# Evaporation Thermodynamics of evaporation

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27 Οκτ 2013 (πριν από 4 χρόνια και 8 μήνες)

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1
Evaporation
• Purpose
– Thermal evaporation of source material
– Transport to the wafer in high-vacuum
• Thermodynamics of evaporation
– Review of some basic thermodynamics
– Evaporation of alloys, phase properties
– Transport to the wafer
Thermodynamics of evaporation
• (a) Closed system. Equilibrium between vapor, v, and
condensed phase, c, (solid or liquid)
– Saturation vapor pressure
– Dynamic situation, Q
c
= Q
v
2
Closed system
• First law of thermodynamics
– dq = dw + dU
• U = ε
kin
+ ε
pot
, ε
pot
> ε
kin
Entropy
• Process involving changes in T and p
• Carried out slowly (close to equilibrium)
• System brought back to original state

 0dS
T
dq
Second law of
thermodynamics
3
Second law
• Clausius definition of entropy: dS = dq/T
• Reversible process
– Total S constant
• Irreversible process
– Total S increases
– (all ”real” processes are irreversible)
• Entropy increase: a measure of the degree of
randomization of energy
Statistical definition of S
• S = k lnΩ
– k = Boltzmann’s constant
– Ω = number of accessible states
• Example
4
Towards equilibrium
• Fixed E
– S tends towards a maximum as the system approaches
equilibrium
• Fixed S
– E tends towards a minimum as the system approaches
equilibrium
• In evaporation (and many other processes) both S and E
is varying
Off equilibrium
• The difference in µ from one phase to another when the
two are not in equilibrium is the driving force for the
system’s motion toward equilibrium.
• Material will move from phases with high µ to those of
low µ until all chemical potentials are equal
• ∆µ is the driving force for all crystal growth and epitaxy
5
Dependence of p
v
on T
• µ
c
= µ
v
• dµ
c
= dµ
v
Vapor pressure example
Reference points
Boiling point of liquid
Sublimation T of solid
6
Evaporation rate
• (b) Effusion cell. Orifice, small enought that
– p ≈ p
v
– Kn > 1 (Kn = mean free path / orifice diameter).
– If orifice thickness smaller than orifice diameter: Knudsen cell
– Evaporation rate:
– Small orifice, Q
e
<< Q
v
, to avoid reducing the pressure
 
21
2
ppA
MRT
N
Q
A
e


Mass balance
• Q
v
= Q
c
+ Q
e
• J = Q/A
• Neglect Q
e
• Know impinging flux, J
i
, from kinetic
theory
• If all impinging flux condensate
– J
i
= J
vo
(upper limit)
– J
vo
the same for an open system
• Metals with atomic vapors
– J
v
= J
vo
• Other materials
– J
v
= α
v
J
vo
, α
v
< 1
– J
c
= α
c
J
i
, α
c
< 1
7
The coefficient,
α
v
• At equilibrium
– J
v
= J
c
– α
v
= α
c
• α
v
determined only for a few materials (function of p and
T). For arsenic, α
v
= 10
-4
. In general, α
v
is not known and
not well understood either.
• So unless evaporation is carried out from a Knudsen
cell, effusion rate can not be predicted but has to be
measured directly.
Evaporation of multicomponent materials
• Alloys
• Compounds
8
Evaporation of multicomponent materials
• Alloys
– Solid solution or mixture of solid phases
– Composition variable over long range
– Example: solder alloy, Pb
x
Sn
1-x
• Compounds
– Specific ratio of elements
– Example: GaAs, CuInSe
2
• Alloy of compounds
– Example: Ga
x
In
1-x
P [i.e. (GaP)
x
(InP)
1-x
]
Evaporation of alloys
• Genaralized binary metal alloy, B
x
C
1-x
, B and C totally
miscible at the evaporation temperature.
– Total equilibrium vapor pressure over melt, p
B
+ p
C
– p
B
= γ
B
xp
vB
– p
C
= γ
C
(1-x)p
vC
– Raoult’s law behaviour: unity activity coefficients
– Metals: unity evaporation coefficients
– Ratio of evaporation fluxes:
– Vapor flux richer than the melt in the more volatile component
B
C
vC
vB
vC
vB
M
M
p
p
x
x
J
J

1
9
Evaporation of compounds
• Compounds behave very
differently from alloys
• Can evaporate as one single
specie or completely
dissociate
• III/Vs dissociate completely
– GaAs(s) → Ga(g) + ½ As
2
(g)
Problems
• 4.2 – vapor pressure and effusion rate
• 4.3 – water vapor example
• Show that the uncertainty function (entropy) must be of
the form Cln(W), where W is the number of outcomes
(with equal probability)