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Electronic superstructures of semiconductor surfaces and of layered transition-metal compounds

  • Erio Tosatti
Chapter
Part of the Advances in Solid State Physics book series (ASSP, volume 15)

Abstract

We review some of the current work on the atomic and electronic structure of reconstructed (111) surfaces of group IV semiconductors. The reasons and the possible mechanisms that lead to formation of superstructures are discussed. Charge and spin density waves that follow from the electronic instability of a model ideal surface are considered in some detail.

The closely analogous problem of superlattices in layered transition-metal dichalcogenides such as 1T-TaS2 is also briefly touched.

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References

  1. [1]
    Halperin, B. I. and Rice, T. M., Solid State Physics 21, 115 (1968).CrossRefGoogle Scholar
  2. [2]
    Kohn, W., in: Many Body Physics, p. 353. C. Dewitt and R. Balian (eds.), Gordon and Breach (1968); Overhauser, A. W., Phys. Rev. 167, 692 (1968).Google Scholar
  3. [3]
    Overhauser, A. W., Phys. Rev. 128, 1437 (1962). Herring, C., in: Magnetism, Vol. 4 G. Rado and H. Suhl (eds.), Academic Press (1966).zbMATHCrossRefADSGoogle Scholar
  4. [4]
    Zeller, H. R., in: Festkörperprobleme XIII, (Advances in Solid State Physics), p. 31. H. J. Queisser (ed.), Pergamon-Vieweg (1974).Google Scholar
  5. [5]
    Gläser, W., in: Festkörperprobleme XIV, (Advances in Solid State Physics), p. 205, H. J. Queisser (ed.), Pergamon-Vieweg (1974).Google Scholar
  6. [6]
    Andersson, S., lecture notes, 1974 Winter College on Surface Science, IAEA-ICTP, Trieste (1974), (to be published).Google Scholar
  7. [7]
    See, e. g., Davison, S. G. and Levine, J. D., Solid State Physics 25, 1 (1970), and references therein.CrossRefGoogle Scholar
  8. [8]
    Mönch, W., in: Festkörperprobleme XIII, (Advances in Solid State Physics) p. 241. H. J. Queisser (ed.), Pergamon-Vieweg (1973).Google Scholar
  9. [9]
    Müller, W. and Mönch, W., Phys. Rev. Letters 27, 250 (1971).CrossRefADSGoogle Scholar
  10. [10]
    Henzler, M, Surface Sci. 24, 209 (1971).CrossRefADSGoogle Scholar
  11. [11]
    Henzler, M., Surface Sci. 19, 159 (1970); 22, 12 (1970),; 36, 109 (1973).CrossRefADSGoogle Scholar
  12. [12]
    Hagstrum, H. D. and Becker, G. E., Phys. Rev. B8, 1580 (1973); B8, 1592 (1973).CrossRefADSGoogle Scholar
  13. [13]
    Fischer, T. E., J. Vac. Sci. Technol. 9, 860 (1972).CrossRefADSGoogle Scholar
  14. [14]
    Eastman, D. E. and Grobman, W. D., Phys. Rev. Lett. 28, 1378 (1972).CrossRefADSGoogle Scholar
  15. [15]
    Wagner, L. F. and Spicer, W. E., Phys. Rev. Lett. 28, 1381 (1972).CrossRefADSGoogle Scholar
  16. [16]
    Erbudak, M. and Fischer, T. E., phys. Rev. Lett. 29, 732 (1972).CrossRefADSGoogle Scholar
  17. [17]
    Rowe, J. E. and Ibach, H., Phys. Rev. Lett. 32, 421 (1974).CrossRefADSGoogle Scholar
  18. [18]
    Rowe, J. E., Traum, M. M. and Smith, N. V., Phys. Rev. Lett. 33, 1333 (1974).CrossRefADSGoogle Scholar
  19. [19]
    Chiarotti, G., Del Signore, G. and Nannarone, S., Phys. Rev. Lett. 21, 1170 (1968); Chiarotti, G., Nannarone, S., Pastore, R. and Chiaradia, P., Phys. Rev. B4, 3398 (1971).CrossRefADSGoogle Scholar
  20. [20]
