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Electrical Transport in Microstructures

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Part of the book series: NATO ASI Series ((NSSB,volume 170))

Abstract

These lectures are intended to provide an introduction to carrier transport in systems with reduced dimensionality. The main application will be to electrons in silicon inversion layers and GaAs heterojunctions and quantum wells. Knowledge of basic aspects of semiconductor physics and of transport in solids, as given, for example, in Kittel1 or Ziman2 will be assumed. More detailed discussions of transport, particularly in semiconductors, can be found in Wilson3 (which includes semiconductors in spite of the title), in “big” Ziman,4 and in Seeger.5 General concepts of heterostructure physics are presented in other lectures in this volume.

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References

  1. C. Kittel, “Introduction to Solid State Physics,” 5th ed., Wiley, New York (1976).

    Google Scholar 

  2. J. M. Ziman, “Principles of the Theory of Solids,” 2nd ed.,Cambridge (1972).

    Google Scholar 

  3. A. H. Wilson, “The Theory of Metals”, 2nd ed., Cambridge (1953).

    Google Scholar 

  4. J. M. Ziman, “Electrons and Phonons,” Oxford (1960).

    Google Scholar 

  5. K. Seeger, “Semiconductor Physics,” Springer, Wien (1973).

    Google Scholar 

  6. S. Hikami, A. I. Larkin, and Y. Nagaoka, Spin-orbit interaction and magnetoresistance in the two dimensional random system, Prog. Theor. Phys. 63: 707 (1980).

    Google Scholar 

  7. H. Fukuyama, Theory of weakly localized regime of the Anderson localization in two dimensions, Surf. Sci. 113: 489 (1982).

    Google Scholar 

  8. P. A. Lee and T. V. Ramakrishnan, Disordered electronic systems, Rev. Mod. Phys. 57: 287 (1985).

    Article  ADS  Google Scholar 

  9. S. Kawaji, Weak localization and negative magnetoresistance in semiconductor two-dimensional systems, Surf. Sci. 170: 682 (1986).

    Google Scholar 

  10. F. Stern and W. E. Howard, Properties of semiconductor surface inversion layers in the electric quantum limit, Phys. Rev. 163: 816 (1967).

    Google Scholar 

  11. G. Fishman, Mobility in a quasi-one-dimensional semiconductor: An analytical approach, Phys. Rev. B 34: 2394 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  12. S. Das Sarma and X. C. Xie, Calculated transport properties of ultrasubmicron quasi-one-dimensional inversion lines, Phys. Rev. B (1987).

    Google Scholar 

  13. F. A. Riddoch and B. K. Ridley, Phonon scattering of electrons in quasi-one-dimensional and quasi-two-dimensional quantum wells, Surf. Sci. 142: 260 (1984).

    Google Scholar 

  14. H. Sakaki, Scattering suppression and high-mobility effect of size-quantized electrons in ultrafine semiconductor wire structures, Jpn. J. Appl. Phys. 19:L735 (1980).

    Article  ADS  Google Scholar 

  15. T. Ando, A. B. Fowler, and F. Stern, Electronic properties of two-dimensional systems, Rev. Mod. Phys. 54: 437 (1982).

    Article  ADS  Google Scholar 

  16. H. L. Stôrmer, A. C. Gossard, and W. Wiegmann, Observation of intersubband scattering in a 2-dimensional electron system, Solid State Commun. 41: 707 (1982).

    Article  ADS  Google Scholar 

  17. M. J. Kane, N. Apsley, D. A. Anderson, L. L. Taylor, and T. Kerr, Parallel conduction in GaAs/AlxGa1-xAs modulation doped hetero- junctions, J. Phys. C 18: 5629 (1985).

    Google Scholar 

  18. D. A. Syphers, K. P. Martin, and R. J. Higgins, Determination of transport coefficients in high mobility heterostructure systems in the presence of parallel conduction, Appl. Phys. Lett. 49: 534 (1986).

    Google Scholar 

  19. F. Stern, Friedel phase-shift sum rule for semiconductors, Phys. Rev. 158: 697 (1967).

    Google Scholar 

  20. T. Ando, Self-consistent results for a GaAs/AlxGa1-xAs heterojunction. II. Low temperature mobility, J. Phys. Soc. Japan 51: 3900 (1982).

    Google Scholar 

  21. F. Stern, Doping considerations for heterojunctions, Appl. Phys. Lett. 43: 974 (1983).

    Article  ADS  Google Scholar 

  22. F. Stern, Calculated temperature dependence of mobility in silicon inversion layers, Phys. Rev. Lett. 44: 1469 (1980).

