Crystal Interfaces

  • Karl W. Böer
  • Udo W. PohlEmail author
Living reference work entry

Latest version View entry history



Interfaces to other semiconductors, producing a heterojunction, or to conductors, acting as contacts, are important parts of almost every semiconductor device. Their basic interface properties are a decisive element of the device operation and its performance. Layers of different semiconductors with a common interface may be coherently strained up to a to a critical layer thickness, which is roughly inverse to the mismatch of their in-plane lattice parameters. In thicker layers strain is at least partially relaxed by misfit dislocations.

The electronic properties of semiconductor heterojunctions and metal-semiconductor contacts are governed by the alignment of their electronic bands. Early models describe band offsets and barrier heights as the difference of two bulk properties. While related chemical trends are found for certain conditions, the band lineup cannot be predicted with sufficient accuracy by a single universal model. Interdiffusion on an atomic scale, defects located at the interface, and leaking out of eigenfunctions from one into the other material create interface dipoles, which modify alignments guessed from simple properties of the bulk materials. Additional shifts originate from strain. Various models exist, each describing certain groups of materials forming interfaces. Linear models define reference levels within each material such as charge neutrality levels or branch-point energies within the bandgap, average interstitial potentials, or use localized states of impurities lying deep in the bandgap. Nonlinear models account for the formation of interface dipoles; such a charge accumulation can be induced by band states near the interface in one semiconductor lying in the bandgap of the other or by disorder at the interface inducing gap states. More recent first-principle approaches model heterointerfaces explicitly or align bands with respect to the vacuum level by including surfaces.


Anderson model Band alignment Band bending Band lineup Bardeen model Blocking contact Debye length Diffusion potential Disorder-induced gap states Electron affinity Heterointerfaces Interface-dipol theory Interfaces Metal-induced gap states Metal-semiconductor interfaces Model-solid theory Ohmic contact Pseudomorhic layer Schottky barrier Schottky-Mott model Space-charge region Strain relaxation Transition-metal reference level Valence-band offset 


  1. Adachi S (2005) Properties of Group IV, III–V and II–VI semiconductors. Wiley, ChichesterCrossRefGoogle Scholar
  2. Adams MJ, Nussbaum A (1979) A proposal for a new approach to heterojunction theory. Solid State Electron 22:783CrossRefADSGoogle Scholar
  3. Anderson RL (1962) Experiments on Ge-GaAs heterojunctions. Solid State Electron 5:341CrossRefADSGoogle Scholar
  4. Aulbur WG, Jönsson L, Wilkins JW (2000) Quasiparticle calculations in solids. Solid State Phys 54:1CrossRefGoogle Scholar
  5. Ball CAB, Van der Merve JH (1983) The growth of dislocation-free layers. In: Nabarro FRN (ed) Dislocations in solids, vol 6. North Holland Publishing, Amsterdam, pp 121–141Google Scholar
  6. Bardeen J (1947) Surface states and rectification at a metal semi-conductor contact. Phys Rev 71:717CrossRefADSGoogle Scholar
