Skip to main content
SpringerLink
Log in

Optical Properties of Intrinsic Excitons in Bulk Semiconductors

  • Chapter
  • First Online:
Semiconductor Optics 1

Part of the book series: Graduate Texts in Physics ((GTP))

  • 2271 Accesses

Abstract

Phonon excitations are necessary to describe the optical properties of semiconductors and of insulators in the IR. Plasmons determine the optical properties of metals from the IR through the visible to the near UV, and in semiconductors, if present at all, they contribute along with the phonons to the IR spectra. Excitons, on the other hand, determine together with their continuum states (or the band-to-band transitions) the optical properties around and above the band gap, i.e., in the visible including the near UV and IR in the case of semiconductors and in the (V)UV for insulators. Although inorganic insulators like the alkali halides and organic ones such as anthracene have specific optical properties, many of the aspects presented in the following for excitons in semiconductors also apply to them. We will present in this chapter the intrinsic linear optical properties of excitons in bulk semiconductors starting from semiconductors with a dipole-allowed, direct band-to-band transition. They exhibit dipole-allowed excitons with the highest oscillator strength. Values of their longitudinal–transverse splitting \(\Delta _{\text {LT}}\) range from 0.1 to beyond 10 meV. However, not all excitons in this group of semiconductors have high oscillator strength. Also some excitons in semiconductors with dipole-forbidden band-to-band transitions may be dipole allowed, but with considerably lower oscillator strength. We will review these cases in Sect. 21.2, ending with some comments on indirect gap materials and intra-excitonic transitions (Sect. 21.3). Again, several experimental techniques will be introduced like use of integrating spheres, spectroscopy in momentum space and attenuated total reflectance.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. M. Hayashi, K. Katsuki, J. Phys. Soc. Jpn. 7, 599 (1952)

    Article  ADS  Google Scholar 

  2. F. Urbach, Phys. Rev. 92, 1324 (1953)

    Article  ADS  Google Scholar 

  3. R.J. Elliot, Phys. Rev. 108, 1384 (1957). Polarons and Excitons, ed. by C.G. Kupper, G.D. Whitfield (Oliver and Boyd, Edinburg, 1963), p. 269

    Google Scholar 

  4. W. Martienssen, J. Phys. Chem. Solids 2, 257 (1957)

    Article  ADS  Google Scholar 

  5. D. Dutton, Phys. Rev. 112, 785 (1958)

    Article  ADS  Google Scholar 

  6. J.J. Hopfield, Phys. Rev. 112, 1555 (1958)

    Article  ADS  Google Scholar 

  7. G. Heiland, E. Mollwo, F. Stöckmann, Solid State Phys. 8, 191 (1959). See also E. Mollwo, Reichsber. Phys. 1, 1 (1944)