    Article  ADS  Google Scholar 

  23. Y. Kawaguchi and S. Kawaji, Lattice scattering mobility of n-in-version layers in Si(100) at low temperatures, Surf. Sci. 98: 211 (1980).

    Google Scholar 

  24. K. M. Cham and R. G. Wheeler, Temperature-dependent resistivitiesin silicon inversion layers at low temperatures, Phys. Rev. Lett. 44: 1472 (1980)

    Article  ADS  Google Scholar 

  25. S. I. Dorozhkin and V. T. Dolgopolov, Conductivity increase of a 2D electron gas with decreasing temperature in Si(100) metal- insulator-semiconductor structures, Pis’ma Zh. Eksp. Teor. Fiz. 40:245 (1984) [JETP Lett. 40:1019 (1984)].

    Google Scholar 

  26. A. Gold and V. T. Dolgopolov, Temperature dependence of the conductivity for the two-dimensional electron gas: Analytical results for low temperatures, Phys. Rev. B 33: 1076 (1986).

    Article  ADS  Google Scholar 

  27. V. M. Pudalov, S. G. Semenchinskii, and V. S. Edel’man, Oscillations of the chemical potential and the energy spectrum of electrons in the inversion layer at a silicon surface in a magnetic field, Zh. Eksp. Teor. Fiz. 89:1870 (1985) [Sov. Phys. JETP 62:1079 (1985)].

    Google Scholar 

  28. R. P. Smith and P. J. Stiles, Temperature dependence of the conductivity of a silicon inversion layer at low temperatures, Solid State Commun. 58: 511 (1986).

    Article  ADS  Google Scholar 

  29. F. Stern and S. Das Sarma, Self-consistent treatment of screening and Coulomb scattering in silicon inversion layers at low temperatures, Solid-State Electron. 28:211 (1985) (extended abstract).

    Google Scholar 

  30. A. Gold and W. Gotze, Localization and screening anomalies in two-dimensional systems, Phys. Rev. B 33: 2495 (1986).

    Article  ADS  Google Scholar 

  31. A. Gold, Transport and cyclotron resonance theory for GaAs-AlGaAsheterostructures, Z. Phys. B 63: 1 (1986).

    Article  ADS  Google Scholar 

  32. A. Gold, Metal insulator transition due to surface roughness scattering in a quantum well, Solid State Commun. 60: 531 (1986).

    Article  ADS  Google Scholar 

  33. J. L. Robert, A. Raymond, L. Konczewicz, C. Bousquet, W. Zawadski,F. Alexandre, I. M. Masson, J. P. Andre, and P. M. Frijlink, Magnetic-field-induced metal-nonmetal transition in GaAs- Ga1-xAlxAs heterostructures, Phys. Rev. B 33:5935 (1986).

    Google Scholar 

  34. P. O. Hahn and M. Henzler, The Si-Si02 interface: Correlation of atomic structure and electrical properties, J. Vac. Sci. Technol. A 2: 574 (1984).

    ADS  Google Scholar 

  35. S. M. Goodnick, D. K. Ferry, C. W. Wilmsen, Z. Liliental, D. Fathy, and O. L. Krivanek, Surface roughness at the Si(100)-Si02 interface, Phys. Rev. B 32: 8171 (1985).

    Google Scholar 

  36. R. E. Prange and T. W. Nee, Quantum spectroscopy of the low-field oscillations in the surface impedance, Phys. Rev. 168: 779 (1968).

    Google Scholar 

  37. Y. Matsumoto and Y. Uemura, Scattering mechanism and low temperature mobility of MOS inversion layers, in “Proceedings of the Second International Conference on Solid Surfaces, Kyoto,” Jpn. J. Appl. Phys. Suppl. 2, Pt. 2, p. 367 (1974).

    Article  ADS  Google Scholar 

  38. A. Gold, Conductivity, plasmon, and cyclotron-resonance anomalies in Si (100) metal-oxide-semiconductor systems, Phys. Rev. B 32:4014 (1985).

    Google Scholar 

  39. J. A. Brum and G. Bastard, Self-consistent calculations of charge transfer and alloy scattering-limited mobility in InP-Ga1-xInxAsyP1-y single quantum wells, Solid State Commun. 53:727 (1985). See also P. K. Basu and B. R. Nag, Estimation of alloy scattering potential in ternaries from the study of two-dimensional electron electron transport, Appl. Phys. Lett. 43:689 (1983).

