Evaporation Thermodynamics of evaporation

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Thermal evaporation of source material. – Transport to the ... Evaporation of alloys, phase properties. – Transport to the ... Evaporation rate. • (b) Effusion cell.
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, Qc = Qv

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Closed system • First law of thermodynamics – dq = dw + dU

• U = εkin + εpot, εpot > εkin

Entropy • Process involving changes in T and p • Carried out slowly (close to equilibrium) • System brought back to original state

dq

 T   dS  0 Second law of thermodynamics

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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

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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

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Dependence of pv on T

• µc = µv • dµc = dµv

Vapor pressure example

Reference points Boiling point of liquid Sublimation T of solid

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Evaporation rate

• (b) Effusion cell. Orifice, small enought that – – – –

p ≈ pv Kn > 1 (Kn = mean free path / orifice diameter). If orifice thickness smaller than orifice diameter: Knudsen cell Evaporation rate: N

Qe 

A

2MRT

A p1  p2 

– Small orifice, Qe