    Google Scholar 

  8. J.J. Hopfield, J. Phys. Chem. Solids 15, 97 (1960)

    Article  ADS  Google Scholar 

  9. J.J. Hopfield, D.G. Thomas, Phys. Rev. 128, 2135 (1962)

    Article  ADS  Google Scholar 

  10. S.J. Pekar, Sov. Phys. Solid State 4, 953 (1962)

    Google Scholar 

  11. M.D. Sturge, Phys. Rev. 127, 768 (1962)

    Article  ADS  Google Scholar 

  12. J.J. Hopfield, D.G. Thomas, Phys. Rev. 132, 563 (1963)

    Article  ADS  Google Scholar 

  13. M.N. Kabler, Phys. Rev. A 136, 1296 (1964)

    Article  ADS  Google Scholar 

  14. G.D. Mahan, J.J. Hopfield, Phys. Rev. A 135, 428 (1964)

    Article  ADS  Google Scholar 

  15. M. Cardona, G. Harbeke, Phys. Rev. A 137, 1467 (1965)

    Article  ADS  Google Scholar 

  16. M. Cardona, M. Weinstein, G.A. Wolff, Phys. Rev. A 140, 633 (1965)

    Article  ADS  Google Scholar 

  17. D.L. Greenaway, G. Harbeke, J. Phys. Soc. Jpn. 21(Suppl.), 151 (1966)

    Google Scholar 

  18. G. Kuwabara, A. Misu, H. Sasaki, J. Phys. Soc. Jpn. 21(Suppl.), 148 (1966)

    Google Scholar 

  19. J. Ringeissen, Phys. Lett. 22, 571 (1966)

    Article  ADS  Google Scholar 

  20. N.J. Harrick, Internal Reflection Spectroscopy (Wiley, New Jersey, 1967)

    Google Scholar 

  21. M.N. Kabler, D.S. Patterson, Phys. Rev. Lett. 19, 652 (1967)

    Article  ADS  Google Scholar 

  22. Y. Onodera, Y. Toyozawa, J. Phys. Soc. Jpn. 22, 833 (1967)

    Article  ADS  Google Scholar 

  23. Y.P. Varshni, Physica 34, 149 (1967)

    Article  ADS  Google Scholar 

  24. W.Y. Liang, A.D. Yoffe, Phys. Rev. Lett. 20, 59 (1968)

    Article  ADS  Google Scholar 

  25. B. Segall, G.D. Mahan, Phys. Rev. 171, 935 (1968)

    Article  ADS  Google Scholar 

  26. Y. Toyozawa, J. Hermanson, Phys. Rev. Lett. 21, 1637 (1968)

    Article  ADS  Google Scholar 

  27. J. Voigt, F. Spiegelberg, Phys. Status Solidi B 30, 659 (1968)

    Article  ADS  Google Scholar 

  28. E.O. Kane, Phys. Rev. 180, 852 (1969)

    Article  ADS  Google Scholar 

  29. O. Madelung, Grundlagen der Halbleiterphysik, vol. 71, Heidelberger Taschenbücher (Springer, Berlin, 1970)

    Book  Google Scholar 

  30. J.P. Walter et al., Phys. Rev. B 1, 2661 (1970)

    Article  ADS  Google Scholar 

  31. D. Fröhlich, E. Mohler, P. Wiesner, Phys. Rev. Lett. 26, 554 (1971)

    Article  ADS  Google Scholar 

  32. M.V. Kurik, Phys. Status Solidi A 8, 9 (1971)

    Article  ADS  Google Scholar 

  33. Y. Petroff, M. Balkanski, Phys. Rev. B 3, 3299 (1971)

    Article  ADS  Google Scholar 

  34. H. Sumi, Y. Toyozawa, J. Phys. Soc. Jpn. 31, 342 (1971)

    Article  ADS  Google Scholar 

  35. D.D. Sell, P. Lawaetz, Phys. Rev. Lett. 26, 311–314 (1971)

    Article  ADS  Google Scholar 

  36. A. Bivas et al., Opt. Commun. 6, 142 (1972)

    Article  ADS  Google Scholar 

  37. H.B. Bebb, E.W. Williams, Semicond. Semimet. 8, 182 (1972)

    Google Scholar 

  38. J.D. Dow, D. Redfield, Phys. Rev. 85, 94 (1972)

    Google Scholar 

  39. L. Kalok, J. Treusch, Phys. Status Solidi A 52, K125 (1972)

    Article  ADS  Google Scholar 

  40. R.L. Weiher, W.C. Tait, Phys. Rev. B 5, 623 (1972)

    Article  ADS  Google Scholar 

  41. E.W. Williams, H.B. Bebb, Semicond. Semimet. 8, 321 (1972)

    Article  Google Scholar 

  42. K. Hümmer, Phys. Status Solidi B 56, 249 (1973)

    Article  ADS  Google Scholar 

  43. G.H. Jensen, T. Skettrup, Phys. Status Solidi B 60, 169 (1973)

    Article  ADS  Google Scholar 

  44. E. Swenberg, N. Geacintov, Org. Mol. Photophys. 1, 489 (1973)

    Google Scholar 

  45. M. Bettini, S. Suga, R. Hanson, Solid State Commun. 15, 1885 (1974)

    Article  ADS  Google Scholar 

  46. S. Suga, T. Koda, Phys. Status Solidi B 66, 255 (1974)

    Article  ADS  Google Scholar 

  47. E. Tomzig, R. Helbig, Solid State Commun. 15, 1513 (1974) and J. Lumin. 14, 403 (1976)

    Google Scholar 

  48. A. Frova et al., Phys. Rev. Lett. 34, 1572 (1975)

    Article  ADS  Google Scholar 

  49. P. Hiesinger et al., Phys. Status Solidi B 67, 641 (1975)

    Article  ADS  Google Scholar 

  50. C. Klingshirn, Dissertation Universität Erlangen (1975)

    Google Scholar 

  51. V.A. Kiselev, B.S. Razbirin, I.N. Uraltsev, Phys. Status Solidi B 72, 161 (1975)

    Article  ADS  Google Scholar 

  52. J. Lagois, K. Hümmer, Phys. Status Solidi B 72, 393 (1975)

    Article  ADS  Google Scholar 

  53. R.W. Pohl, Optik und Atomphysik, 13th edn. (Springer, Berlin, 1976)

    Book  Google Scholar 

  54. F. Spiegelberg, E. Gutsche, J. Voigt, Phys. Status Solidi B 77, 233 (1976)

    Article  ADS  Google Scholar 

  55. E. Strauss, V. Gerhardt, H. Riederer, J. Lumin. 12/13, 239 (1976)

    Google Scholar 

  56. S. Suga et al., J. Lumin. 12/13, 109 (1976)

    Google Scholar 

  57. G.A. Thomas, M. Capizzi, in Proceedings of the 13th International Conference on the Physics of Semiconductors, Rome, ed. by F.G. Fumi (North-Holland, Amsterdam/New York, 1976), p. 915

