1. Growth Chemistry
Can view deposition as a well-controlled phase transition:
III(g) + ½ V2(g) ↔ III-V(s)
Can model this as a chemical reaction:
aA + bB ↔ cC + dD
At equilibrium :
Forward reaction rate = reverse reaction rate
Flux arriving at surface = flux leaving surface (no growth)
For film growth to occur, drive reaction to the right

2. Gibbs Free Energy
Gibbs free energy of a state:
G = H – TS
H = enthalpy = E + PV = heat content of a system
E = internal (potential) energy of a system
PV = translational (kinetic) energy of a system
S = entropy = randomness in the system

3. The stable state is the one with the lowest Gibbs free energy
Driving Force for MBE
The stable state is the one with the lowest Gibbs free energy
From
Tsao, Fig. 2.3, p. 39

4. Si MBE at 800 K, 10-6 Torr produces g(Si) - g<Si>c ~ 2.5 eV
Driving Force for MBE
Si MBE at 800 K, 10-6 Torr produces g(Si) - g<Si>c ~ 2.5 eV
This is the driving force for MBE
From Tsao, Fig. 2.3, p. 39

5. Second Law of Thermodynamics
For a change in state
DG = DH - TDS
DG = 0 at equilibrium
Forward and reverse reaction rates are equal
e.g., at the melting point of a solid, Gsolid = G liquid
DG < 0 for a spontaneous reaction
DG > 0 for a non-spontaneous reaction

6. Reaction Quotient
For the chemical reaction:
aA + bB ↔ cC + dD
DG = cGC + dGD - aGA - bGB

7. Standard State
Gibbs free energy defined relative to a reference or standard state
Standard state is the stable form of the substance at STP (T = 298 K and P = 1 atm)
Define activity:
Gi = Gio + RT lnai
Gio = Gibbs free energy in standard state
ai = activity of species i

8. Reaction Quotient
For the chemical reaction:
aA + bB ↔ cC + dD
DG = cGC + dGD - aGA - bGB
= (cGCo + dGDo – aGAo – bGBo)
+ RT ln aCcaDd / aAaaBb
Define Gibbs free energy of formation
DGo = cGCo + dGDo – aGAo – bGBo
Define reaction quotient
Q = aCcaDd / aAaaBb
Then DG = DGo + RT lnQ

9. Equilibrium Constant
Define reaction quotient at equilibrium, Q = K:
K = equilibrium constant
= (aCo)c (aDo)d / (aAo)a (aBo)b
(law of mass action)
Then
DG = 0 = DGo + RT lnQ
DGo = -RT lnK
DGo versus T is linear

10. Gibbs Free Energy of Formation
Plot of DGo versus T is called an Ellingham diagram
From
Ohring,
Fig. 1.10,
p. 25

11. Gibbs Free Energy of Formation
DGo also available is standard reference tables
From Mahan, Table III.2, p. 78

12. Gibbs Free Energy
DG = - RT lnK + RT lnQ
= RT ln(Q/K)
Q = K
DG = 0
Equilibrium (forward and reverse
reaction rates are equal)
Q < K
DG < 0
Reaction proceeds left to right
Q > K
DG > 0
Reaction proceeds right to left

13. Gibbs Free Energy
aA + bB ↔ cC + dD
DG = RT ln(Q/K)
= RT ln [(aC/aCo)c (aD/aDo)d / (aA/aAo)a (aB/aBo)b ]
 ai / aio > 1
Supersaturation of the species i
Reaction is driven to the right if there exists a supersaturation of reactants and a subsaturation of products (Chatelier’s Principle)

14. Activity
Pure solid or liquid: ai = 1
 Solutions: ai = giXi
gi = activity coefficient
Xi = mole fraction of
species i
Vapors: ai = Pi / Pref
Pi = partial pressure
of species i
Pref = 1 atm

15. Gibbs Free Energy
III(g) + ½ V2(g) ↔ III-V(s)
Q = (PIII/Pref)-1(PV2/Pref)-½
K = (PIIIo/Pref)-1(PV2o/Pref)-½
Growth occurs when Q < K, or
PIIIPV2½ > PIIIo PV2o ½ (supersaturation)

16. Three-Temperature Method
A method for the deposition of a compound, AB (e.g., III-V)
The three temperatures refer to the temperatures of the A cell, the B cell, and the substrate

17. Three-Temperature Method
Step 1: Choose TA
Growth rate determined by A (the element with the lowest vapor pressure)
Choose a VP of A corresponding to a reasonable growth rate
Want negligible re-evaporation
 Want equilibrium VP of A over substrate << deposition flux
 Tsub << TA
From
Mahan,
Fig. III.10,
p. 68

18. Three-Temperature Method
Step 2: Choose TB
Choose VP of B such that B/A flux ratio > 1
All of A is consumed
Excess B re-evaporates
From
Mahan,
Fig. III.10,
p. 68

19. Three-Temperature Method
Step 3: Choose Tsub
If Tsub is too high
The VP of B over AB is below the equilibrium VP
B is subsaturated
The film AB will not form
From
Mahan,
Fig. III.10,
p. 68

20. Three-Temperature Method
If Tsub is too low
The VP of B over pure B and the VP of B over AB is above the equilibrium vapor pressure
B is supersaturated wrt B and AB
Favors the formation of two phases, B and AB
From
Mahan,
Fig. III.10,
p. 68

21. Three-Temperature Method
Within DTsub (condensation window)
B vapor is supersaturated with respect to AB but subsaturated with respect to B
Favors formation of AB but not B
From
Mahan,
Fig. III.10,
p. 68

22. Congruent Sublimation Temperature
The substrate temperature, Tc, at which the equilibrium flux of P leaving the surface is equal to the equilibrium flux of In leaving the surface
Equal to the crossing point of the P and In equilibrium VP curves
From Panish & Temkin, Fig. 2.6, p. 24

23. Congruent Sublimation Temperature
Above Tc, the group V flux leaving the surface exceeds the group III flux leaving the surface
Tc (InP) ~ 365 °C
Tc (GaAs) ~ 660 °C
From Panish & Temkin, Fig. 2.5, p. 23

24. Congruent Sublimation Temperature
Above Tc, liquid III forms on the surface
Above Tc, we need a group V flux equal to the equilibrium VP to prevent liquid III formation
From Mahan, Fig. III.6, p. 61