1 / 53

Growth Physics

Explore equilibrium vapor pressures, sticking coefficients, nucleation rates, alloy sticking coefficients, film structure, growth modes, and surface energies in MBE experiments for precise growth control.

parkerchristopher
Download Presentation

Growth Physics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Growth Physics • The first MBE Experiments: • Equilibrium vapor pressure of Ga over GaAs at 500 °C is low • xGa = cGaFGa • cGa = 1 (sticking or incorporation coefficient)

  2. Growth Physics • The first MBE Experiments: • Sticking coefficient of As2 depends on presence of Ga As2 on GaAs As2 on Ga-covered GaAs From Ohring, Fig. 7-23, p. 341 • cAs ~ 0 without Ga • cAs > 0 with Ga

  3. Growth Physics • As2 requires presence of Ga to stick • Grow with excess flux of As (V/III > 1) • Excess As2 is desorbed • Do not require 1:1 flux ratio of As:Ga to achieve film stoichiometry • Growth rate is set by Ga flux

  4. Growth Physics • Physisorption • Adatoms • No electron transfer (van der Waals bonding) • E < ~ 0.4 eV • Chemisorption • Involves electron transfer (chemical binding occurs with the substrate atoms) • E > ~ 1 – 10 eV

  5. Growth Physics From Mahan, Fig. III.2, p. 47

  6. Nucleation Rate • Adatoms will migrate until they find a binding site • If adatoms do not find a binding site within the time t they will desorb • t = n-1 exp (Edes/kT) • = surface lifetime before desorption or incorporation • = attempt frequency ~ 1012 s-1 Edes = barrier to desorption • Growth temperature must allow for sufficient surface diffusion for atoms to find binding sites and to overcome potential barrier (As2 → 2As)

  7. Growth Physics • Rate equation for adatoms : • dN/dt = rate of chemisorption • – rate of desorption • Rate of adsorption = d (1 - q) z • Rate of desorption = N/t • d = trapping probability • q = surface coverage = fraction of filled surface sites • z = impingement rate • N = surface adatom density • t = surface lifetime before desorption or incorporation Sticking coefficient, c

  8. Growth Physics • At equilibrium, dN/dt = 0 : • q = QP / (1 + QP) • Q = d(2pmkT)-½ / [Nn exp(-Edes / kT)] • (Langmuir adsorption isotherm) From Mahan, Fig. III.1, p. 51

  9. Alloy Sticking Coefficients • e.g., In1-xGaxAsyP1-y • x / (1- x) = FGa / Fin • Assumes equilibrium VP at the growth temperature are not too high

  10. Alloy Sticking Coefficients • e.g., In1-xGaxAsyP1-y • V/V’ ratios ratios in the solid depend on the relative sticking coefficients of As2 and P2 which depend on the relative equilibrium vapor pressures • y / (1-y) = c Y / (1-Y) • c = cAs/cP • Rearranging, y = cY / [ 1 + (c-1)Y ]

  11. Alloy Sticking Coefficients • Experimentally, c > 1 • Sticking coefficient of As2 is greater than P2 • Due to higher equilibrium VP of P2 compared to As2 LaPierre, Ph.D. thesis

  12. Film Structure Amorphous Crystalline Polycrystalline

  13. Growth Modes Growth Modes Volmer- Weber Franke- van der Merwe Stranski- Krastanov Step-flow

  14. Growth Modes • Island (or Volmer-Weber) • Atoms are more strongly bound to each other than to the substrate From Ohring, Fig. 5-2, p. 197

  15. Growth Modes • Layer (or Franke-van der Merwe) • Atoms are more strongly bound to the substrate than to each other From Ohring, Fig. 5-2, p. 197

  16. Growth Modes • Layer Plus Island (Stranski-Krastanov) • Layer-by-layer initially favored followed by islanding • e.g., strained-layer epitaxy (above critical thickness/strain) From Ohring, Fig. 5-2, p. 197

  17. Growth Modes • Step-flow • Atoms migrate on surface terraces and stick preferentially to step edges

  18. Growth Modes • Vicinal surfaces From Tsao, Fig. 6.5, p. 208

  19. Surface Energy • g = Interfacial energy per unit area • = Work required to create unit area of interface DG = gdA = FdA • g = F • Surface energy (Jm-2) = surface tension (Nm-1) F = Force per unit length From Porter & Easterling, Fig. 3.1, p. 112

  20. Surface Energy • Broken bond model of surface energy From Porter & Easterling, Fig. 3.3, p. 114

  21. Surface Energy • e.g., (111) surface • 12 nearest neighbors in bulk • 3 missing neighbors at surface • e/2 energy per broken bond • Surface energy = 3e/2 per surface atom • Surface density, Ns • Surface energy, g ~ 3Nse/2 • ~ 1015 eVcm-2 • ~ 1 Jm-2 From Porter & Easterling, Fig. 3.2, p. 112

  22. Homogeneous Nucleation Change in G due to material formation: DG = VDGv + Avfgvf = (4/3 pr3) DGv + (4pr2) gvf Volume, V Surface Area, Avf Radius, r

  23. Homogeneous Nucleation • Trade-off between decrease in G due to volume formation but increase in G due to surface energy • dDG/dr = 0 • DG* = 16pgvf3/ 3(DGv)2 • r* = -2g/DGv From Ohring, Fig. 1-19, p. 42

  24. Homogeneous Nucleation • Critical nucleus, r* = - 2gvf / DGv • Clusters smaller than r* are unstable (DG > 0) and will evaporate (shrink by losing atoms) • Clusters larger than r* are stable (DG < 0) and will grow by accumulating atoms • DG* is the energy barrier to nucleation From Ohring, Fig. 1-19, p. 42