    Google Scholar 

  58. T. Timusk et al., Phys. Rev. B 13, 3511 (1976)

    Article  ADS  Google Scholar 

  59. A. Coret, A. Fort, Il Nuovo Cim. 39B, 544 (1977)

    Article  ADS  Google Scholar 

  60. H. Venghaus, S. Suga, K. Cho, Phys. Rev. B 16, 4419 (1977)

    Article  ADS  Google Scholar 

  61. G. Winterling, E.S. Koteles, M. Cardona, Phys. Rev. Lett. 39, 1286 (1977)

    Article  ADS  Google Scholar 

  62. P.D. Bloch, C. Schwab, Phys. Rev. Lett. 41, 514 (1978)

    Article  ADS  Google Scholar 

  63. G.G. Grosso et al., Solid State Commun. 25, 435 (1978)

    Article  ADS  Google Scholar 

  64. K. Hümmer, Habilitation Thesis, Erlangen (1978)

    Google Scholar 

  65. K. Hümmer, P. Gebhardt, Phys. Status Solidi B 85, 271 (1978)

    Article  ADS  Google Scholar 

  66. J. Lagois, B. Fischer, Festkörperprobleme/Adv. Solid State Phys. 18, 197 (1978)

    Google Scholar 

  67. W. Stößel, H.J. Wagner, Phys. Stat. Sol. (b) 89, 403 (1978)

    Article  ADS  Google Scholar 

  68. T. Timusk et al., Solid State Commun. 25, 217 (1978)

    Article  ADS  Google Scholar 

  69. R.G. Ulbrich, C. Weisbuch, Festkörperprobleme/Adv. Solid State Phys. 28, 217 (1978)

    Google Scholar 

  70. W. Ekardt, K. Lösch, D. Bimberg, Phys. Rev. B 20, 3303 (1979)

    Article  ADS  Google Scholar 

  71. Y. Masumoto et al., J. Phys. Soc. Jpn. 47, 1844 (1979)

    Article  ADS  Google Scholar 

  72. A. Mysyrowicz, D. Hulin, A. Antonetti, Phys. Rev. Lett. 43, 1123 (1979)

    Article  ADS  Google Scholar 

  73. J. Puls, J. Voigt, Phys. Status Solidi B 94, 199 (1979)

    Article  ADS  Google Scholar 

  74. B. Sermage, G. Fishman, Phys. Rev. Lett. 43, 1043 (1979)

    Article  ADS  Google Scholar 

  75. R.G. Ulbrich, G.W. Fehrenbach, Phys. Rev. Lett. 43, 963 (1979)

    Article  ADS  Google Scholar 

  76. J. Voigt, F. Spiegelberg, M. Senoner, Phys. Status Solidi B 91, 189 (1979)

    Article  ADS  Google Scholar 

  77. I. Broser, M. Rosenzweig, Phys. Rev. B 22, 2000 (1980)

    Article  ADS  Google Scholar 

  78. K. Bohnert, G. Schmieder, C. Klingshirn, Phys. Status Solidi B 98, 175 (1980)

    Article  ADS  Google Scholar 

  79. I. Broser, M. Rosenzweig, Solid State Commun. 36, 1027 (1980)

    Article  ADS  Google Scholar 

  80. W. Dreybrodt et al., Phys. Rev. B 21, 4692 (1980)

    Article  ADS  Google Scholar 

  81. M. Fukui, V.C.-Y. So, G.I. Stegeman, Phys. Rev. B 22, 1010 (1980)

    Article  ADS  Google Scholar 

  82. I.V. Makarenko, I.N. Uraltsev, V.A. Kiselev, Phys. Status Solidi B 98, 773 (1980)