    Ibach, H., in: Fetskörperprobleme XI, (Advances in Solid State Physics), p. 135. H. J. Queisser (ed.), Pergamon-Vieweg (1971).Google Scholar
  21. [21]
    Ibach, H., in: Proceedings of the 12th International Conference on the Physics of Semiconductors, p. 655, M. Pilkuhn (ed.), Teubner, Stuttgart (1974).Google Scholar
  22. [22]
    Haneman, D., Phys. Rev. 170, 705 (1968).CrossRefADSGoogle Scholar
  23. [23]
    Lander, J. J. and Morrison, J., J. Appl. Phys. 34, 1403 (1963).CrossRefADSGoogle Scholar
  24. [24]
    Handler, P., J. Phys. Chem. Solids 14, 1 (1960).CrossRefADSGoogle Scholar
  25. [25]
    Lander, J. J., Gobeli, G. W. and Morrison, J. Appl. Phys. 34, 2298h (1963).CrossRefADSGoogle Scholar
  26. [26]
    Haneman, D., Phys. Rev. 121, 1093 (1961).CrossRefADSGoogle Scholar
  27. [27]
    Haneman, D. and Heron, D. L., in: The Structure and Chemistry of Solid Surfaces, p. 24, G. A. Somorjai (ed.), Wiley, New York, (1969).Google Scholar
  28. [28]
    Feuchtwang, T. E., Phys. Rev. 155, 717 (1967).ADSGoogle Scholar
  29. [29]
    Trullinger, S. E. and Cunningham, S. L., Phys. Rev. Lett. 30, 913 (1973).CrossRefADSGoogle Scholar
  30. [30]
    Blandin, A., Castiel, D. and Dobrzynski, L., Sol. St. Comm. 13, 1175 (1973).CrossRefADSGoogle Scholar
  31. [31]
    Forstmann, F., in: Festkörperprobleme XIII, (Advances in Solid State Physics), p. 275, H. J. Queisser (ed.), Pergamon-Vieweg (1973).Google Scholar
  32. [32]
    Pendry, J. B., Low Energy Electron Diffraction, Academic Press (1974).Google Scholar
  33. [33]
    Phillips, J. C., Surface Sci. 40, 459 (1973).CrossRefADSGoogle Scholar
  34. [34]
    Van Bommel, A. J. and Meyer, F., Surface Sci. 8, 467 (1967).CrossRefADSGoogle Scholar
  35. [35]
    Ibach, H. and Rowe, J. E., (to be published).Google Scholar
  36. [36]
    Ibach, H., (private communication).Google Scholar
  37. [37]
    Palmberg, P. W. and Peria, W. T., Surface Sci. 6, 57 (1967).CrossRefADSGoogle Scholar
  38. [38]
    Ibach, H., Phys. Rev. Lett. 27, 253 (1971).CrossRefADSGoogle Scholar
  39. [39]
    Chiarotti, G., Chiaradia, P., and Nannarone, S., (Surface Sci., to appear).Google Scholar
  40. [40]
    Froitzheim, H., Mönch, W., and Ibach, H., (to be published). Rowe, J. E., Ibach, H., and Froitzheim, H., Surface Sci. 48, 44 (1975); Henzler, M. and Heiland, G., Solid State Comm. 4, 499 (1966).Google Scholar
  41. [41]
    Henzler, M., Phys., Stat. Solidi 19, 833 (1967).CrossRefADSGoogle Scholar
  42. [42]
    Heiland, G. and Lamatsch, H., Surface Sci. 2, 18 (1964).CrossRefADSGoogle Scholar
  43. [43]
    Tosatti, E. and Anderson, P. W., Solid St. Comm. 14, 713 (1974); Proceedings of the 2nd International Conference on Solid Surfaces, Kyoto 1974, Japan. J. Appl. Phys. Suppl. 2, Pt. 2, 381 (1974).CrossRefGoogle Scholar
  44. [44]
    Heine, V., Proc. Roy. Soc. A331, 307 (1972).CrossRefADSGoogle Scholar
  45. [45]
    Dobrzynski, L. and Mills, D. L., Phys. Rev. B7, 2367 (1973).CrossRefADSGoogle Scholar
  46. [46]
    Koutecký, J. and Tomašek, M., Phys. Rev. 120, 1212 (1960).CrossRefADSGoogle Scholar
  47. [47]
    Tomašek, M., Surface Sci. 2, 8 (1964); Czech. J. Phys. B16, 828 (1966).CrossRefADSGoogle Scholar
  48. [48]
    Pugh, D., Phys. Rev. Lett. 12, 390 (1964).CrossRefADSGoogle Scholar
  49. [49]
    Hirabayashi, K., J. Phys. Soc. Japan 27, 1475 (1969).ADSCrossRefGoogle Scholar