  7. Bauer RS, Zurcher P, Sang HW Jr (1983) Inequality of semiconductor heterojunction conduction-band-edge discontinuity and electron affinity difference. Appl Phys Lett 43:663CrossRefADSGoogle Scholar
  8. Bauer S, Rosenauer A, Link P, Kuhn W, Zweck J, Gebhardt W (1993) Misfit dislocations in epitaxial ZnTe/GaAs (001) studied by HRTEM. Ultramicroscopy 51:221CrossRefGoogle Scholar
  9. Bechstedt F, Enderlein R (1988) Semiconductor surfaces and interfaces. Akademie-Verlag, BerlinGoogle Scholar
  10. Brillson LJ (1978) Transition in Schottky barrier formation with chemical reactivity. Phys Rev Lett 40:260CrossRefADSGoogle Scholar
  11. Brillson LJ (1982) The structure and properties of metal-semiconductor interfaces. Surf Sci Rep 2:123CrossRefADSGoogle Scholar
  12. Calandra C, Bisi O, Ottavian G (1985) Electronic properties on silicon-transition metal interface compounds. Surf Sci Rep 4:271CrossRefADSGoogle Scholar
  13. Caldas MJ, Fazzio A, Zunger A (1984) A universal trend in the binding energies of deep impurities in semiconductors. Appl Phys Lett 45:671CrossRefADSGoogle Scholar
  14. Capasso F, Margaritondo G (eds) (1987) Heterojunction band discontinuities. North Holland, AmsterdamGoogle Scholar
  15. Chadi DJ, Cohen ML (1975) Tight-binding calculations of the valence bands of diamond and zincblende crystals. Phys Status Solidi B 68:405CrossRefADSGoogle Scholar
  16. Chiaradia P, Katnani AD, Sang HW Jr, Bauer RS (1984) Independence of Fermi-level position and valence-band edge discontinuity at GaAs-Ge(100) interfaces. Phys Rev Lett 52:1246CrossRefADSGoogle Scholar
  17. Davydov B (1938) The rectifying action of semiconductors. J Tech Phys USSR 5:87Google Scholar
  18. Dixon RH, Goodhew PJ (1990) On the origin of misfit dislocations in InGaAs/GaAs strained layers. J Appl Phys 68:3163CrossRefADSGoogle Scholar
  19. Flores F, Tejedor C (1979) Energy barriers and interface states at heterojunctions. J Phys C Solid State Phys 12:731CrossRefADSGoogle Scholar
  20. Flores F, Tejedor C (1987) On the formation of semiconductor interfaces. J Phys C Solid State Phys 20:145CrossRefADSGoogle Scholar
  21. Franciosi A, Van de Walle CG (1996) Heterojunction band offset engineering. Surf Sci Rep 25:1CrossRefADSGoogle Scholar
  22. Frank FC, Van der Merve JH (1949) One-dimensional dislocations. I. Static theory. Proc Roy Soc Lond A 198:205, One-dimensional dislocations. II. Misfitting monolayers and oriented overgrowth. Proc Roy Soc Lond A 198:216; One-dimensional dislocations. III. Influence of the second harmonic term in the potential representation, on the properties of the model. Proc Roy Soc Lond A 200:125CrossRefADSzbMATHGoogle Scholar
  23. Frensley WR, Kroemer H (1977) On the formation of semiconductor interfaces. Phys Rev B 16:2642CrossRefADSGoogle Scholar
  24. Grant RW, Kraut EA, Waldrop JR, Kowalczyk SP (1987) Interface contributions to heterojunction band discontinuities: x-ray photoemission spectroscopy investigations. In: Capasso F, Margaritondo G (eds) Heterojunction band discontinuities. North Holland, Amsterdam, pp 167–206Google Scholar
  25. Grüneis A, Kresse G, Hinuma Y, Oba F (2014) Ionization potentials of solids: the importance of vertex corrections. Phys Rev Lett 112:096401CrossRefADSGoogle Scholar
  26. Harrison WA (1977) Elementary theory of heterojunctions. J Vac Sci Technol 14:1016CrossRefADSGoogle Scholar