    Article  ADS  Google Scholar 

  83. E.S. Koteles, G. Winterling, Phys. Rev. Lett. 44, 948 (1980)

    Article  ADS  Google Scholar 

  84. I. Broser et al., Solid State Commun. 39, 1209 (1981)

    Article  ADS  Google Scholar 

  85. K. Cho, Y. Yamane, Solid State Commun. 40, 121 (1981)

    Article  ADS  Google Scholar 

  86. T. Itho et al., Solid State Commun. 37, 925 (1981)

    Article  ADS  Google Scholar 

  87. W.B. Jackson et al., Appl. Opt. 20, 1333 (1981)

    Article  ADS  Google Scholar 

  88. C. Klingshirn, H. Haug, Phys. Rep. 70, 315 (1981)

    Article  ADS  Google Scholar 

  89. R. Kuhnert, R. Helbig, K. Hümmer, Phys. Status Solidi B 107, 83 (1981)

    Article  ADS  Google Scholar 

  90. R. Kuhnert, R. Helbig, App. Opt. 20, 4149 (1981)

    Article  ADS  Google Scholar 

  91. J. Lagois, Phys. Rev. B 23, 5511 (1981)

    Article  ADS  Google Scholar 

  92. D.C. Reynolds, T.C. Collins, Excitons: Their Prooperties and Uses (Academic, New York, 1981)

    Google Scholar 

  93. Ch. Uihlein, D. Fröhlich, R. Kenklies, Phys. Rev. B 23, 2731 (1981)

    Article  ADS  Google Scholar 

  94. G. Blattner et al., Phys. Rev. B 25, 7413 (1982)

    Article  ADS  Google Scholar 

  95. G. Blattner, private communication

    Google Scholar 

  96. I. Hirabayashi, Q. Tokura, T. Kada, J. Phys. Soc. Jpn. 51, 2934 (1982)

    Article  ADS  Google Scholar 

  97. M. Itoh, I. Ogura, J. Appl. Phys. 53, 5140 (1982)

    Article  ADS  Google Scholar 

  98. N.V. Joshi, B. Vincent, Solid State Commun. 44, 439 (1982)

    Article  ADS  Google Scholar 

  99. C. Klingshirn, in Application of High Magnetic Fields in Semiconductor Physics, Lecture Notes in Physics, vol. 177 ed. by G. Landwehr (Springer, Berlin, 1982)

    Google Scholar 

  100. O. Madelung, U. Rössler (ed.), Landolt–Börnstein. New Series, Group III, vol. 17 a to i, 22 a and b, 41 A to D (Springer, Berlin, 1982–2001)

    Google Scholar 

  101. V.M. Agranovich, A.A. Maradudin (eds.), Modern Problems in Condensed Matter Sciences, (North Holland, Amsterdam, 1982 ff) Surface Polaritons, vol. 1 ed. by V.M. Agranovich, D.L. Mills. Surface Excitations, vol. 9, ed. by V.M. Agranovich, R. Landon

    Google Scholar 

  102. Y. Onodera, T.  Oshikiri, J. Phys. Soc. Jpn. 49, 1845 (1980) and ibid. 51, 2194 (1982)

    Google Scholar 

  103. S. Permogorov, in Excitons, vol. 2, Modern Problems in Condensed Matter Sciences, ed. by E.I. Rasha, M.D. Sturge (North Holland, Amsterdam, 1982), p. 177

