

Gas density at 1 Pascal at room temp.

N/V = n = P/kT = (1 N/m2)/(1.3807x10-23J/K)(300 K)= [1 (kg-m/s2)/m2]/[4.1x10-21 kg-m2/s2]= 2.4x1020 atoms per m3

= 2.4x1014 cm-3 …at 1 Pa

Rule of Thumb

n(T) = 3.2x1013 cm-3 x (300/T) …at a pressure of 1 mTorr


Mean free path(1) average distance between molecular collisions in the gas

cm)Torr(p

10×5=

σp2

kT=

nσ2

1=λ

3

= molecular cross section ~ projected area of the molecule (the last form of the equation is for air at 20oC)

p (Torr) (molec./cm2-s) 760 2.9x1023 67 nm

1 3.8x1020 51 m

1x10-3 3.8x1017 51 mm

1x10-6 3.8x1014 51 m

1x10-9 3.8x1011 51 km

When > the smallest dimension of the flow path, the flow is free molecule,If < apparatus dimension, the flow is viscous

Or, =.0066/P (P mbar)


Mean free path(2) • Mean Free Path:

• MFP increases as the pressure decreases: (cm) ~= .005 / P (torr)

– at 1 atm, MFP = 0.02 microns

– at 1mT, MFP = 5.08 cm– at 10-9 torr (UHV), MFP = 50 km

Mean Free Path vs. Pressure

1.00E-061.00E-041.00E-02

1.00E+001.00E+021.00E+041.00E+061.00E+08

1.00E-10

1.00E-08

1.00E-06

1.00E-04

1.00E-02

1.00E+00

1.00E+02

1.00E+04

Pressure (Torr)

MF

P (

cm

)

MFP


Mean free path(3)

Molecular density and mean free path

1013 mbar (atm) 1 x 10-3 mbar 1 x 10-9 mbar

#mol/cm3

MFP

3 x 10 19

(30 million trillion)4 x 10 13

(40 trillion)4 x 10 7

(40 million)

2.5 x 10-6 in6.4 x 10-5 mm

2 inches5.1 cm

31 miles50 km


Collisions and Mean Free Path

Gas Densityn = P/ kT

n

Cross-section~ d2

d

Rigorous Hard Sphere Collisions: = kT / 2 d2P

Arcm8 / P (mTorr)15 22.6 10 cm Ar


Atom & molecule dimensions

• Atom dimension=3 A0

• Average molecule separation in at atm perrsure :

In 1 cm3 nitrogen gas is 2.5 X1019 molecules so:

1/2.5X10 19= 4X10 -20 cm=34 A0


Average molecular separation

• At atmospheric Pressure:

• 2.5X10 19 molecules occupy 1 cm3;

• the volume of one molecules =1/2.5x10 19 =4x10 -20 cm3

• the length of each molecules =(4x10 -20 )1/3=3.4x10 -7 cm=34 A0

3 A0

34 A0


Impingement rate/flux, J per unit area, surface incidence rate

21

21

)2(

)2(

14588

4

MRT

PNJ

RkN

mNM

mKT

PJ

M

T

M

RT

m

kTV

VnJ

av

av

av

1cm2


Maxwellian Distribution

kT

mv

evkT

mNvN 222

3 2

)2

(4)(

kT

mdvev

kT

m

N

N

N

vdvevkT

mN

N

vdvvN

v v

kT

mv

2)

2(

4)

2(4)(

2

2

0

32

30

222

3

0

20

3

2

12

dvev v

m

kT

m

kT

kT

mv

8

)2

(2

1)

2(4 22

3

The speed of molecules whose speed is between v, v+dv


Maxwellian Distributionvrms

0

42

3

222

3

0

2

2

2)

2(

4)

2(4)(

2

2

kT

mdvev

kT

m

N

N

N

dvvevkT

mN

N

dvvvN

v v

kT

mv

m

kTvv

kT

mv

rms

3

8

3)

2(4

2

52

32



m

kTv

vkT

mvve

kT

mvvve

kT

mN

evdv

d

kT

mN

dv

vdN

dv

vdN

p

kT

mv

kT

mv

kT

mv

2

0)2(0)2

22()

2(4

0)()2

(4)(

0)(

22

222

3

222

3

22

2


Surface incidence rate

kT

mv

kT

m

v

vPvf

2exp

24

)()(

22/3

2

0

2_ 8

4)(m

kTdvvvfvcv

vndvvfvnvnZv

zzz 4

1)( 3

0


Average speed of an atom:

Flux of atoms to the x-y plane surface:

(Campbell)

Very important!


