Growth Chemistry

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

4. 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 PV2o½(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