    Google Scholar 

  104. M. Rosenzweig, Ph.D. Thesis, TU Berlin (1982)

    Google Scholar 

  105. T. Skettrup, Phys. Status Solidi B 109, 663 (1982)

    Article  ADS  Google Scholar 

  106. L. Schultheis, J. Lagois, Solid State Commun. 44, 1557 (1982) and Phys. Rev. B 29, 6784 (1984)

    Google Scholar 

  107. R. Grasser, R. Scharmann, N.A.T.O.A.S.I. Ser, B 88, 317 (1983)

    Google Scholar 

  108. W. Maier, G. Schmieder, C. Klingshirn, Z. Phys. B 50, 193 (1983)

    Google Scholar 

  109. Y. Segawa, Y. Aoyagi, S. Namba, J. Phys. Soc. Jpn. 52, 3664 (1983)

    Article  ADS  Google Scholar 

  110. H. Schweizer et al., Phys. Rev. Lett. 51, 698 (1983)

    Article  ADS  Google Scholar 

  111. M. Fukui, A. Kamada, O. Tada, J. Phys. Soc. Jpn. 53, 1185 (1984)

    Article  ADS  Google Scholar 

  112. M.V. Lebedev et al., JETP Lett. 39, 366 (1984)

    Google Scholar 

  113. M. Matsushita, J. Wicksted, H.Z. Cummins, Phys. Rev. B 29, 3362 (1984)

    Article  ADS  Google Scholar 

  114. T. Mita, N. Nagasawa, Solid State Commun. 44, 1003 (1984)

    Article  ADS  Google Scholar 

  115. A. Manoogian, J.C. Woolley, Can. J. Phys. 62, 285 (1984)

    Article  ADS  Google Scholar 

  116. S. Nikitine, J. Phys. Chem. Solids 45, 949 (1984)

    Article  ADS  Google Scholar 

  117. R. Ruppin, Phys. Rev. B 29, 2232 (1984)

    Article  ADS  Google Scholar 

  118. T. Shigenari, X.Z. Lu, H.Z. Cummins, Phys. Rev. B 30, 1962 (1984)

    Article  ADS  Google Scholar 

  119. J. Wicksted et al., Phys. Rev. B 29, 3350 (1984)

    Article  ADS  Google Scholar 

  120. F. Beerwerth, D. Fröhlich, Phys. Rev. Lett. 55, 2603 (1985)

    Article  ADS  Google Scholar 

  121. B. Hönerlage et al., Phys. Rep. 124, 161 (1985)

    Article  ADS  Google Scholar 

  122. K. Inoue et al., Solid State Commun. 54, 193 (1985)

    Article  ADS  Google Scholar 

  123. J.G. Liebler, S. Schmitt-Rink, H. Haug, J. Lumin. 34, 1 (1985)

    Article  Google Scholar 

  124. F. Beerwerth, D. Fröhlich, Phys. Rev. Lett. 57, 1344 (1986)

    Article  ADS  Google Scholar 

  125. M. Ueta, H. Kazanki, K. Kobayashi, Y. Toyozawa, E. Hanamura, Excitonic Processes in Solids, Springer Series in Solid State Sciences, vol. 60 (Springer, Berlin, 1986)

    Book  Google Scholar 

  126. C.W. Tang, S.A. Vanslyke, Appl. Phys. Lett. 51, 913 (1987)

    Article  ADS  Google Scholar 

  127. A. Juhl, D. Bimberg, J. Appl. Phys. 64, 303 (1988)

    Article  ADS  Google Scholar 

  128. D. Labrie et al., Phys. Rev. Lett. 61, 1882 (1988)

    Article  ADS  Google Scholar 

  129. J.H. Burroughes et al., Nature 347, 539 (1990)

    Article  ADS  Google Scholar 

  130. H. Kuzmany, Festkörperspektroskopie (Springer, Berlin, 1990)

    Book  Google Scholar 

  131. J.D. Lambkin et al., Appl. Phys. Lett. 57, 1986 (1990)

    Article  ADS  Google Scholar 

  132. S. Rudin, T.L. Reinecke, B. Segall, Phys. Rev. B 42, 11218 (1990)

    Article  ADS  Google Scholar 

  133. D. Bimberg, T. Wolf, J. Böhrer, NATO ASI Series B, Advances in nonradiative processes in solids, B. Di Bartolo ed. vol. 249 (Plenum, New York, 1991), p. 529

    Google Scholar 

  134. D. Fröhlich et al., Phys. Rev. Lett. 67, 2343 (1991)

    Article  ADS  Google Scholar 

  135. T. Ogawa, T. Takagahara, Phys. Rev. B 43, 14325 (1991)

    Article  ADS  Google Scholar 

  136. R. Ulbrich, in Materials Science and Technology, vol. 4, ed. by W. Schröter (VCH, Weinheim, 1991), p. 65

    Google Scholar 

  137. M. Fiebig, D. Fröhlich, Ch. Pahlke-Lerch, Phys. Status Solidi B 177, 187 (1993)

    Article  ADS  Google Scholar 

  138. H. Haug, S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 2nd edn. (World Scientific, Singapore, 1993)

    Book  MATH  Google Scholar 

  139. C. Klingshirn, N.A.T.O.A.S.I. Ser, B 301, 119 (1993)

    Google Scholar 

  140. J.L. Lin, J.P. Wolfe, Phys. Rev. Lett. 71, 1222 (1993)

    Article  ADS  Google Scholar 

  141. F.M. Mirabella (ed.), Internal Reflection Spectroscopy: Theory and Applications (Marcel Dekker Inc., New York, 1993)

    Google Scholar 

  142. Y. Ma et al., Phys. Rev. Lett. 71, 3725 (1993)

    Article  ADS  Google Scholar 

  143. N. Peyghambarian, S.W. Koch, A. Mysyrowicz, Introduction to Semiconductor Optics (Prentice Hall, Englewood Cliffs, 1993)

    Google Scholar 

  144. M. Vening, D.J. Dunstan, K.P. Homewood, Phys. Rev. B 48, 2412 (1993)

    Article  ADS  Google Scholar 

  145. D. Fröhlich in Nonlinear Spectroscopy of Solids: Advances and Application (1993). NATO ASI Series B, vol. 339 (Plenum Press, New York, 1994), p. 289