    Google Scholar 

  40. T. S. Kuan, T. F. Kuech, W. I. Wang, and E. L. Wilkie, Long-range order in AlxGa1-xAs, Phys. Rev. Lett. 54: 201 (1985).

    Google Scholar 

  41. P. J. Price, Two-dimensional electron transport in semiconductor layers. I. Phonon scattering, Ann. Phys. (N.Y.) 133: 217 (1981).

    Google Scholar 

  42. B. K. Ridley, The electron-phonon interaction in quasi-two-dimensional quantum-well structures, J. Phys. C 15: 5899 (1982).

    ADS  Google Scholar 

  43. P. J. Price, Two-dimensional electron transport in semiconductor layers. II. Screening, J. Vac. Sci. Technol. 19: 599 (1981).

    ADS  Google Scholar 

  44. S. Kawaji, The two-dimensional lattice scattering mobility in a semiconductor inversion layer, J. Phys. Soc. Japan 27: 906 (1969).

    ADS  Google Scholar 

  45. P. J. Price, Electron transport in polar heterolayers, Surf. Sci. 113: 199 (1982).

    Google Scholar 

  46. H. Ezawa, S. Kawaji, and K. Nakamura, Surfons and the electron mobility in silicon inversion layers, Jpn. J. Appl. Phys. 13:126 (1974); 14: 921 (E) (1975).

    Google Scholar 

  47. M. A. Paalanen, D. C. Tsui, A. C. Gossard, and J. C. M. Hwang, Temperature dependence of electron mobility in GaAs-AlxGa1-xAs heterostructures from 1 to 10 K, Phys. Rev. B 29: 6003 (1984).

    Google Scholar 

  48. E. E. Mendez, P. J. Price, and M. Heiblum, Temperature dependence of the electron mobility in GaAs-GaAlAs heterostructures, Appl. Phys. Lett. 45: 294 (1984).

    Google Scholar 

  49. B. J. F. Lin, D. C. Tsui, and G. Weimann, Mobility transition in the two-dimensional electron gas in GaAs-AlGaAs heterostructures, Solid State Commun. 56:287 ( 1985 ); B. J. F. Lin, Ph. D. Thesis, Electrical Engineering Department, Princeton University (1985).

    Google Scholar 

  50. B. Vinter, Low-temperature phonon-limited electron mobility in modulation-doped heterostructures, Phys. Rev. B 33:5904 (1986); Maximum finite-temperature mobility in heterostructures: Influence of screening of electron-acoustic phonon interactions, Surf. Sci. 170: 445 (1986).

    Google Scholar 

  51. K. Hirakawa and H. Sakaki, Energy relaxation of two-dimensional electrons and the deformation potential constant in selectively doped AlGaAs/GaAs heterojunctions, Appl. Phys. Lett. 49: 889 (1986).

    Google Scholar 

  52. F. Stern and S. Das Sarma, Self-consistent treatment of screening and Coulomb scattering in silicon inversion layers at low temperatures, Solid-State Electron. 28: 211 (1985) (abstract).

    Article  ADS  Google Scholar 

  53. K. Hirakawa and H. Sakaki, Mobility of the two-dimensional electron gas at selectively doped n-type AlxGa1-xAs/GaAs heterojunctions with controlled electron concentrations, Phys. Rev. B 33: 8291 (1986).

    Google Scholar 

  54. C. Guillemot, M. Baudet, M. Gauneau, A. Regreny, and J. C. Portal, Temperature dependence of electron mobility in GaAs-Ga1-xAlxAs modulation-doped quantum wells, Phys. Rev. B. 35: 2799 (1987).

    Google Scholar 

  55. P. J. Price, Heterolayer mobility in the Bloch-Griineisen range, Solid State Commun. 51: 607 (1984).

    Article  ADS  Google Scholar 

  56. P. J. Price, Hot electrons in a GaAs heterolayer at low temperature, J. Appl. Phys. 53: 6863 (1982).

    Article  ADS  Google Scholar 

  57. W. Walukiewicz, H. E. Ruda, J. Lagowski, and H. C. Gatos, Electron mobility in modulation-doped heterostructures, Phys. Rev. B. 30: 4571 (1984).

    Article  ADS  Google Scholar 

  58. E. E. Mendez, Electronic mobility in semiconductor heterostructures, IEEE J. Quant. Electron. QE-22: 1720 (1986).

    Google Scholar 

  59. W.I. Wang, E. E. Mendez, Y. Iye, B. Lee, M. H. Kim, and G. E. Stillman, High mobility two-dimensional hole gas in an Al0.26Gao.74As/GaAs heterojunction, J. Appl. Phys. 60:1834 -(1986).