  27. Harrison WA (1980) Electronic structure and the properties of solids. WH Freeman, San FranciscoGoogle Scholar
  28. Harrison WA, Tersoff J (1986) Tight-binding theory of heterojunction band lineups and interface dipoles. J Vac Sci Technol B 4:1068CrossRefGoogle Scholar
  29. Harrison WA, Kraut EA, Waldrop JR, Grant RW (1978) Polar heterojunction interfaces. Phys Rev B 18:4402CrossRefADSGoogle Scholar
  30. Hasegawa H, Ohno H (1986) Unified disorder induced gap state model for insulator–semiconductor and metal–semiconductor interfaces. J Vac Sci Technol B 4:1130CrossRefGoogle Scholar
  31. Hasegawa H, Ohno H, Sawada T (1986) Orbital energy for heterojunction band lineup. Jpn J Appl Phys 25:L265CrossRefADSGoogle Scholar
  32. Hayes WM, Lide DR, Bruno TJ (eds) (2013) CRC handbook of chemistry and physics, 94th edn. CRC Press, Boca RatonGoogle Scholar
  33. Hedin L (1965) New method for calculating the one-particle Green’s function with application to the electron-gas problem. Phys Rev 139:A796CrossRefADSGoogle Scholar
  34. Heine V (1965) Theory of surface states. Phys Rev 138:A1689CrossRefADSzbMATHGoogle Scholar
  35. Heinrich H, Langer JM (1986) Band offsets in heterostructures. In: Grosse P (ed) Festkörperprobleme/advances in solid state physics, vol 16. Vieweg, Braunschweig, pp 251–275Google Scholar
  36. Henisch HK (1984) Semiconductor contacts. Claredon Press, OxfordGoogle Scholar
  37. Heyd J, Scuseria GE, Ernzerhof M (2003) Hybrid functionals based on a screened Coulomb potential. J Chem Phys 118:8207CrossRefADSGoogle Scholar
  38. Hinuma Y, Grüneis A, Kresse G, Oba F (2014) Band alignment of semiconductors from density-functional theory and many-body perturbation theory. Phys Rev B 90:155405CrossRefADSGoogle Scholar
  39. Höffling B, Schleife A, Rödl C, Bechstedt F (2012) Band discontinuities at Si-TCO interfaces from quasiparticle calculations: comparison of two alignment approaches. Phys Rev B 85:035305CrossRefADSGoogle Scholar
  40. Katnani AD (1987) Trends in semiconductor heterojunctions. In: Capasso F, Margaritondo G (eds) Heterojunction band discontinuities. North Holland, Amsterdam, pp 115–166Google Scholar
  41. Katnani AD, Bauer RS (1986) Commutativity and transitivity of GaAs-AlAs-Ge(100) band offsets. Phys Rev B 33:1103CrossRefADSGoogle Scholar
  42. Katnani AD, Margaritondo G (1983) Microscopic study of semiconductor heterojunctions: photoemission measurement of the valance-band discontinuity and of the potential barriers. Phys Rev B 28:1944CrossRefADSGoogle Scholar
  43. Katnani AD, Chiaradia P, Cho Y, Mahowald P, Pianetta P, Bauer RS (1985) Effect of an Al interlayer on the GaAs/Ge(100) heterojunction formation. Phys Rev B 32:4071CrossRefADSGoogle Scholar
  44. Kroemer H (1975) Problems in the theory of heterojunction discontinuities. Crit Rev Solid State Sci 5:555CrossRefGoogle Scholar
  45. Kroemer H (1983) Heterostructure devices: a device physicist looks at interfaces. Surf Sci 132:543CrossRefADSGoogle Scholar
  46. Kroemer H (1984) Barrier control and measurements: abrupt semiconductor heterojunctions. J Vac Sci Technol B 2:433CrossRefGoogle Scholar
  47. Kurtin S, McGill TC, Mead CA (1969) Fundamental transition in the electronic nature of solids. Phys Rev Lett 22:1433CrossRefADSGoogle Scholar
  48. Langer JM, Heinrich H (1985a) Deep-level impurities: a possible guide to prediction of band-edge discontinuities in semiconductor heterojunctions. Phys Rev Lett 55:1414CrossRefADSGoogle Scholar
