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Physics of Thin Films

PES 449 / PHYS 549

Kinetic Theory of Gasses

Ohring: Chapter 2, sections 1, 2

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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 %

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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)

 

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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.

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Kinetic Theory of Gasses - Interactions with surface

How many gas molecules collide with a surface each second ?

F = 0.25 n v_rms

F = collision rate of gas molecules

n = number of molecules per unit volume

v_rms = 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 ?

t_m = time to form a monolayer (in seconds)

n = number of molecules per unit volume

v_rms = average velocity of the molecules

d = diameter of a molecule

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

t_m = 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

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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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