    Google Scholar 

  60. W. Walukiewicz, Hole-scattering mechanisms in modulation-doped heterostructures, J. Appl. Phys. 59: 3577 (1986).

    Article  ADS  Google Scholar 

  61. T. P. McLean and E. G. S. Paige, A theory of the effects of carrier-carrier scattering on mobility in semiconductors, J. Phys. Chem. Solids 16:220 (1960),

    Google Scholar 

  62. R. A. Hopfel, J. Shah, P. A. Wolff, and A. C. Gossard, Negative absolute mobility of minority electrons in GaAs quantum wells, Phys. Rev. Lett. 56: 2736 (1986).

    Article  ADS  Google Scholar 

  63. K. Hess, Aspects of high-field transport in semiconductor hetero-layers and semiconductor devices, Adv. Electronics Electron Phys. 59: 239 (1982).

    Google Scholar 

  64. L. Reggiani, ed., “Hot-Electron Transport in Semiconductors,” Springer, Berlin (1985).

    Google Scholar 

  65. W. T. Masselink, T. S. Henderson, J. Klem, W. F. Kopp, and H. Morkoc, The dependence of 77 K electron velocity-field characteristics on low-field mobility in AlGaAs-GaAs modulation-doped structures, IEEE Trans. Electron Dev. ED-33: 639 (1986).

    Google Scholar 

  66. P. J. Price, Hot phonon effects in heterolayers, Physica 134B: 164 (1985).

    Google Scholar 

  67. J. Higman and K. Hess, Comment on the use of the electron temperature concept for nonlinear transport problems in semiconductor p-n junctions, Solid-State Electron. 29: 915 (1986).

    Article  ADS  Google Scholar 

  68. S. Selberherr, “Analysis and Simulation of Semiconductor Devices,” Springer, Wien (1984).

    Google Scholar 

  69. J. J. H. Miller, “NASECODE IV: Proceedings of the Fourth International Conference on the Numerical Analysis of Semiconductor Devices and Integrated Circuits,” Boole Press, Dublin (1985).

    Google Scholar 

  70. K. Blotekjaer, Transport equations for electrons in two-valley semiconductors, IEEE Trans. Electron Dev. ED-17: 38 (1970).

    Google Scholar 

  71. R. K. Cook and J. Frey, Two-dimensional numerical simulation of energy transport effects in Si and GaAs MESFETs, IEEE Trans. Electron Dev. ED-29: 970 (1982).

    Google Scholar 

  72. M. Rudan and F. Odeh, Multidimensional discretization scheme for the hydrodynamic model of semiconductor devices, COMPEL 5: 149 (1986).

    MathSciNet  MATH  Google Scholar 

  73. P. J. Price, Monte Carlo calculation of electron transport in solids, in “Semiconductors and Semimetals,” ed. by R. K. Willardson and A. C. Beer, Academic Press, New York (1979), Vol. 14, p. 249.

    Google Scholar 

  74. C. Jacoboni and L. Reggiani, The Monte Carlo method for the solution of charge transport in semiconductors with applications to covalent materials, Rev. Mod. Phys. 55: 645 (1983).

    Article  ADS  Google Scholar 

  75. K. Yokoyama and K. Hess, Monte Carlo study of electronic transport in Al1-xGaxAs/GaAs single-well heterostuctures, Phys. Rev. B 33: 5595 (1986).

    Google Scholar 

  76. J. G. Ruch and W. Fawcett, Temperature dependence of the transport properties of gallium arsenide determined by a Monte Carlo method, J. Appl. Phys. 41: 3843 (1970).

    Article  ADS  Google Scholar 

  77. M. V. Fischetti, D. J. DiMaria, L. Dori, J. Batey, E. Tierney, and J. Stasiak, Ballistic electron transport in thin silicon dioxide films, Phys. Rev. B 35: 4404 (1987).

    Article  ADS  Google Scholar 

  78. P. T. Nguyen, D. H. Navon, and T. W. Tang, Boundary conditions in regional Monte Carlo device analysis, IEEE Trans. Electron Dev. ED-32: 783 (1985).

    Google Scholar 

  79. Y. Aharonov and D. Bohm, Significance of electromagnetic potentials in quantum theory, Phys. Rev. 115: 485 (1959).

    Google Scholar 

  80. Another scale length, the thermal length LT = (hD/kBT)1/2, also enters under some conditions. See, for example, A. D. Stone and Y. Imry, Periodicity of the Aharonov-Bohm effect in normal-metal rings, Phys. Rev. Lett. 56: 189 (1986).

