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)

## Comments 0

Log in to post a comment