Surface incidence rate rate at which molecules of gas strike a unit area of surface (also exit a vessel with a small orifice into a vacuum)

mkT

p

m

kT

kT

pvnJ

2

841

41

scm

surfacestrikingmolecules

MT

)Torr(p105.32

22

• n = molecular density in gas, molecules/cm3

• = mean velocity of Maxwell Boltzmann distribution• k = Boltzmann’s constant• m = mass of molecule• T = absolute temperature in Kelvins (K)

The numerical form is obtained by multiplying numerator and denominator by Avogadro’s number, NAv, and noting that NAvk = R, the gas constant and NAvm = M, the molecular weight of the species in the gas

v


Example

A vacuum chamber has a base pressure of 10-6 Torr. Assuming that this is dominated by water vapor, what is the flux of H2O to a substrate placed in this chamber?

n = 3.2x1013 cm-3/mTorr * 10-3 mTorr = 3.2x1010 cm-3

<v> = (8kT/M)1/2 = 59200 cm/s

z = (¼)n<v> = 4.74x1014 molecules per cm2 per sec!

This is approximately one monolayer of H2O every secondat 10-6 Torr base pressure.


Equilibrium between a liquid and it vapor

Ec JmkT

PJ

210

)2(

P0= saturation vapor pressure


Collision frequency

• V=xt• The average distance traveled in one second :

V=x(1)• Collision frequency=V/l l= mean free path

• For N2 (at room temperature and atm pressure

• C.F=470/6.6x10 -6 =7.1x10 9 per second

• at low pressure C.F increase or decrease?• At which pressure the C.F is 1 second?


n, J, l at various P for N2 at 295K• P(mbar) n(m-3) I(M.F.P) J(cm-2 m-1)

103 -1 atm 2.5X10 25 6.6X10-6 2.9X10 23

1 2.5X10 22 6.6X10-3 2.9X10 20

10-3 2.5X10 19 6.6 cm 2.9X10 17

10-6 2.5X10 16 6.6 m 2.9X10 14

10-10 2.5X10 12 660 km 2.9X10 10


Outgassing

• The release of gas from internal surface into the vacuum, occurs by desorption of molecules from bound states on the solid surface.

vacuum

Outgassing

Chamber wall molecules

Absorbed molecules


adsorption & absorpbtion

Adsorption Absorption

Adsorption Absorption

Desorbtion = removing the molecules

q

q adsorption=15-32 kcal/mol q absorption =2-10 kcal/mol


Meam adsorption stay time

• Adsorb molecules have limited lifetimes on the surface

• kT at room temperature is 1/40 eV

• Meam adsorption stay time is the avarege lifetimes of an adsorbed molecules ()

• =10 -13 exp(q/kT)=10 -13 exp(40q)

• “De Boer equation”


Meam adsorption stay time

• Values of for various q at 295 K

q(eV) 0.2 3x10 -10

0.4 1s

0.6 20 ms

0.9 400 s

1.1 1.2x 10 6 s (= 2 weeks)


Gasses and pumping

Drifting molecules

Adsorb molecules

Outgassing

pump


Gas flow and throughput

• Gas flow down a pipe

P1 A Flow A` P2

P1>P2

Pressure is constant across any cross section

We define throughput as:

0PVdt

dVPQ mbar l s-1

Q is constant down the pipe


Q is constant down the pipe

Usually, throughput is conserved. (Steady state

Q Q Q

Q = P1V`1=P2 V`2=P3V`3

P1P2 P3

V1

V2 V3


Q = P1S1 = P2S2

pump 25 ℓ/s

pump 1500 ℓ/s

P1

P2

P2 = 100 P1

Throughput: quantity of gas removed by pump per unit time:

Q = p(dV/dt) = pS (Torr-liter/s)

Throughput (example)


