Advertisement

Conduction by Polarons in Ionic Crystals

  • Frederick C. Brown

Abstract

Strongly ionic crystals such as the alkali or silver halides have filled valence bands which are separated from empty conduction bands by forbidden regions as wide as several electron-volts. Consequently these materials are insulators at low temperature. On the other hand, small photocurrents can be made to flow when the crystals are illuminated with light capable of producing electrons and holes. Photoexcitation takes place in highly perfect crystals either by a one-photon process across the band gap or, at very high light intensity, by a two-photon process. In the latter case, the sum of the photon energies must be equal to or greater than the band gap. Defects which become electron donors can be introduced into ionic crystals just as in semiconductors. In the alkali halides, the most common donor is the F center, or electron trapped at a negative-ion vacancy, and this defect can be formed either by radiation, for example, X-rays, or by heating in alkali metal vapor, i.e., additive coloration. The F-center electron in its ground state is bound with too great an energy to be thermally ionized at room temperature. Therefore, colored alkali halide crystals can be made conducting most conveniently by illuminating with light whose quantum energy is equal to or greater than the ionization energy of the F center, usually 3 or 4 eV.

Keywords

Cyclotron Resonance High Electric Field Hall Mobility Ionic Crystal Alkali Halide 
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.

References

  1. 1.
    H. Fröhlich, Advan. Phys. 3, 325 (1954).ADSCrossRefGoogle Scholar
  2. 2.
    S. Pekar, Untersuchungen über die Electronentheorie der Kristalle (Akademie-Verlag, Berlin, 1954).Google Scholar
  3. L. D. Land au and S. I. Pekar, Zh. Eksperim. i Teor. Fiz. 18, 419 (1948).Google Scholar
  4. 3.
    C. G. Kuper and G. D. Whitfield (Eds.), Polarons and Excitons (Oliver and Boyd, Edinburgh, 1963).Google Scholar
  5. 3a.
    F. C. Brown, Ibid., p. 323.Google Scholar
  6. 4.
    J. Appel, in Solid State Physics, Vol. 21, Ed. by F. Seitz, D. Turnbull, and H. Ehrenreich (Academic Press, New York, 1968).Google Scholar
  7. 5.
    L. D. Landau, Phys. Z. Sowjet. 3, 664 (1933).MATHGoogle Scholar
  8. 6.
    N. F. Mott, Proc. Phys. Soc. London (extra part) 49, 3 (1937).CrossRefGoogle Scholar
  9. 7.
    H. Fröhlich, H. Pelzer, and S. Zienau, Phil. Mag. 41, 221 (1950).MATHGoogle Scholar
  10. 8.
    H. Fröhlich, in Ref. 3, Chapter 1.Google Scholar
  11. 9.
    C. Kittel, Quantum Theory of Solids (Wiley, New York, 1963).Google Scholar
  12. 10.
    W. B. Fowler, Phys. Rev. 135, A1725 (1967).CrossRefGoogle Scholar
  13. 11.
    A. H. Kahn, Phys. Rev. 172, 813 (1968).ADSCrossRefGoogle Scholar