  25. Heterogeneous Nucleation Change in G due to island formation: DG = VDGv + Avfgvf- Afsgsv + Afsgfs Volume, V Surface Area, Avf Area of substrate covered = Afs

  26. Heterogeneous Nucleation • DG = VDGv + Avfgvf + Afsgfs- Afsgsv • = a3r3DGv + a1r2gvf + a2r2gfs – a2r2gsv • a1 = 2p ( 1 – cosq ) • a2 = p sin2q • a3 = p ( 2 – 3cosq + cos3q) / 3 From Ohring, Fig. 5-3, p. 199

  27. Heterogeneous Nucleation • Equilibrium among interfacial tensions : • gsv = gfs + gvf cosq (Young’s eqn.) From Ohring, Fig. 5-3, p. 199

  28. Heterogeneous Nucleation • gsv = gfs + gvf cosq (Young’s eqn.) • Island growth: • q > 0 • gsv < gfs + gvf From Ohring, Fig. 5-3, p. 199

  29. Heterogeneous Nucleation • gsv = gfs + gvf cosq (Young’s eqn.) • Layer growth: • q = 0 • gsv = gfs + gvf From Ohring, Fig. 5-3, p. 199

  30. Heterogeneous Nucleation • DG = VDGv + Avfgvf + Afsgfs- Afsgsv • = a3r3DGv + a1r2gvf + a2r2gfs – a2r2gsv • At equilibrium, dDG/dr = 0 • Gives maximum in DG(r) curve • Energy barrier • DG* = (16pgvf3 / 3DGv2) [ (2-3cosq + cos3q) / 4 ] • = (homogeneous barrier)*(shape factor) • 0 < shape factor < 0.5 • DG*(heterogeneous) < DG*(homogeneous) • Critical nucleus • r* = -2gvf / DGv • Same as homogeneous nucleation

  31. Heterogeneous Nucleation Critical nucleus, r* = - 2gvf / DGv Clusters smaller than r* are unstable and will evaporate (shrink by losing atoms) • Clusters larger than r* are stable and will grow by accumulating atoms From Ohring, Fig. 5-3, p. 199

  32. Growth Process 1. Growth Flux 2. Island Formation (Nucleation) 3. Island Growth and Coalescence

  33. Film Formation • Film formation occurs by nucleation, growth and coalescence of islands From Ohring, Fig. 5-1, p. 196

  34. Growth Process Number of islands, N* Many, small islands (N* large)  Amorphous or fine-grained polycrystalline film Few, large islands (N* small)  Single crystal or coarse-grained polycrystalline film

  35. Growth Process What is the effect of growth conditions? Temperature, T Growth Rate, R Change the rate of nuclei formation, dN*/dt

  36. dN*/dt ~ exp [ Edes – DG* – Edif) / kT)] • DG* is the energy barrier to nucleation Nucleation Barrier As T increases More adatoms have sufficient energy to overcome energy barrier to island formation (more nuclei are formed) From Ohring, Fig. 1-19, p. 42

  37. Diffusion Barrier dN*/dt ~ exp [ Edes – DG* – Edif) / kT)] Adatoms diffuse a distance X ~  Dt during the surface lifetime, t As T increases  Diffusion coefficient increases D = Doexp(-Edif/kT)  Adatom diffusion length is longer  Adatoms more likely to diffuse and be captured by existing island edges (fewer nuclei are formed)

  38. Desorption Barrier dN*/dt ~ exp [ Edes – DG* – Edif) / kT)] • As T increases • Surface lifetime is reduced due to desorption • t = (1/n) exp(Edes/kT) • Adatom diffusion length is shorter •  Adatoms less likely to diffuse and be captured by existing island edges (more nuclei are formed)

  39. Nucleation Rate • Higher growth rate and lower T • Smaller and greater number of nuclei • Polycrystalline or amorphous films • Lower growth rate and higher T • Larger and fewer nuclei • Large crystallites or monocrystalline films

  40. Nucleation Rate From Ohring, Fig. 5-13, p. 227

  41. Nucleation Rate From Ohring, Fig. 5-4, p. 205

  42. Atomistic Models • Surface dangling bonds energetically unfavorable • Surface atoms and bonds rearrange from their bulk positions to minimize surface energy • Results in surface reconstruction

  43. Atomistic Models • Surface reconstruction determined using combination of LEED, RHEED, STM From Ohring, Fig. 7-4, p. 312

  44. Atomistic Models • In 2-D, 5 unit meshes or nets are possible From Ohring, Fig. 7-5, p. 313

  45. Atomistic Models • Surface reconstruction phase diagram L. Daweritz and K. Ploog, Semicond. Sci. & Technol. 9 (1994) 123.

  46. Atomistic Models (2x4) III-V surface, e.g., GaAs at growth conditions (V/III > 1, 550 °C) Farrell et al, JVST B 5 (1987) 1482

  47. Atomistic Models • Electron counting model : • Bonding orbitals are completely filled (2 electrons) • Non-bonding (dangling) orbitals are either completely empty (above the Fermi level) or completely filled (below the Fermi level) Filled dangling orbital Farrell et al, JVST B 5 (1987) 1482

  48. Atomistic Models • Ga atom has three valence electrons • and three (sp2) orbitals From Oxtoby & Nachtrieb, Fig. 13-17, p. 477

  49. Atomistic Models • Ga inserted at As dangling bond has only one covalent bond and one half-filled dangling orbital Filled As dangling orbital Farrell et al, JVST B 5 (1987) 1482 From Oxtoby & Nachtrieb, Fig. 13-17, p. 477

  50. Atomistic Models • Formation of Ga dimers is more stable configuration (lower energy) Farrell et al, JVST B 5 (1987) 1482

More Related