  49. Langer JM, Heinrich H (1985b) On a direct connection of the transition metal impurity levels to the band edge discontinuities in semiconductor heterojunctions. Physica B 134:444CrossRefGoogle Scholar
  50. Ledebo L-Å, Ridley BK (1982) On the position of energy levels related to transition-metal impurities in III-V semiconductors. J Phys C Solid State Phys 15:L961CrossRefGoogle Scholar
  51. Lee RJ (1985) Some comments on Nussbaum’s heterojunction lineup theory. IEEE Electron Device Lett 6:130CrossRefADSGoogle Scholar
  52. LeLay G (1983) Electronic and atomic structure of Ag–Si(111) and Ag–Ge(111). J Vac Sci Technol B 1:354CrossRefGoogle Scholar
  53. LeLay G, Derien J, Boccara N (eds) (1987) Semiconductor interfaces: formation and properties. Springer, BerlinGoogle Scholar
  54. Li Y-H, Walsh A, Chen S, Yin W-J, Yang J-H, Li J, Da Silva JLF, Gong XG, Wei S-H (2009) Revised ab initio natural band offsets of all group IV, II-VI, and III-V semiconductors. Appl Phys Lett 94:212109CrossRefADSGoogle Scholar
  55. Mailhiot C, Duke CB (1986) Many-electron model of equilibrium metal-semiconductor contacts and semiconductor heterojunctions. Phys Rev B 33:1118CrossRefADSGoogle Scholar
  56. Margaritondo G (1983) Microscopic investigations of semiconductor interfaces. Solid State Electron 26:499CrossRefADSGoogle Scholar
  57. Margaritondo G, Perfetti P (1987) The problem of heterojunction band discontinuities. In: Capasso F, Margaritondo G (eds) Heterojunction band discontinuities. North Holland, Amsterdam, pp 59–114Google Scholar
  58. Matthews JW (1975) Coherent interfaces and misfit dislocations. In: Matthews JW (ed) Epitaxial growth, Part B. Academic Press, New York, pp 559–609CrossRefGoogle Scholar
  59. Matthews JW, Blakeslee AE (1974) Defects in epitaxial multilayers I. Misfit dislocations. J Cryst Growth 27:118ADSGoogle Scholar
  60. Milnes AG, Feucht DL (1972) Heterojunctions and metal-semiconductor junctions. Academic Press, New YorkGoogle Scholar
  61. Mönch W (1970) On metal-semiconductor surface barriers. Surf Sci 21:443CrossRefADSGoogle Scholar
  62. Mönch W (1996) Empirical tight-binding calculation of the branch-point energy of the continuum of interface-induced gap states. J Appl Phys 80:5076CrossRefADSGoogle Scholar
  63. Mott NF (1938) Note on the contact between a metal and an insulator or semi-conductor. Proc Cambridge Phil Soc 34:568CrossRefADSGoogle Scholar
  64. Mott NF (1939) The theory of crystal rectifiers. Proc R Soc (London) A 171:27ADSzbMATHGoogle Scholar
  65. Niles DW, Margaritondo G (1986) Heterojunctions: definite breakdown of the electron affinity rule. Phys Rev B 34:2923CrossRefADSGoogle Scholar
  66. Niles DW, Margaritondo G, Perfetti P, Quaresima C, Capozi M (1985) Heterojunction band discontinuity control by ultrathin intralayers. Appl Phys Lett 47:1092CrossRefADSGoogle Scholar
  67. Perdew JP, Burke K, Ernzerhof M (1996) Generalized gradient approximation made simple. Phys Rev Lett 77:3865CrossRefADSGoogle Scholar
  68. Rhoderick EH (1978) Metal-semiconductor contacts. Claredon Press, OxfordGoogle Scholar
  69. Robertson J (2013) Band offsets, Schottky barrier heights, and their effects on electronic devices. J Vac Sci Technol A 31:050821CrossRefGoogle Scholar