  50. [50]
    Alstrup, I., Surface Sci. 20, 335 (1970).CrossRefADSGoogle Scholar
  51. [51]
    Bortolani, V., Calandra, C. and Kelly, M. J., J. Phys. C6, L349 (1973).CrossRefADSGoogle Scholar
  52. [52]
    Pandey, K. C. and Phillips, J. C., Phys. Rev. Lett. 32, 1433 (1974).CrossRefADSGoogle Scholar
  53. [53]
    Chaves, C. M., Majlis, N. and Cardona, M., Sol. St. Comm. 4, 271 (1964).CrossRefGoogle Scholar
  54. [54]
    Jones, R. O., Proc. Phys. Soc. 89, 443 (1968); J. Phys. C5, 1615 (1972).CrossRefADSGoogle Scholar
  55. [55]
    Elices, M. and Yndurain, E., J. Phys. C5, L146 (1972).CrossRefADSGoogle Scholar
  56. [56]
    Appelbaum, J. A. and Hamann, D. R., Phys. Rev. Lett. 31, 106 (1973); 32, 225 (1974).CrossRefADSGoogle Scholar
  57. [57]
    Elices, M., Flores, F., Louis, E., and Rubio, J., (to be published).Google Scholar
  58. [58]
    Appelbaum, J. A. and Hamann, D. R., in: Proceedings of the 12th International Conference on the Physics of Semiconductors, p. 675, M. Pilkuhn (ed.), Stuttgart (1974).Google Scholar
  59. [59]
    In the following, all vectors are understood to be 2-dimensional, with zero z-component. Three-dimensional vectors are denoted (k, kz).Google Scholar
  60. [60]
    See, e. g., Allen, R. E., Alldredge, G. P. and de Wette, F. W., Phys. Rev. B4, 1661 (1971). For results specifically on valence semiconductors the reader is referred to the work of W. Ludwig (ref. 57). (to be published)CrossRefADSGoogle Scholar
  61. [61]
    Ludwig, W., private communication, and to be published.Google Scholar
  62. [62]
    In our model (4.1) an exact fit is accidentally possible for 1.5 electrons/DB, when the FS is a hexagonn, and is fit by any 2n×2n distortion. In 1-dimensional systems, where E (k) depends only on one direction of k, the, fit is always perfect. Systems with flat parallel pieces of FS are effectively one-dimensional in this sense.Google Scholar
  63. [63]
    If one had t<0, that is if E (k) were a minimum at k=0, then v should be replaced by 2-v. Values larger than 1 become smaller than 1, and viceversa.Google Scholar
  64. [64]
    Schrieffer, J. R., Theory of Superconductivity, Benjamin (1966).Google Scholar
  65. [65]
    Stern, F., Phys. Rev. Lett. 18, 54 (1967).CrossRefADSGoogle Scholar
  66. [66]
    Hubbard, J., Proc. Roy. Soc. (London) A243, 336 (1957).ADSMathSciNetCrossRefGoogle Scholar
  67. [67]
    Chan, S. K. and Heine, V., J. Phys. F3, 795 (1973). Agreement between the results of Sections 5 and 7, and those found in this paper is obtained by removing a factor 2 in front of their coulomb interaction uq.CrossRefADSGoogle Scholar
  68. [68]
    Lee, P. A., Rice, T. M. and Anderson, P. W., Sol. St. Comm. 14, 703 (1974).CrossRefADSGoogle Scholar
  69. [69]
    Fröhlich, H., Proc. Roy. Soc. London A223, 296 (1954).zbMATHADSCrossRefGoogle Scholar
  70. [70]
    Overhauser, A. W., Phys. Rev. B3, 3173 (1971).CrossRefADSGoogle Scholar
  71. [71]
    Brüesch, P. and Zeller, H. R., Sol. St. Comm. 14, 1037 (1974).CrossRefADSGoogle Scholar
  72. [72]
    Des Cloizeaux, J., J. Phys. Chem. Solids 26, 259 (1965).CrossRefADSGoogle Scholar
  73. [73]
    Rice, T. M., Barker, A. S., Halperin, B. I. and McWhan, D. B., J. Appl. Phys. 40, 1337 (1969).CrossRefADSGoogle Scholar
  74. [74]
