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# Physics of Thin Films

## Kinetic Theory of Gasses

Ohring: Chapter 2, sections 1, 2

### Pressure and Vacuum

Many thin film processes involve vacuum.

"vacuum" = lower molecular density than in our atmosphere

results in a lower pressure of gas - so typically measure this

MANY different units are commonly used.

 mbar Pascals (N/m2) atmospheres Torr (mm Hg) microns (µm Hg) psi (lb/in2) dyne/cm2 molecules / m3 1 mbar = 1 100 9.87x10-4 0.75 750 0.0145 1000 2.65x1022 1 Pa = 0.01 1 9.87x10-6 7.5x10-3 7.5 1.45x10-4 10 2.65x1020 1 atm = 1010 10,100 1 760 7.6x105 14.69 1.01x106 2.69x1025 1 Torr = 1.333 133.3 1.31x10-3 1 1000 0.0193 1333 3.53x1022 1 µm = 1.33x10-3 0.133 1.31x10-6 0.001 1 1.93x10-5 1.333 3.53x1019 1 psi = 68.94 6.89x103 0.068 51.71 5.17x104 1 6.89x104 1.83x1024 1 dyne/cm2 = 0.001 0.10 9.87x10-7 7.50x10-4 0.75 1.45x10-5 1 2.65x1019 1 molecule/m3 = 3.77x10-23 3.77x10-21 3.72x10-26 2.83x10-23 2.83x10-20 5.47x10-25 3.77x10-20 1

### Pressure Conversion Calculator

enter exponents as "e-7"
for example: 5.3x10-7 should be entered 5.3e-7

-- still has some trouble displaying very small or very large numbers --

## Pressure Conversion Calculator

mbar

Pascals

atmospheres

Torr

microns
psi
dyne/cm2
molecules/m3

Composition of gas in vacuum chamber is very different from atmosphere

pumps remove certain gasses preferentially

 Component Volume % in dry air Volume % in ion pumped chamber at 2x10-9 torr N2 78 % trace O2 21 % trace Ar 0.93 % trace CO2 0.03 % 3 % CH4 trace 3 % H2O trace 5 % CO trace 6 % H2 trace 78 %

### Ideal Gas Law

much of vacuum technology can be understood from the ideal gas law

more correctly: the equation of state of an ideal gas

PV = NkT

where

• P = absolute pressure
• V = volume
• N = number of gas molecules
• k = Boltzmann's constant
• T = gas temperature (in K)

### Kinetic Theory of Gasses - Gas Flow

Assumptions:
• Gasses are composed of a very large number of very small particles.
• "very small" => very small compared to the distance between particles
• Particles are always moving rapidly in a straight line.
• Particles exert no forces except during collisions.

Freeze other molecules and examine motion of one molecule:

What is the distribution of velocities ?

determine most properties from this

Maxwell velocity distribution

higher T: shifts curve to right; broadens and lowers it

lighter mass: shifts curve to right; broadens and lowers it

See Figure 2-1 in Ohring.

How fast are the molecules moving ?

k = Boltzmann's constant

T = temperature of the gas (K)

m = mass of the molecule

Not surprising:

The hotter it is, the faster they move.

The lighter they are, the faster they move.

At room temperature:
 Molecule vrms (m/sec) vrms (miles/hour) H2 1700 3790 N2 450 1000 Ar 380 850

How far does a molecule travel before it collides with another molecule ?

l = mean free path

d = diameter of a molecule

n = number per unit volume

For air at room temperature, the mean free path can be expressed as:

P = pressure in torr

l will be in cm.

 Pressure Mean Free Path 1 atm 6.7 x 10-6 cm 1 torr 5 x 10-3 cm 1 millitorr 5 cm 10-6 torr 50 m 10-9 torr 50 km

Gas Flow:

three regimes:
• viscous flow
• mean free path << size of the system (D)
• gas - gas collisions dominate
• molecules "drag" one another along in the flow
• when D(cm) P (Torr) > 0.5
• for air at room temperature
• intermediate (transition) flow
• mean free path comparable to size of system (D)
• complicated flow
• molecular flow
• mean free path >> size of system
• gas - wall collisions dominate
• molecules move independently of one another
• when D(cm) P (Torr) < 0.005
• for air at room temperature

This information is summarized in Ohring Figure 2-3.

### Kinetic Theory of Gasses - Interactions with surface

How many gas molecules collide with a surface each second ?
F = 0.25 n vrms

F = collision rate of gas molecules

n = number of molecules per unit volume

vrms = average velocity of a gas molecule

In terms of things we can directly measure:

F will be in molecules/ cm2 - sec

P is the pressure in torr

M is the molecular weight of the gas molecule

T is the temperature in K

For example:

Nitrogen (N2) has a molecular weight M = 28. If we have a chamber with nitrogen at room temperature (293 K) and a pressure of 1 x 10-7 torr:

F = 3.88 x 1013 molecules/cm2 - sec

How long does it take to form a single complete layer of gas on a surface ?

tm = time to form a monolayer (in seconds)

n = number of molecules per unit volume

vrms = average velocity of the molecules

d = diameter of a molecule

For air at room temperature, we can express this as:

tm = 1.86 x 10-6 / P

where P is the pressure in torr.

 pressure tm 1 atm 2 x 10-9 sec 10-6 torr 2 seconds 10-9 torr 31 minutes

### Vapor Pressure

in equilibrium, a certain pressure ot atoms (vapor pressure) will exist above solid surfaces

Do not make high vacuum chambers out of Zinc. If you heat it to 200 C (476 K) the vapor pressure of Zn is 6 x 10-6 torr.

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