  70. Schleife A, Fuchs F, Rödl C, Furthmüller J, Bechstedt F (2009) Branch-point energies and band discontinuities of III-nitrides and III-/II-oxides from quasiparticle band-structure calculations. Appl Phys Lett 94:012104CrossRefADSGoogle Scholar
  71. Schottky W (1939) Zur Halbleitertheorie der Sperrschicht- und Spitzengleichrichter. Z Phys 113:367 (On the semiconductor theory of junction and point rectifiers, in German)CrossRefADSzbMATHGoogle Scholar
  72. Schottky W, Störmer R, Waibel F (1931) Über die Gleichrichterwirkungen an der Grenze von Kupferoxydul gegen aufgebrachte Metallelektroden. Z Hochfrequenztech 37:162 (On the rectifying action of cuprous oxide at the junction to metal electrodes, in German)Google Scholar
  73. Sharma BL (ed) (1984) Metal-semiconductor schottky barrier junctions and their applications. Plenum Press, New York, ch 3Google Scholar
  74. Sheldon P, Jones KM, Al-Jassim MM, Yacobi BG (1988) Dislocation density reduction through annihilation in lattice-mismatched semiconductors grown by molecular-beam epitaxy. J Appl Phys 63:5609CrossRefADSGoogle Scholar
  75. Spicer WE, Chye PW, Skeath PR, Su CY, Lindau I (1979) New and unified model for Schottky barrier and III-V insulator interface states formation. J Vac Sci Technol 16:1422CrossRefADSGoogle Scholar
  76. Stevanovic V, Lany S, Ginley DS, Tumas W, Zunger A (2014) Assessing capability of semiconductors to split water using ionization potentials and electron affinities only. Phys Chem Chem Phys 16:3706CrossRefGoogle Scholar
  77. Tersoff J (1984a) Theory of semiconductor heterojunctions: the role of quantum dipoles. Phys Rev B 30:4874CrossRefADSGoogle Scholar
  78. Tersoff J (1984b) Schottky barrier heights and the continuum of gap states. Phys Rev Lett 52:465CrossRefADSGoogle Scholar
  79. Tersoff J (1985) Schottky barriers and semiconductor band structures. Phys Rev B 32:6968CrossRefADSGoogle Scholar
  80. Tersoff J (1986) Band lineups at II-VI heterojunctions: failure of the common-anion rule. Phys Rev Lett 56:2755CrossRefADSGoogle Scholar
  81. Van de Walle CG (1989) Band lineups and deformation potentials in the model-solid theory. Phys Rev B 39:1871CrossRefADSGoogle Scholar
  82. Van de Walle CG, Martin RM (1985) Theoretical study of Si/Ge interfaces. J Vac Sci Technol B 3:1256CrossRefGoogle Scholar
  83. Van de Walle CG, Martin RM (1986) Theoretical calculations of semiconductor heterojunction discontinuities. J Vac Sci Technol B 4:1055CrossRefGoogle Scholar
  84. Van de Walle CG, Martin RM (1987) Theoretical study of band offsets at semiconductor interfaces. Phys Rev B 35:8154CrossRefADSGoogle Scholar
  85. Van de Walle CG, Neugebauer J (2003) Universal alignment of hydrogen levels in semiconductors, insulators and solutions. Nature 423:626CrossRefADSGoogle Scholar
  86. Van der Merve JH (1962) Crystal interfaces II. Finite overgrowth. J Appl Phys 34:123Google Scholar
  87. Vogl P, Baranowski JM (1985) Electronic structure of 3d-transition metal impurities in semiconductors. Acta Phys Pol A 67:133Google Scholar
  88. Wei S-H, Zunger A (1993) Band offsets at the CdS/CuInSe2 heterojunction. Appl Phys Lett 63:2549CrossRefADSGoogle Scholar
  89. Zunger (1986) Electronic structure of 3d transition-atom impurities in semiconductors. Solid State Phys 39:275–464CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.NaplesUSA
  2. 2.Institut für Festkörperphysik, EW5-1Technische Universität BerlinBerlinGermany

Personalised recommendations