    Barker, A. S. and Ditzenberger, J. A., Phys. Rev. B1, 4378 (1970).CrossRefADSGoogle Scholar
  75. [75]
    Rice, M. J. and Strässler, S., Sol. St. Comm. 13, 125 (1972).CrossRefGoogle Scholar
  76. [76]
    Allender, D., Bray, J. W. and Bardeen, J. Phys. Rev. B9, 119 (1974).CrossRefADSGoogle Scholar
  77. [77]
    Selloni, A. and Tosatti, E., Sol. St. Comm. (to be published).Google Scholar
  78. [78]
    Bassani, F., and Pastori-Parravicini, G., Optical Properties of Solids, Pergamon Press (to be published).Google Scholar
  79. [79]
    Lomer, W. M., Proc. Phys. Soc. 80, 489 (1962).CrossRefADSGoogle Scholar
  80. [80]
    Rice, T. M. and Halperin, B. I., Phys. Rev. B1, 509 (1970).CrossRefADSGoogle Scholar
  81. [81]
    Wilson, J. A. and Yoffe, A. D., Adv. Phys. 18, 193 (1969).CrossRefADSGoogle Scholar
  82. [82]
    Yoffe, A. D., in: Festkörperprobleme XIII, (Advances in Solid State Physics), p. 1. H. J. Queisser (ed.), Pergamon-Vieweg (1973).Google Scholar
  83. [83]
    Williams, P. M., Parry, G. S. and Scruby, C. B., Phil. Mag. 29, 695 (1974); Scruby, C. B., Williams, P. M., and Parry, G. S., Phil. Mag. 31, 255 (1975).CrossRefADSGoogle Scholar
  84. [84]
    Shepherd, F. R., Williams, P. M., Young, D. A. and Scruby, C. B., in: Proceedings of the 12th International Conference on the Physics of Semiconductors, p. 1329, M. Pikuhn (ed.), Teubner, Stuttgart (1974). We are grateful to Dr. Williams for providing the diffraction pictures of Fig. 25.Google Scholar
  85. [85]
    Thompson, R. H., Gamble, F. R. and Revelli, J. F., Sol. St. Comm. 14, 497 (1974).CrossRefGoogle Scholar
  86. [86]
    Wilson, J. A., Di Salvo, F. J., andMahajan, S., (to be published).Google Scholar
  87. [87]
    Williams, P. M., and Scruby, C. B., (private communication).Google Scholar
  88. [88]
    Mattheiss, L. F., Phys. Rev. B8, 3719 (1973).CrossRefADSGoogle Scholar
  89. [89]
    An “experimental” determination of energy bands in 1T-TaS2 and 1T-Se2 has been performed by means of angle-resolved photoemission by Smith, N. V., Traum, M. M. and Di Salvo, F. J., (to be published).Google Scholar
  90. [90]
    Wilson, J. A., Di Salvo, F. J. and Mahajan, S., Phys. Rev. Lett. 32, 833 (1974).CrossRefGoogle Scholar
  91. [91]
    Beal, A. R. and Liagn, W. Y., Phil. Mag. 27, 1397 (1973).CrossRefADSGoogle Scholar
  92. [92]
    Grant, A. J., Griffiths, T. M., Pitt, G. D. and Yoffe, A. D., J. Phys. C7 L249 (1974); Proc. XII Int. Conf. on the Physics of Semiconductors, p. 592, M. Pilkuhn (ed.), Teubner, Stuttgart (1974).CrossRefADSGoogle Scholar
  93. [93]
    Hughes, H. P. and Liang, W. Y., J. Phys. C7, L162 (1974).CrossRefADSGoogle Scholar
  94. [94]
    Thompson, A. H., Phys. Rev. Lett. 24, 520 (1975).CrossRefADSGoogle Scholar
  95. [95]
    See, e. g., Lee, P. A., Rice, T. M. and Anderson, P. W., Phys. Rev. Lett. 31, 462 (1973). for a treatment of the 1-dimensional case.CrossRefADSGoogle Scholar
  96. [96]
    Florio, J. V. and Robertson, W. D., Surface Sci. 22, 459 (1970). *** DIRECT SUPPORT *** A00AX015 00005CrossRefADSGoogle Scholar

Copyright information

© Friedr. Vieweg & Sohn Verlagsgesellschaft mbH 1975

Authors and Affiliations

  • Erio Tosatti
    • 1
  1. 1.G.N.S.M.-C.N.R., Isituto di FisicaUniversitá di RomaRomaItaly

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