Mass flow rate and throughput

kT

Qm

dt

dNm

kT

Q

dt

dNkT

PV

dt

dV

kT

P

kT

PVdtd

dt

dN

NkTPV

0

))(())((

Example: A fan moves atmospheric air through a room at rate of 0.9 m3 per minute. What is the through in (mbar litter s -1)

Answer: 0.9 m3=900 l and V`=900/60=15 l s-1

Q = PV`=1000x15=15000

Mass flow rate


Speed

1

0

lsP

QS

PPVdt

dVPQ

dt

dVP

Where gas enters a pipe from a vessel and where it emerges from the pipe to enter a pump . The volumertic flow rates V` is defined as the speed Pump speed: volume of gas taken in by the pump per unit time


S and S*

SS*

vessel

pumpQ

S*>SS/S*=1 Perfect system


Conductance

Conductance – gives the capacity of a tube to allow a volume of gas pass from one end to another in unit time

P1 P2Q

C=Q/(P1-P2)

P1-P2

P1>P2


Speed of pump at the vessel

S, P

C

S*, P*Q

Q=SP

Q=C(P-P*)=SP=S*P*

S=S*[C/(S*+C)]

The relation between S, S*, C

Vesselpump


Pumping Speed

• Pumping Speed and Conductance are related as follows:

Seff is the effective pumping speed at the chamber

Sp is the pumping speed (capability) of the pump

Ctotal is the total conductance of the system between the chamber and the pump.

TPEFF CSS

111 Sp

CT SEFF


Vacuum system & electrical system

V1 V2P1 P2

V

Battery =Pump

P V

Q I

P=ZQ

V=RI

P=Q/C

C=1/Z

C=Q/(p1-P2)

P


Conductance• Conductance: the ease with which a gas is drawn

through a vacuum component (pipe, valve, etc.)– conductance is dependent on the diameter, length, and shape

of a pipe or orifice

• Conductance Units: volume/time

– liters/second

• Conductance can be the LIMITING factor in a pumping system:

– Example: A pump that has a pumping speed of 400 l/sec, that is pumping through a conductance of 100 l/sec, is reduced to an effective pumping speed at the chamber of less than 100 l/sec.

Answer:S*=400 l/sec, C=100 l/sec S=?

S=S*[C/(S*+C)]

S=400[100/(400+100)]= 80 l/sec


Viscous and Molecular Flow

Viscous Flow(momentum transferbetween molecules)

Molecular Flow(molecules moveindependently)


Flow regims

• Viscous Flow: “mob mentality”– the type of gas flow that occurs when

gas molecules are so close together that there are constant collisions

– mean free path is relatively short– gas flows like a liquid from high

pressure to lower pressure– predominantly in the rough vacuum

regime


Flow regims • Molecular Flow: “loner mentality”

– the type of gas flow that occurs when gas molecules’ direction of movement is completely random (not necessarily towards lower pressure)

– there are few collisions between molecules in the chamber

– mean free path is long

– predominantly in the high and ultra-high vacuum regimes

• Knudsen Flow (or Transition Range)– transition region between viscous and molecular flows

(some behaviors from both)– medium vacuum regime


Flow Regimes

Mean Free PathCharacteristic Dimension

Viscous Flow: is less than 0.01


Molecular Flow: is greater than 1


Transition Flow: is between 0.01 and 1

()

(d)

VT

M

P

C


Knuden`s Number

/d=10.01Viscous flow Molecular flow

T.F


Flow Regims • Which flow regime you are in determines the type of vacuum

hardware you will be using:• Viscous Flow:

– displacement pumps: rotary vane, roots, diaphragm

– direct pressure gauges: manometers, bourdon tubes

– elastomer seals

– less limited by the conductance of the system

• Molecular Flow:– momentum transfer or entrapment pumps: turbo, ion, cryo

– indirect pressure gauges: ion gauges

– metal seals

– VERY limited by the conductance of the system

• More on these later ...


Conductance in Viscous Flow

Under viscous flow conditions doubling thepipe diameter increases the conductance Sixteen(16) times.The conductance is INVERSELY related to the pipe length


Conductance in Molecular Flow (round long tubes)

Under molecular flow conditions doublingthe pipe diameter increases the conductanceeight times(8).The conductance is INVERSELY related tothe pipe length.


