Advertisement

Electrical Transport

  • Peter Y. Yu
  • Manuel Cardona
Part of the Graduate Texts in Physics book series (GTP)

Summary

In this chapter we have discussed the transport of charges in semiconductors under the influence of external fields. We have used the effective mass approximation to treat the free carriers as having classical charge and renormalized masses. We first considered the case of weak fields in which the field does not distort the carrier distribution but causes the entire distribution to move with a drift velocity. The drift velocity is determined by the length of time, known as the scattering time, over which the carriers can accelerate in the field before they are scattered. We also defined mobility as the constant of proportionality between drift velocity and electric field. We calculated the scattering rates for carriers scattered by acoustic phonons, optical phonons, and ionized impurities. Using these scattering rates we deduced the temperature dependence of the carrier mobilities. Based on this temperature dependence we introduced modulation doping as a way to minimize scattering by ionized impurities at low temperatures. We discussed qualitatively the behavior of carriers under high electric fields. We showed that these hot carriers do not obey Ohm’s law. Instead, their drift velocities at high fields saturate at a constant value known as the saturation velocity. We showed that the saturation velocity is about 107 cm/s in most semiconductors as a result of energy and momentum relaxation of carriers by scattering with optical phonons. In a few n-type semiconductors, such as GaAs, the drift velocity can overshoot the saturation velocity and exhibit negative differential resistance. This is the result of these semiconductors having secondary conduction band valleys whose energies are of the order of 0.1 eV above the lowest conduction band minimum. The existence of negative differential resistance leads to spontaneous current oscillations at microwave frequencies when thin samples are subjected to high electric fields, a phenomenon known as the Gunn effect. Under the combined influence of an electric and magnetic field, the transport of carriers in a semiconductor is described by an antisymmetric second rank magneto-conductivity tensor. One important application of this tensor is in explaining the Hall effect. The Hall coefficient provides the most direct way to determine the sign and concentration of charged carriers in a sample.

Keywords

Drift Velocity Optical Phonon Acoustic Phonon Electrical Transport Negative Differential Resistance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Chapter 5