    Google Scholar 

  146. F. Fuchs et al., Superlatt. Microstruct. 16, 35 (1994)

    Article  ADS  Google Scholar 

  147. E.I. Haskal, Y. Zhang, P.E. Burrows, S.R. Forrest, Chem. Phys. Lett. 219 325 (1994); Phys. Rev. B 51, 4449 (1995)

    Google Scholar 

  148. C. Janowitz et al., Phys. Rev. B 50, 2181 (1994)

    Article  ADS  Google Scholar 

  149. M. Watanabe, T. Hayashi, J. Phys. Soc. Jpn. 63, 785 (1994)

    Article  ADS  Google Scholar 

  150. F. Bassani, G. Czajkowski, A. Terdicucci, Z. Phys. B 98, 39 (1995)

    Google Scholar 

  151. E. Daub, P. Würfel, Phys. Rev. Lett. 74, 1020 (1995)

    Article  ADS  Google Scholar 

  152. G.E. van Dorssen et al., Rev. Sci. Instrum. 66, 1480 (1995)

    Article  ADS  Google Scholar 

  153. H. Schneider, K. Köhler, Phys. Rev. B 52, R14364 (1995)

    Article  ADS  Google Scholar 

  154. P. Würfel, S. Finkbeiner, E. Daub, Appl. Phys. A 60, 67 (1995)

    Article  ADS  Google Scholar 

  155. V. Bulovic et al., Chem. Phys. 210, 1 (1996)

    Article  Google Scholar 

  156. H. Kalt, Optical Properties of IIIV Semiconductors: The Infuence of Multi-Valley Band Structures, Springer Series in Solid-State Sciences, vol. 120 (Springer, Berlin, 1996)

    Google Scholar 

  157. A. Mysyrowicz et al., Phys. Rev. Lett. 77, 896 (1996)

    Article  ADS  Google Scholar 

  158. U. Neukirch et al., Phys. Status Solidi B 196, 473 (1996)

    Article  ADS  Google Scholar 

  159. S. Tanaka, Y. Kayanuma, Solid State Commun. 100, 77 (1996)

    Article  ADS  Google Scholar 

  160. N. Grigorchuk, Phys. Lett. A 231, 245 (1997)

    Article  ADS  Google Scholar 

  161. A. Jolk, Diplom Thesis, Universität Karlsruhe (TH) (1997)

    Google Scholar 

  162. S. Nüsse et al., Phys. Rev. B 55, 4620 (1997)

    Article  ADS  Google Scholar 

  163. U. Neukirch et al., Phys. Rev. B 55, 15408 (1997) and ibid. 57, 9208 (1998)

    Article  ADS  Google Scholar 

  164. M.Y. Shen et al., Phys. Rev. B 56, 13 066 (1997)

    Google Scholar 

  165. J. Wrzensinski, D. Fröhlich, Phys. Rev. B 56, 13087 (1997)

    Article  ADS  Google Scholar 

  166. R. Westphäling et al., J. Lumin. 72–74, 980 (1997)

    Article  Google Scholar 

  167. A. Jolk, C. Klingshirn, Phys. Stat. Sol. (b) 206, 841 (1998)

    Article  ADS  Google Scholar 

  168. M. Kira, F. Jahnke, S.W. Koch, Phys. Rev. Lett. 81, 3263 (1998)

    Article  ADS  Google Scholar 

  169. K. Henneberger, Phys. Rev. Lett. 80, 2889 (1998)

    Article  ADS  Google Scholar 

  170. R. Westphäling et al., J. Appl. Phys. 84, 6871 (1998); and J. Cryst. Growth 184/185, 1072 (1998)

    Google Scholar 

  171. A. Agui et al., Phys. Rev. B 59, 10792 (1999)

    Article  ADS  Google Scholar 

  172. J.S. Dodge et al., Phys. Rev. Lett. 83, 4650 (1999)

    Article  ADS  Google Scholar 

  173. L. Hanke, D. Fröhlich, A.L. Ivanov, P.B. Littlewood, H. Stolz, Phys. Rev. Lett. 83, 4365 (1999)

    Article  ADS  Google Scholar 

  174. A. Jolk et al., in Proceedings of the 24th International Conference on the Physics of Semiconductors, Jerusalem, 1998, CD, File II C4 (1999)