Calculation the usal pipes conductance

Conductance in usual pipes

(molecular flow)

CL

C0

L

Lpipe CC

CCC

0

0


Molecular flow conductance of an aperture(1)

P1, J1, n1

P2, J2,n2

J1 J2

)(2

)(2

)2(

)(

)(

2121

210

21

PPAm

RTPPA

m

kTQ

mkT

PJ

dt

dNkTQ

AJJdt

dN


Molecular flow conductance of an aperture(2)

Am

RTC

PPAm

RTQ

PPCQ

2

)(2

)(

0

21

21

Conductance of an aperture

C0=9.3 D2 l/s -1 for a circular aperture

Maximums speed of a pump:

S*=C inlet=C0= 9.3D2


Transmission probability

WJ1 A

J1

WJ2 A

J2

0210

0

2121

21

21

)(2

)(2

)(2

)(

)(

WCCPPWCQ

AM

RTC

PPAWM

RTPPAW

m

kTQ

AWJJkTQ

kT

AJJW

pipe


Calculation of the C for Long and usual pipes

sec/81.33

litM

T

l

dCL

sec/2

1038.1 214

2 litpp

l

dCL

Conductance in viscous flow (long pipes)

Conductance in molecular flow (long pipes)

Conductance in usual pipes (molecular flow)

L

Lpipe CC

CCC

0

0


Calculation the transmission probability

M

RT

L

dCL

26

3

AM

RTC

20

L

Lpipe CC

CCC

0

0

Ld

C

dL

C

CC

CC L

L

Lpipe 3414311

0

0

0WCC pipe dL

W431

1


Conductance


SYSTEM

PUMP

C1

C2

Series Conductance

RT = R1 + R2

1 = 1 + 1C1 C2CT

1 = C1 + C2

C1 x C2CT

CT = C1 x C2

C1 + C2


Pumping Speed

• Pumping Speed and Conductance are related as follows:

Seff is the effective pumping speed at the chamber

Sp is the pumping speed (capability) of the pump

Ctotal is the total conductance of the system between the chamber and the pump.

TPEFF CSS

111 Sp

CT SEFF


pump500 ℓ/s

P1,

P2

connecting tube, conductance

S1

S2

21 S

1

C

1

S

1

L

D12C

3

D = diameter, in cmL = length, in cmC = conductance, in ℓ/s

example 1D = 15 cmL = 20 cmC = 2025 ℓ/sS1= 401 ℓ/s

example 2D = 10 cmL = 20 cmC = 600 ℓ/sS1= 273 ℓ/s

Pump is expensive. Tube is cheap.

@ molecular flowC


Sample vacuum situations and calculations

500 l/sec pump + “infinite” conductance

EPS = 500 l/sec

500 l/sec pump + 500 l/sec conductance

1/EPS = 1/500 + 1/500 = 2/500 l/secor EPS = 250 l/sec

two 500 l/sec pumps connected in parallel

EPS = 500 + 500= 1000 l/sec

S1

S2 C

1/S1=1/C+1/S2



EPS = 100 l/sec

maximum pressure0.03 torr

throughput pressure pumping speed

Problem:If the effective pumping speed from a chamber is 100 l/sec and the chamber pressure must not exceed 0.03 torr, what must the gas flow into (or the throughput out of) the chamber be ?

Solution: maximum throughput = (100 l/sec)(0.03 torr),or 3 torr-liter/second

throughput 3 torr-liter/second

gas flow3 torr-liter/sec

Q=PS



EPS = 250 l/sec

steady-state pressure410-4 torr

Problem:Suppose the effective pumping speed from a chamber is 250 l/sec and we wish to inject a gas flow of 0.1 torr-liter/second flow of gas into the chamber. What will the steady-state pressure be?

Solution: 0.1 torr-liter/second 250 liter/second

throughput 0.1 torr-liter/second

gas flow0.1 torr-liter/sec

= 410-4 torr

P=Q/S



EPS = 67 l/sec

chamber pressure1.510-6 torr

Problem:A calibrated N2 leak of 810-3 sccm is attached to a chamber and the measured pressure is 1.5 10-6 torr. What is the effective pumping speed of the chamber in liters/sec?