  14. 12.
    P. M. Platzman, Phys. Rev. 125, 1961 (1962).ADSMATHCrossRefGoogle Scholar
  15. 13.
    D. M. Larsen, Phys. Rev. 187, 1147 (1969).ADSCrossRefGoogle Scholar
  16. 14.
    A. M. Stoneham, J. Phys. C, Solid State Physics 3, L131 (1970).ADSCrossRefGoogle Scholar
  17. 15.
    D. M. Larsen, Phys. Rev. 180, 919 (1969); 135, A419 (1964).ADSCrossRefGoogle Scholar
  18. 16.
    K. K. Bajaj, Phys. Rev. 170, 694 (1968).ADSCrossRefGoogle Scholar
  19. 17.
    T. Lee, F. Low, and D. Pines, Phys. Rev. 90, 297 (1953).MathSciNetADSMATHCrossRefGoogle Scholar
  20. 18.
    D. M. Larsen, Phys. Rev. 174, 1046 (1968).ADSCrossRefGoogle Scholar
  21. 19.
    J. Devreese and R. Evrard, Phys. Stat. Sol. 3, 2133 (1963); Physics Letters 11, 278 (1966)ADSCrossRefGoogle Scholar
  22. E. Kartheuser, R. Evrard, and J. Devreese, Phys. Rev. Letters 22, 94 (1969).ADSCrossRefGoogle Scholar
  23. 20.
    R. P. Feynman, Phys. Rev. 97, 660 (1955).ADSMATHCrossRefGoogle Scholar
  24. 21.
    M. Porsch, Phys. Stat. Sol. 39, 477 (1970).MathSciNetADSCrossRefGoogle Scholar
  25. 22.
    D. Matz and B. C. Burkey, Phys. Rev. B3, 3487 (1971); D. Matz, to be published.ADSGoogle Scholar
  26. 23.
    D. C. Langreth, Phys. Rev. 159, 717 (1967).ADSCrossRefGoogle Scholar
  27. 24.
    J. J. O’Dwyer, Theory of Dielectric Breakdown of Solids (Oxford University Press, 1964)Google Scholar
  28. J. J. O’Dwyer, J. Appl. Phys. 37, 599 (1966); J. Phys. Chem. Solids 28, 1137 (1967).ADSCrossRefGoogle Scholar
  29. 25.
    J. R. Hanscomb, J. Appl. Phys. 41, 3597 (1970).ADSCrossRefGoogle Scholar
  30. 26.
    R. M. Handy, J. Appl. Phys. 37, 4620 (1966)ADSCrossRefGoogle Scholar
  31. E. P. Savoy and D. E. Anderson, J. Appl. Phys. 38, 3245 (1967).ADSCrossRefGoogle Scholar
  32. 27.
    A. M. Goodman, J. Electrochem. Soc. 115, 276C (1968); Phys. Rev. 164, 1145 (1967).CrossRefGoogle Scholar
  33. 28.
    J. Dressner, Phys. Rev. 143, 558 (1966); J. Phys. Chem. Solids 25, 505 (1964).ADSCrossRefGoogle Scholar
  34. 29.
    J. R. Macdonald and J. E. Robinson, Phys. Rev. 95, 44 (1954).ADSCrossRefGoogle Scholar
  35. 30.
    R. C. Hanson, J. Phys. Chem. 66, 2376 (1962).CrossRefGoogle Scholar
  36. 31.
    M. Onuki, J. Phys. Soc. Japan 16, 981 (1961).ADSCrossRefGoogle Scholar
  37. 32.
    G. Jaffe, Ann. Physik 16, 217 (1933).ADSCrossRefGoogle Scholar
  38. 33.
    J. R. Macdonald, J. Chem. Phys. 40, 1 (1964).CrossRefGoogle Scholar
  39. 34.
    J. R. Haynes and W. Schockley, Physical Society Bristol Conference Report, p. 151 (1948); see also Solid Luminescent Materials (Cornell Conference) (Wiley, New York, 1948), p. 430.Google Scholar
  40. 35.
    J. R. Haynes and W. Schockley, Phys. Rev. 82, 935 (1951).ADSCrossRefGoogle Scholar
  41. 36.
    R. Hofstadter, Nucleonics 4(4), 2 (1949); 4 (5), 29 (1949).Google Scholar