  1. 5.1
    J.M. Ziman: Principles of Theory of Solids, 2nd edn. (Cambridge Univ. Press, Cambridge 1972) pp. 129–178CrossRefGoogle Scholar
  2. 5.2
    B.K. Ridley: Quantum Processes in Semiconductors, 2nd edn. (Clarendon, Oxford 1988)Google Scholar
  3. 5.3
    H.S. Robertson: Statistical Thermophysics (Prentice Hall, Englewood Cliffs, NJ 1993) pp. 445–449Google Scholar
  4. 5.4
    C. Jacoboni, P. Lugli: The Monte Carlo Method for Semiconductor Device Simulation (Springer, Wien 1989) pp. 104–160Google Scholar
  5. 5.5
    D.K. Ferry: Semiconductors (Macmillan, New York 1991)Google Scholar
  6. 5.6
    S.S. Devlin: Transport properties, in Physics and Chemistry of II–VI Compounds, ed. by M. Aven, J. S. Prener (North-Holland, Amsterdam 1967)Google Scholar
  7. 5.7
    C. Kittel: Introduction to Solid State Physics, 7th edn. (Wiley, New York 1995)Google Scholar
  8. 5.8
    E.M. Conwell, M.O. Vassel: High-field distribution function in GaAs. IEEE Trans. ED-13, 22–27 (1966)CrossRefGoogle Scholar
  9. 5.9
    C.L. Collins, P.Y. Yu: Nonequilibrium phonon spectroscopy: A new technique for studying intervalley scattering in semiconductors. Phys. Rev. B 27, 2602–2604 (1983)CrossRefGoogle Scholar
  10. 5.10
    D.L. Rode: Low field electron transport. Semiconductors and Semimetals 10, 1–89 (Academic, New York 1982)Google Scholar
  11. 5.11
    D. Long: Scattering of conduction electrons by lattice vibrations in silicon. Phys. Rev. 120, 2024–2032 (1960)CrossRefGoogle Scholar
  12. 5.12
    J.L. Birman, M. Lax, R. Loudon: Intervalley-scattering selection rules in III–V semiconductors. Phys. Rev. 145, 620–622 (1966)CrossRefGoogle Scholar
  13. 5.13
    D.K. Ferry: First-order optical and intervalley scattering in semiconductors. Phys. Rev. B 14, 1605–1609 (1976)CrossRefGoogle Scholar
  14. 5.14
    H. Brooks: Scattering by ionized impurities in semiconductors. Phys. Rev. 83, 879 (1951)Google Scholar
  15. 5.15
    E.M. Conwell, V. Weisskopf: Theory of impurity scattering in semiconductors. Phys. Rev. 77, 388–390 (1950)CrossRefGoogle Scholar
  16. 5.16
    R.L. Liboff: Quantum Mechanics (Addison-Wesley, Reading, MA 1980) p. 625Google Scholar
  17. 5.17
    S.M. Sze: Semiconductor Devices (Wiley, New York 1985) p. 33Google Scholar
  18. 5.18
    G.E. Stillman, C. M. Wolfe, J.O. Dimmock: Hall coefficient factor for polar mode scattering in n-type GaAs. J. Phys. Chem. Solids 31, 1199–1204 (1970)CrossRefGoogle Scholar
  19. 5.19
    K. Fletcher, P.N. Butcher: An exact solution of the linearized Boltzmann equation with applications to the Hall mobility and Hall factor of n-GaAs. J. Phys. C 5, 212–224 (1972)CrossRefGoogle Scholar
  20. 5.20
    H.L. Störmer, R. Dingle, A.C. Gossard, W. Wiegmann, R. A. Logan: Electronic properties of modulation-doped GaAs-AlxGa1−xAs Superlattices, in Physics of Semiconductors 1978, ed. by B. L. H. Wilson (Inst. Phys., Bristol 1979) pp. 557–560Google Scholar
  21. 5.21
    W. Walukiewicz, H. E. Ruda, J. Lagowski, H.C. Gatos: Electron mobility in modulation-doped heterostructures. Phys. Rev. B 30, 4571–4582 (1984)CrossRefGoogle Scholar
  22. 5.22
    S. Wang: Fundamentals of Semiconductor Theory and Device Physics (Prentice Hall, Englewood Cliffs, NJ 1989)Google Scholar
  23. 5.23
    E.M. Conwell: High Field Transport in Semiconductors. Solid State Physics, Suppl. 9 (Academic, New York 1967)Google Scholar
  24. 5.24
    E.J. Yoffa: Dynamics of dense laser-induced plasmas. Phys. Rev. B 21, 2415–2425 (1980)CrossRefGoogle Scholar
  25. 5.25
    W.H. Knox, C. Hirlimann, D. A.B. Miller, J. Shah, D. S. Chemla, C.V. Shank: Femtosecond excitation of nonthermal carrier populations in GaAs Quantum Wells. Phys. Rev. Lett. 56, 1191–1193 (1986)CrossRefGoogle Scholar
  26. 5.26
    K. Seeger: Semiconductor Physics, 5th edn., Springer Ser. Solid-State Sci., Vol. 40 (Springer, Berlin, Heidelberg 1991)Google Scholar
  27. 5.27
    B. Carnez, A. Cappy, A. Kaszynski, E. Constant, G. Salmer: Modeling of a submicrometer gate field-effect transistor including effects of nonstationary electron dynamics. J. Appl. Phys. 51, 784–790 (1980)CrossRefGoogle Scholar
  28. 5.28
    J. Singh: Physics of Semiconductors and Their Heterostructures (McGraw-Hill, New York 1993) pp. 524–531Google Scholar
  29. 5.29
    J.S. Blakemore: Semiconducting and other major properties of gallium arsenide. J. Appl. Phys. 53, R123–181 (1982)CrossRefGoogle Scholar
  30. 5.30
    J. Shah, B. Deveaud, T.C. Damen, W.T. Tsang, A.C. Gossard, P. Lugli: Determination of intervalley scattering rates in GaAs by subpicosecond luminescence spectroscopy. Phys. Rev. Lett. 59, 2222–2225 (1987)CrossRefGoogle Scholar
  31. 5.31
    D.S. Kim, P.Y. Yu: Hot-electron relaxation and hot phonons in GaAs studied by subpicosecond Raman scattering. Phys. Rev. B 43, 4158–4169 (1991)CrossRefGoogle Scholar
  32. 5.32
    P.J. Vinson, C. Pickering, A.R. Adams, W. Fawcett, G.D. Pitt: The band structure of GaAs from transferred electron effects at high pressure, in: Physics of Semiconductors 1976, ed. by. F.G. Fumi (Tipografia Marves, Rome 1976) pp. 1243–1246Google Scholar
  33. 5.33
    J.B. Gunn: Microwave oscillations of current in III–V semiconductors. Solid State Commun. 1, 88–91 (1963)CrossRefGoogle Scholar
  34. 5.34
    J.B. Gunn: Microwave oscillations of current in III–V semiconductors. IBM J. Res. Dev. 8, 141–159 (1964)CrossRefGoogle Scholar
  35. 5.35
    R. Dalven: Introduction to Applied Solid State Physics, 2nd edn. (Plenum, New York 1990) pp. 158–165CrossRefGoogle Scholar
  36. 5.36
    K. Seeger: Semiconductor Physics, 5th edn., Springer Ser. Solid-State Sci., Vol. 40 (Springer, Berlin, Heidelberg 1991) pp. 217–272Google Scholar
  37. 5.37
    C. Herring, E. Vogt: Transport and deformation potential theory for manyvalley semiconductors with anisotropic scattering. Phys. Rev. 101, 944–961 (1956); erratum 105, 1933 (1956)CrossRefGoogle Scholar
  38. 5.38
    E.H. Hall: On a new action of the magnet on electric current. Am. J. Math. 2, 287–292 (1879)CrossRefGoogle Scholar
  39. 5.39
    L. van der Pauw: A method of measuring specific resistivity and Hall effect of discs of arbitrary shape. Philips Res. Rep. 13, 1–9 (1958)Google Scholar