    Google Scholar 

  81. R. A. Webb, S. Washburn, C. P. Umbach, and R. B. Laibowitz, Observation of h/e Aharonov-Bohm oscillations in normal-metal rings, Phys. Rev. Lett. 54: 2696 (1985).

    Article  ADS  Google Scholar 

  82. S. Datta and S. Bandyopadhyay, Aharonov-Bohm effect in semiconductor microstructures, Phys. Rev. Lett. 58: 717 (1987).

    Article  ADS  Google Scholar 

  83. P. A. Lee and A. D. Stone, Universal conductance fluctuations in metals, Phys. Rev. Lett. 55: 1622 (1985).

    Article  ADS  Google Scholar 

  84. C. P. Umbach, S. Washburn, R. B. Laibowitz, and R. A. Webb, Magnetoresistance of small, quasi-one-dimensional, normal-metal rings and lines, Phys. Rev. B 30: 4048 (1984).

    Article  ADS  Google Scholar 

  85. J. C. Licini, D. J. Bishop, M. A. Kastner, and J. Melngailis, Aperiodic magnetoresistance oscillations in narrow inversion layers in Si, Phys. Rev. Lett. 55: 2987 (1985).

    Article  ADS  Google Scholar 

  86. S. B. Kaplan and A. Hartstein, Universal conductance fluctuations in narrow Si accumulation layers, Phys. Rev. Lett. 56: 2403 (1986).

    Article  ADS  Google Scholar 

  87. W. J. Skocpol, P. M. Mankiewich, R. E. Howard, L. D. Jackel, D. M. Tennant, and A. D. Stone, Universal conductance fluctuations in silicon inversion-layer nanostructures, Phys. Rev. Lett. 56: 2865 (1986).

    Article  ADS  Google Scholar 

  88. A. D. Benoit, S. Washburn, C. P. Umbach, R. B. Laibowitz, and R. A. Webb, Asymmetry in the magnetoconductance of metal wires and loops, Phys. Rev. Lett. 57: 1765 (1986).

    Article  ADS  Google Scholar 

  89. A. B. Fowler, A. Hartstein, and R. A. Webb, Conductance in restricted-dimensionality accumulation layers, Phys. Rev. Lett 48: 196 (1982).

    Article  ADS  Google Scholar 

  90. P. A. Lee, Variable-range hopping in finite one-dimensional wires, Phys. Rev. Lett. 53: 2042 (1984).

    Article  ADS  Google Scholar 

  91. J. A. Mclnnes and P. N. Butcher, Numerical calculations of variable-range hopping in one-dimensional MOSFETs, J. Phys. C 18: L921 (1985).

    Google Scholar 

  92. M. Ya. Azbel, A. Hartstein, and D. P. DiVincenzo, T dependence of the conductance in quasi one-dimensional systems, Phys. Rev. Lett. 52:1641 (1984); M. Ya. Azbel and D. P. DiVincenzo, Fin-ite-temperature conductance in one dimension, Phys. Rev. B 30: 6877 (1984).

    Google Scholar 

  93. A. B. Fowler, G. L. Timp, J. J. Wainer, and R. A. Webb, Observation of resonant tunneling in silicon inversion layers, Phys. Rev. Lett. 57: 138 (1986).

    Article  ADS  Google Scholar 

  94. See, for example, the papers cited in F. Stern, Recent progress in electronic properties of quasi-two-dimensional systems, Surf. Sci. 58:333 (1976), or p. 520 of Ref. 15.

    Google Scholar 

  95. S. Washburn and R. A. Webb, Aharonov-Bohm effect in normal metal quantum coherence and transport, Adv. Phys. 35: 375 (1986).

    Google Scholar 

  96. M. Buttiker, Four-terminal phase-coherent conductance, Phys. Rev. Lett. 57:1761 (1986); Voltage fluctuations in small conductors, Phys. Rev. B 35: 4123 (1987).

    Google Scholar 

  97. G. D. Mahan, Quantum transport equation for electric and magnetic fields, Phys. Repts. 145: 251 (1987).

    Google Scholar 

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Stern, F. (1987). Electrical Transport in Microstructures. In: Mendez, E.E., von Klitzing, K. (eds) Physics and Applications of Quantum Wells and Superlattices. NATO ASI Series, vol 170. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5478-9_6

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