  42. 37.
    K. A. Yamakawa, Phys. Rev. 82, 522 (1951).ADSCrossRefGoogle Scholar
  43. 38.
    F. C. Brown and J. C. Street, Phys. Rev. 84, 1183 (1951)ADSCrossRefGoogle Scholar
  44. F. C. Brown, Phys. Rev. 97, 355 (1955).ADSCrossRefGoogle Scholar
  45. 39.
    F. C. Brown and F. E. Dart, Phys. Rev. 108, 281 (1957)ADSCrossRefGoogle Scholar
  46. F. C. Brown, J. Phys. Chem. Solids 4, 206 (1958).ADSCrossRefGoogle Scholar
  47. 40.
    R. S. Van Heyningen, Phys. Rev. 128, 2112 (1962).ADSCrossRefGoogle Scholar
  48. 41.
    R. K. Ahrenkiel, Phys. Rev. 180, 859 (1969).ADSCrossRefGoogle Scholar
  49. 42.
    R. G. Kepler, Phys. Rev. 119, 1226 (1960).ADSCrossRefGoogle Scholar
  50. 43.
    H. Hirth and U. Todheide-Haupt, Phys. Stat. Sol. 31, 425 (1969).ADSCrossRefGoogle Scholar
  51. 44.
    N. F. Mott and R. W. Gurney, Electronic Processes in Ionic Crystals (Oxford University Press, 1948), p. 117-124; see also R. S. Van Heyningen and F. C. Brown, Phys. Rev. 111, 462 (1958).ADSCrossRefGoogle Scholar
  52. 45.
    P. J. Van Heerden, Phys. Rev. 106, 468 (1957); 108, 230 (1957)ADSCrossRefGoogle Scholar
  53. S. M. Ryvikin, Soviet Phys.—Tech. Phys. 1, 2580 (1956).Google Scholar
  54. 46.
    P. Mark and W. Helfrich, J. Appl. Phys. 33, 205 (1961).ADSCrossRefGoogle Scholar
  55. 47.
    A. Many and G. Rakavy, Phys. Rev. 126, 1980 (1962).ADSCrossRefGoogle Scholar
  56. 48.
    I. P. Batra and H. Seki, Phys. Rev. B1, 3409 (1970).Google Scholar
  57. 49.
    A. G. Redfield, Phys. Rev. 94, 526 (1954); 94, 537 (1954).ADSCrossRefGoogle Scholar
  58. 50.
    F. C. Brown, Phys. Rev. 92, 502 (1953).ADSCrossRefGoogle Scholar
  59. 51.
    K. Kobayashi and F. C. Brown, Phys. Rev. 113, 507 (1959); J. Phys. Chem. Solids 8, 300 (1959).ADSCrossRefGoogle Scholar
  60. 52.
    T. Masumi, R. K. Ahrenkiel, and F. C. Brown, Phys. Stat. Sol. 11, 163 (1965).ADSCrossRefGoogle Scholar
  61. 53.
    D. C. Burnham, F. C. Brown, and R. S. Knox, Phys. Rev. 119, 1560 (1960).ADSCrossRefGoogle Scholar
  62. 54.
    F. C. Brown and N. Inchauspe, Phys. Rev. 121, 1303 (1961).ADSCrossRefGoogle Scholar
  63. 55.
    R. K. Ahrenkiel and F. C. Brown, Phys. Rev. 136, A223 (1964).ADSCrossRefGoogle Scholar
  64. 56.
    T. Kawai, K. Kobayashi, and H. Fujita, J. Phys. Soc. Japan 21, 453 (1966).ADSCrossRefGoogle Scholar
  65. 57.
    H. Fujita, K. Kobayashi, and T. Kawai, and K. Shiga, J. Phys. Soc. Japan 20, 109 (1965).ADSCrossRefGoogle Scholar
  66. 58.
    F. Nakazawa and H. Kanzaki, J. Phys. Soc. Japan 27, 1185 (1969).ADSGoogle Scholar
  67. 59.
    G. Jacobs, private communications.Google Scholar
  68. 60.
    C. H. Seager and D. Emin, Phys. Rev. B2, 3421 (1970)ADSGoogle Scholar
  69. C. H. Seager, Phys. Rev. B3, 3479 (1971).ADSGoogle Scholar
  70. 61.