    Google Scholar 

  175. R. Pässler, Phys. Status Solidi B 216, 975 (1999)

    Article  ADS  Google Scholar 

  176. A.V. Rodina et al., Phys. Status Solidi B 216, 21 (1999)

    Article  ADS  Google Scholar 

  177. L. Hanke et al., Phys. Status Solidi B 221, 287 (2000)

    Article  ADS  Google Scholar 

  178. J. Tignon et al., Phys. Rev. Lett. 84, 3382 (2000)

    Article  ADS  Google Scholar 

  179. M. Jörger et al., Phys. Rev. B 64, 113204 (2001)

    Article  ADS  Google Scholar 

  180. K. Johnsen, G.M. Kavoulakis, Phys. Rev. Lett. 86, 858 (2001)

    Article  ADS  Google Scholar 

  181. J.S. Nägerl et al., Phys. Rev. B 63, 235202 (2001)

    Article  ADS  Google Scholar 

  182. A.V. Rodina et al., Phys. Rev. B 64, 115204 (2001)

    Article  ADS  Google Scholar 

  183. H.C. Schneider et al., Phys. Rev. B 63, 045202 (2001)

    Article  ADS  Google Scholar 

  184. R. Lécuiller et al., Phys. Rev. B 66, 125205 (2002)

    Article  ADS  Google Scholar 

  185. S.F. Chichibu et al., J. Appl. Phys. 93, 756 (2003)

    Article  ADS  Google Scholar 

  186. G. Dasbach et al., Phys. Status Solidi B 238, 541 (2003) and Phys. Rev. Lett. 91, 107401 (2003)

    Google Scholar 

  187. T. Fleck, M. Schmidt, C. Klingshirn, Phys. Status Solidi (a) 198, 248 (2003)

    Article  ADS  Google Scholar 

  188. M. Jörger et al., Phys. Status Solidi B 238, 470 (2003)

    Article  ADS  Google Scholar 

  189. R.A. Kaindl et al., Phys. Status Solidi B 238, 451 (2003)

    Article  ADS  Google Scholar 

  190. M. Knupfer, Appl. Phys. A 77, 623 (2003)

    Article  ADS  Google Scholar 

  191. H. Zhao, H. Kalt, Phys. Rev. B 68, 125309 (2003)

    Article  ADS  Google Scholar 

  192. S. Glutsch, Excitons in Low-Dimensional Semiconductors (Springer, Berlin, 2004)

    Book  Google Scholar 

  193. M. Jörger, Ph.D. Thesis, Karlsruhe (2004); J. Lumin. 112, 21 (2005)

    Google Scholar 

  194. M. Kuwata-Gonokami et al., J. Phys. Soc. Jpn. 73, 1065 (2004) and Solid State Commun. 134, 127 (2005)

    Article  ADS  Google Scholar 

  195. K. Karpinska, P.H.M. van Loosdrecht, I.P. Handayani, Solid state Commun. 134, (2005); EXCON 04, Cracow, 2004; J. Lumin. 112, 17 (2005)

    Google Scholar 

  196. C. Klingshirn et al., Solid State Commun. 134, 155 (2005)

    Article  ADS  Google Scholar 

  197. T. Koida et al., Appl. Phys. Lett. 84, 1079 (2004)

    Article  ADS  Google Scholar 

  198. S. Schumacher et al., Phys. Rev. B 70, 235340 (2004)

    Article  ADS  Google Scholar 

  199. X. Yang, D. Neher, D. Hertel, T. Daubler, Adv. Mater. 16, 161 (2004)

    Article  Google Scholar 

  200. D. Fröhlich et al., Solid State Commun. 134, 139 (2005)

    Article  ADS  Google Scholar 

  201. J. Grabowska et al., Phys. Rev. B 71, 115439 (2005)

    Article  ADS  Google Scholar 

  202. R. Huber et al., Phys. Rev. B 72, 161314 (2005)

    Article  ADS  Google Scholar 

  203. R. Hauschild et al., Phys. Status Solidi C 3, 976 (2006)

    Article  ADS  Google Scholar 

  204. R. Huber et al., Phys. Rev. Lett. 96, 017402 (2006)

    Article  ADS  Google Scholar 

  205. S.W. Koch et al., Nat. Mater. 5, 523 (2006)

    Article  ADS  Google Scholar 

  206. J. Kasprzak et al., Nature 443, 409 (2006)

    Article  ADS  Google Scholar 

  207. T. Tayagaki et al., Phys. Rev. B 74, 245127 (2006)

    Article  ADS  Google Scholar 

  208. J. Brandt et al., Phys. Rev. Lett. 99, 217403 (2007)

    Article  ADS  Google Scholar 

  209. C. Klingshirn, Phys. Status Solidi B 244, 3027 (2007)

    Article  ADS  Google Scholar 

  210. C. Klingshirn et al., Phys. Rev. B 75, 115203 (2007)

    Article  ADS  Google Scholar 

  211. M. Hauser et al., Appl. Phys. Lett. 92, 211105 (2008)

    Article  ADS  Google Scholar 

  212. K.G. Lagoudakis et al., Nat. Phys. 4, 706 (2008)

    Article  Google Scholar 

  213. A. Köhler, H. Pässler, Mater. Sci. Eng. R 66, 71 (2009)

    Article  Google Scholar 

  214. T. Leinß et al., Phys. Status Solidi C 6, 156 (2009)

    Article  ADS  Google Scholar 

  215. M. Fox, Optical Properties of Solids, 2nd edn. (Oxford University Press, Oxford, 2010)

    Google Scholar 

  216. C. Klingshirn, Phys. Status Solidi B 247, 1424 (2010)

    Article  ADS  Google Scholar 

  217. C. Klingshirn, B.K. Meyer, A. Waag, A. Hoffmann, J. Geurts, Zinc Oxide: From Fundamental Properties Towards Novel Applications, Springer Series in Materials Science, vol. 120 (Springer, Heidelberg, 2010)