Solution:810-3 sccm = (8/60)10-3 standard cc/sec

= (8/60)10-6 standard liter/sec = 760(8/60)10-6 torr-liter/sec = 1.01 10-4 torr-liter/sec

We divide by the indicated pressure to get:1.01 10-4 torr-liter/sec 1.5 10-6 torr

throughput 810-3 sccm

N2 flow810-3 sccm

= 67 liters/sec

standard cm3 per minute

“standard” = “atmospheric pressure”

S=Q/p

1.01x10-4/1.5x10-6


pump 2100 ℓ/s

pump 1500 ℓ/s

Chamber 1

gas inlet, N2

1x10-3 torr ℓ/s

connecting tube1 cm inner diameter10 cm length

gas inlet, O2

1x10-4 torr ℓ/s

Chamber 2

Estimate:

P(N2) in chamber 1

P(N2) in chamber 2

P(O2) in chamber 1

exercise


Conductance Maximum or Minimum?

• Obviously, in most cases, we want to maximize conductance.

• But sometimes, we DO want to limit conductance:– Slow pumping to minimize pressure “shock” to the system.– Throttling to maintain desired pressure in system.


Pumping Speed• Pump speed: volume of gas taken in by the pump per unit time • at the pressure of the pump inlet:

• S = dV/dt (in lit/sec), S f(p)

• Pumping Speed: the rate at which a vacuum pump removes gasses from a system.– Also known as volumetric flow rate

• Pumping Speed Units: volume/time– liters/second or ft3/minute (CFM)

• Pumping Speed and Conductance are NOT synonymous– Conductance is a property of

a component in a vacuum system.

– Pumping Speed refers to the flow of gas across a plane in a system.


Basic equation of flow and pump speed

T

T

QSPdt

dPV

dtQSPdtVdP

)(S

QP Tu

)}(exp{

)(

0 SVtPP

dtV

S

p

dP

Steady state

If QT= 0

)ln()( 0 PPSVt Re-expressed

The time necessary for the pressure to fall from P0 to P


Pump down time

SPt

PV

d

d

S

Vτ

e PP

PV

S

t

P

t/τ-0

d

d

equation for the throughput

exampleV = 1000 ℓS = 500 ℓ /s = 2 severy 2.3, 10 x pressure drop

Why in the real world, it takes much longer from 10-6 torr to 10-7 torr?

Surface outgas

P

t


Examples

1:

In a vacuum chamber, V=40 lit, and S=0.5 lit/s. what is the time taken for the pressure to fall from P0=1000 mbar to 1 mbar?.

t= (40/0.5)ln 10 3=552 s= 9 min

2:

If a volume of 1m3 has to be pumped down from 1000 mbar to 10 mbar in 5 min what is the pump speed?

S=(V/t)ln(P0/P)

S=(1000/300)ln(10 2)=900 lit min -1 =5.4 m3 h-1


Gas Sources• Outgassing: the natural evolution of

species inside the chamber, at low pressure, contributing to the gas load– Sublimation of solid chamber surfaces– Desorption from the walls of physically

adsorbed molecules– Out-Diffusion of gas that has been

absorbed into the grain boundaries of the metal

– Vaporization of liquids or solids in the chamber with relatively high vapor pressure


Backstreaming(1)

•Movement of gases (including pump oil vapor) from pumps into the vacuum chamber. It can be an important issue with diffusion pumps.

•Design of diffusion pumps can make some difference. Placement of a continuous operation cold plate over the diffusion would be the best solution, but it is rarely included in microprobe design.

•Oil diffusion pumps have a long history and are considered by many to be less costly and easier to use in a multiple user facility.


Oil back streaming

2

PRESSURE LEVELS: LESS THAN 0.2 mbar


Backstreaming(2)

– an ideal pump only removes molecules and does not give any back

– real pumps “regurgitate” some gasses back into the system

• oil from diffusion pumps and rotary vane pumps (draw)

– oil-based pumping systems are designed with ballast, anti-suckback valves, and cold traps to minimize backstreaming

– this is the primary reason for the gradual replacement of oil-based pumps with “dry” pumps



Pumpdown CurveP

ress

ure

(m

bar

)

Time (sec)

10-11

10 1 10 3 10 5 10 7 10 9 10 11 10 13 10 15 10 17

10+1

10-1

10-3

10-5

10-7

10-9

Volume

Surface Desorption

Diffusion

Permeation

Documents

3 Vacuum Basic Concepts