    J. A. Borders and J. W. Hodby, Rev. Sci. Instr. 39, 722 (1968).ADSCrossRefGoogle Scholar
  71. 62.
    G. C. Smith, Rev. Sci. Instr. 40, 1454 (1969).ADSCrossRefGoogle Scholar
  72. 63.
    H. H. Tippins and F. C. Brown, Phys. Rev. 129, 2554 (1963).ADSCrossRefGoogle Scholar
  73. 64.
    D. N. Lyon and T. H. Geballe, Rev. Sci. Instr. 21, 769 (1950).ADSCrossRefGoogle Scholar
  74. 65.
    G. Delacote and M. Schott, Solid State Comm. 4, 177 (1966).ADSCrossRefGoogle Scholar
  75. 66.
    J. Wei, private communication.Google Scholar
  76. 67.
    J. W. Hodby and J. A. Borders, F. C. Brown, and S. Foner, Phys. Rev. Letters 19, 952 (1967).ADSCrossRefGoogle Scholar
  77. 68.
    J. Waldman, D. M. Larsen, P. E. Tannenwald, C. C. Bradley, D. R. Cohn, and B. Lax, Phys. Rev. Letters 23, 1033 (1969).ADSCrossRefGoogle Scholar
  78. 69.
    M. Mikkor, K. Kanazawa, and F. C. Brown, Phys. Rev. 162, 848 (1967).ADSCrossRefGoogle Scholar
  79. 70.
    J. W. Hodby, Solid State Comm. 7, 811 (1969).ADSCrossRefGoogle Scholar
  80. 71.
    G. Ascarelli and F. C. Brown, Phys. Rev. Letters 9, 209 (1962).ADSCrossRefGoogle Scholar
  81. 72.
    D. J. Howarth and E. H. Sondheimer, Proc. Roy. Soc. A219, 53 (1953).ADSGoogle Scholar
  82. 73.
    R. L. Petritz and W. W. Scanlon, Phys. Rev. 97, 1620 (1958).ADSCrossRefGoogle Scholar
  83. 74.
    F. Low and D. Pines, Phys. Rev. 98, 414 (1958).ADSCrossRefGoogle Scholar
  84. 75.
    T. Schultz, Phys. Rev. 116, 529 (1959).ADSCrossRefGoogle Scholar
  85. 76.
    R. P. Feynman, R. W. Hellwerth, C. K. Iddings, and P. M. Platzman, Phys. Rev. 127, 1004 (1962).ADSMATHCrossRefGoogle Scholar
  86. 77.
    D. C. Langreth and L. P. Kadanoff, Phys. Rev. 133, A1070 (1964).ADSCrossRefGoogle Scholar
  87. 78.
    D. C. Langreth, Phys. Rev. 137, A760 (1965).ADSCrossRefGoogle Scholar
  88. 79.
    L. P. Kadanoff, Phys. Rev. 130, 1364 (1963).MathSciNetADSCrossRefGoogle Scholar
  89. 80.
    Y. Osaka, Progr. Theoret. Phys. (Kyoto) 22, 437 (1959).ADSCrossRefGoogle Scholar
  90. 81.
    D. C. Langreth, Phys. Rev. 159, 717 (1967).ADSCrossRefGoogle Scholar
  91. 82.
    T. Schultz, Thesis, Massachusetts Institute of Technology, 1956 (unpublished).Google Scholar
  92. 83.
    K. K. Thornber and R. P. Feynman, Phys. Rev. B1, 4099 (1970).ADSGoogle Scholar
  93. 84.
    D. W. Berreman, Phys. Rev. 130, 2193 (1963).ADSCrossRefGoogle Scholar
  94. 85.
    J. R. D. Copley, R. W. Macpherson, and T. Timusk, Phys. Rev. 182, 965 (1969).ADSCrossRefGoogle Scholar
  95. 86.
    P. R. Vijayaraghavan, R. M. Nicklow, H. G. Smith, and M. K. Wilkinson, Phys. Rev. B1, 4819 (1970).ADSGoogle Scholar
  96. 87.
    D. M. Larsen, Phys. Rev. 172, 967 (1968).ADSCrossRefGoogle Scholar
  97. 88.
    K. K. Thornber, Phys. Rev. B3, 1929 (1971).ADSGoogle Scholar
  98. 89.