Transport Properties

  1. Dalven R.: Introduction to Applied Solid State Physics 2nd edn. (Plenum, New York 1990)CrossRefGoogle Scholar
  2. Ferry D. K.: Semiconductors (Macmillan, New York 1991)Google Scholar
  3. Rode D. L.: Low field electron transport. Semiconductors and Semimetals 10, 1–89 (Academic, New York 1982)Google Scholar
  4. Kittel C.: Introduction to Solid State Physics 7th edn. (Wiley, New York 1995)Google Scholar
  5. Nag B. R.: Electron Transport in Compound Semiconductors, Springer Ser. Solid-State Sci., Vol. 11 (Springer, Berlin, Heidelberg 1980)Google Scholar
  6. Ridley B. K.: Quantum Processes in Semiconductors, 2nd edn. (Clarendon, Oxford 1988)Google Scholar
  7. Seeger K.: Semiconductor Physics, 5th edn., Springer Ser. Solid-State Sci., Vol. 40 (Springer, Berlin, Heidelberg 1991); J. Shah: Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, 2nd edn., Springer Ser. Solid-State Sci., Vol. 115 (Springer, Heidelberg, 1999)Google Scholar
  8. Wiley J.D.: Mobility of holes in III–V compounds. Semiconductors and Semimetals 10, 91–174 (Academic, New York 1982)Google Scholar
  9. Ziman J. M.: Principles of the Theory of Solids, 2nd edn. (Cambridge Univ. Press, Cambridge 1972)CrossRefGoogle Scholar

Hot Carriers

  1. Conwell E. M.: High Field Transport in Semiconductors, Solid State Physics, Suppl. 9 (Academic, New York 1967)Google Scholar
  2. Conwell E. M.: In Handbook of Semiconductors (North-Holland, Amsterdam 1982) Vol. 1, pp. 513–561Google Scholar
  3. Jacoboni C., P. Lugli: The Monte Carlo Method for Semiconductor Device Simulation (Springer, New York 1989)CrossRefGoogle Scholar

Devices

  1. Singh J.: Physics of Semiconductors and Their Heterostructures (McGraw-Hill, New York 1993)Google Scholar
  2. Sze S. M.: Semiconductor Devices (Wiley, New York 1985)Google Scholar
  3. Wang, S.: Fundamentals of Semiconductor Theory and Device Physics (Prentice Hall Englewood Cliffs, NJ 1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter Y. Yu
    • 1
  • Manuel Cardona
    • 2
  1. 1.Department of PhysicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Max-Planck-Institut für FestkörperforschungStuttgartGermany

Personalised recommendations