    T. Masumi, Phys. Rev. 129, 2564 (1963); Phys. Rev. 159, 761 (1967).ADSCrossRefGoogle Scholar
  99. 90.
    H. H. Tippins and F. C. Brown, Phys. Rev. 129, 2554 (1963).ADSCrossRefGoogle Scholar
  100. 91.
    W. Schockley, Bell System Tech. J. 30, 991 (1951).Google Scholar
  101. 92.
    F. Seitz, Phys. Rev. 76, 1376 (1949).ADSMATHCrossRefGoogle Scholar
  102. 93.
    D. Matz and F. Garcia-Moliner, Phys. Stat. Sol. 5, 495 (1964); J. Phys. Chem. Solids 26, 551 (1965).ADSCrossRefGoogle Scholar
  103. 94.
    M. Mikkor and F. C. Brown, Phys. Rev. 162, 841 (1967).ADSCrossRefGoogle Scholar
  104. 95.
    J. Borders, Thesis, University of Illinois, 1968 (unpublished).Google Scholar
  105. 96.
    F. Nakazawa and H. Kanzaki, J. Phys. Soc. Japan 27, 1184 (1969); 22, 844 (1967); 20, 468 (1965).ADSCrossRefGoogle Scholar
  106. 97.
    S. Bolte and F. C. Brown, in Proc. Third Int. Conf. on Photoconductivity (J. Phys. Chem. Solids Suppl.), Ed. by E. M. Pell (Pergamon Press, New York, 1970).Google Scholar
  107. 98.
    J. W. Hodby, J. A. Borders, and F. C. Brown, J. Phys. C, Solid State Phys. 3, 335 (1970).ADSCrossRefGoogle Scholar
  108. 99.
    A. B. Kunz, Phys. Stat. Sol. 29, 115 (1968); J. Phys. Chem. Solids 31, 265 (1970); J. Phys. C, Solid State Phys. 3, 1542 (1970).ADSCrossRefGoogle Scholar
  109. 100.
    M. Mikkor, K. Kanazawa, and F. C. Brown, Phys. Rev. 162, 848 (1967).ADSCrossRefGoogle Scholar
  110. 101.
    E. Hanamura, T. Inui, and Y. Toyozawa, J. Phys. Soc. Japan 17, 666 (1963).ADSGoogle Scholar
  111. 102.
    R. Stratton, Proc. Roy. Soc. A242, 355 (1957); A246, 406 (1958).ADSGoogle Scholar
  112. 103.
    H. F. Budd, Phys. Rev. 131, 1520 (1964); Phys. Rev. 140, A2170 (1965).ADSCrossRefGoogle Scholar
  113. 104.
    J. W. Hodby, J. Phys. E, Sci. Instr. 2, 796 (1969); J. Phys. E. Sci. Instr. 3, 229 (1970).ADSCrossRefGoogle Scholar
  114. 105.
    J. H. Hodby, J. Phys. C, Solid State Phys. 4, L9 (1971).CrossRefGoogle Scholar
  115. 106.
    G. Whitfield and R. Puff, Phys. Rev. 139, A338 (1965).ADSCrossRefGoogle Scholar
  116. 107.
    D. M. Larsen, Phys. Rev. 144, 697 (1966).ADSCrossRefGoogle Scholar
  117. 108.
    B. Velicky, in International School of Physics, Enrico Fermi, Vol. XXXIV, Ed. by J. Tauc (Academic Press, New York, 1966), p. 379; E. Kartheuser, Ph.D. thesis, University of Liege, 1968 (unpublished).Google Scholar
  118. 109.
    J. W. Hodby, Phys. Rev. Letters 23, 1235 (1969).ADSCrossRefGoogle Scholar
  119. 110.
    A. Honig, Phys. Rev. Letters 17, 186 (1966).ADSCrossRefGoogle Scholar
  120. 111.
    R. Maxwell and A. Honig, Phys. Rev. Letters 17, 188 (1966).ADSCrossRefGoogle Scholar
  121. 112.
    L. I. Schiff, Quantum Mechanics, 3rd Ed. (McGraw-Hill, New York, 1968), p. 393.Google Scholar
  122. 113.
    F. Porret and F. Liity, Phys. Rev. Letters 26, 843 (1971).ADSCrossRefGoogle Scholar
  123. 114.
    J. W. Hodby, J. Phys. C 3, 592 (1970).ADSCrossRefGoogle Scholar
  124. 115.
    W. S. Baer, Phys. Rev. 144, 734 (1966); Phys. Rev. 154, 785 (1967).ADSCrossRefGoogle Scholar
  125. 116.
    R. C. Brandt and F. C. Brown, Phys. Rev. 181, 1241 (1969)ADSCrossRefGoogle Scholar
  126. R. C. Brandt, D. M. Larsen, P. P. Crooker, and G. B. Wright, Phys. Rev. Letters 23, 240 (1969).ADSCrossRefGoogle Scholar
  127. 117.
    R. P. Khosla, Phys. Rev. 183, 827 (1970).Google Scholar
  128. 118.
    F. Moser, D. Matz, and S. Lyu, Phys. Rev. 182, 808 (1968).ADSCrossRefGoogle Scholar
  129. 119.
    K. K. Bajaj and T. D. Clark, Solid State Comm. 8, 825 (1970).ADSCrossRefGoogle Scholar
  130. 120.
    J. Waldman, D. M. Larsen, P. E. Tannenwald, C. C. Bradley, D. R. Cohn, and B. Lax, Phys. Rev. Letters, 23, 1033 (1969).ADSCrossRefGoogle Scholar
  131. 121.
    E. Burstein, in Lattice Dynamics, Proc. Int. Conf., Copenhagen, August 1963 (Pergamon Press, New York, 1964).Google Scholar
  132. 122.
    R. P. Lowndes, Physics Letters 21, 26 (1966)ADSCrossRefGoogle Scholar
  133. R. P. Lowndes and D. H. Martin, Proc. Roy. Soc. (London) A316, 351 (1970).ADSGoogle Scholar
  134. 123.
    K. Højendahl, K. dansk vidensk. Selsk. 16, No. 2 (1938).Google Scholar
  135. 124.
    R. P. Lowndes and D. H. Martin, Proc. Roy. Soc. A308, 473 (1969).ADSGoogle Scholar
  136. 125.
    R. C. Brand t and F. C. Brown, Phys. Rev. 181, 1241 (1969).ADSCrossRefGoogle Scholar
  137. 126.
    E. R. Cowley and A. Okazaki, Proc. Roy. Soc. (London) A300, 45 (1967).ADSGoogle Scholar
  138. 127.
    R. Z. Bachrach, Solid State Comm. 7, 1023 (1969).ADSCrossRefGoogle Scholar
  139. 128.
    G. O. Jones, D. H. Martin, P. A. Mawer, and C. H. Perry, Proc. Roy. Soc. A261, 10 (1961).ADSGoogle Scholar
  140. 129.
    J. T. Jenkin, J. W. Hodly, and U. Gross, J. Phys. C. (Solid State Phys.) 4, L89 (1971).ADSCrossRefGoogle Scholar
  141. 130.
    J. E. Baxter, G. Ascarelli, and S. Rodriguez, Phys. Rev. Letters 27, 100 (1971).ADSCrossRefGoogle Scholar
  142. 131.
    H. Tamura, T. Masumi, and K. Kobayashi, in Proc. Third Int. Conf. on Photoconductivity (J. Phys. Chem. Solids Suppl.), Ed. by E. M. Pell (Pergamon Press, New York, 1970).Google Scholar
  143. 132.
    A. P. Marchetti and G. L. Bottger, Phys. Rev. B3, 2604 (1971); also G. L. Bottger, private communication.ADSGoogle Scholar
  144. 133.
    G. L. Bottger and A. L. Geddes, J. Chem. Phys. 56 (1972).Google Scholar
  145. 134.
    American Institute of Physics Handbook, 2nd ed., McGraw-Hill, New York (1963), Vol. 6, p. 97.Google Scholar

Copyright information

© Plenum Press, New York 1972

Authors and Affiliations

  • Frederick C. Brown
    • 1
  1. 1.Department of PhysicsUniversity of IllinoisUrbanaUSA

Personalised recommendations