    Book  Google Scholar 

  218. E. Wertz et al., Nat. Phys. 6, 860 (2010)

    Article  Google Scholar 

  219. S. Tanaka et al., Phys. Status Solidi A 207, 1474 (2010)

    Article  ADS  Google Scholar 

  220. P.Y. Yu, M. Cardona, Fundamentals of Semiconductors, 4th edn. (Springer, Berlin, 2010)

    Book  MATH  Google Scholar 

  221. H.M. Gibbs, G. Khitrova, S.W. Koch, Nat. Photonics 5, 275 (2011)

    Article  ADS  Google Scholar 

  222. W. Brütting, C. Adachi (eds.), Physics of Organic Semiconductors, (Wiley-VCH, Weinheim, 2012)

    Google Scholar 

  223. M. Milosevic, Internal Reflection and ATR Spectroscopy (Wiley, New Jersey, 2012)

    Book  Google Scholar 

  224. I.E. Castelli et al., APL Mater. 2, 081514 (2014)

    Article  ADS  Google Scholar 

  225. M. Grätzel, Nat. Mater. 13, 838 (2014)

    Article  ADS  Google Scholar 

  226. T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, M. Bayer, Nature 514, 343 (2014)

    Article  ADS  Google Scholar 

  227. M. Saba et al., Nat. Commun. 5, 5049 (2014)

    Article  ADS  Google Scholar 

  228. C, Sekine et al., Sci. Technol. Adv. Mater. 15, 034203 (2014)

    Google Scholar 

  229. A. Miyata et al., Nat. Phys. 11, 582 (2015)

    Article  Google Scholar 

  230. J. Thewes et al., Phys. Rev. Lett. 115, 027402 (2015)

    Article  ADS  Google Scholar 

  231. M. Aßmann, J. Thewes, D. Fröhlich, M. Bayer, Nat. Mater. 15, 741 (2016)

    Article  ADS  Google Scholar 

  232. K. Galkowski et al., Energy Environ. Sci. 9, 962 (2016)

    Article  Google Scholar 

  233. B.R. Sutherland, E.H. Sargent, Nat. Photonics 10, 295 (2016)

    Article  ADS  Google Scholar 

  234. F. Schöne et al., Phys. Rev. B 93, 075203 (2016)

    Article  ADS  Google Scholar 

  235. F. Schweiner, J. Main, M. Feldmaier, G. Wunner, C. Uihlein, Phys. Rev. B 93, 195203 (2016)

    Article  ADS  Google Scholar 

  236. S.A. Veldhuis et al., Adv. Mater. 28, 6804 (2016)

    Article  Google Scholar 

  237. E.M. Hutter et al., Nat. Mater. 16, 115 (2017)

    Article  ADS  Google Scholar 

  238. J. Heckötter et al., Phys. Rev. B 96, 125142 (2017)

    Article  ADS  Google Scholar 

  239. J. Heckötter et al., Phys. Rev. B 95, 035210 (2017)

    Article  ADS  Google Scholar 

  240. J.E. Moser, Nat. Mater. 16, 4 (2017)

    Article  ADS  Google Scholar 

  241. F. Schweiner et al., Phys. Rev B 95, 035202 (2017)

    Article  ADS  Google Scholar 

  242. Z. Yang et al., J. Phys. Chem. Lett. 8, 1851 (2017)

    Article  Google Scholar 

  243. T. Ruf et al., Appl. Phys. Lett. 112, 083902 (2018). https://doi.org/10.1063/1.5017943

    Article  ADS  Google Scholar 

  244. T. Ruf et al., in IEEE 7th World Conference on Photovoltaic Energy Conversion (WCPEC), (Waikoloa, HI, 2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Physics, Karlsruhe Institute of Technology, Karlsruhe, Baden-Württemberg, Germany

    Heinz Kalt & Claus F. Klingshirn

Authors
  1. Heinz Kalt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claus F. Klingshirn
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Heinz Kalt .

Problems

Problems

21.1

Make a plot of the longitudinal-transverse splitting of \(n_{{\text {B}}}\,{=}\,1\) exciton resonances as a function of the exciton binding energy. Include only semiconductors with direct, dipole-allowed band-to-band transitions. Compare with similar figures in Chap. 20.

21.2

Consider a band-to-band transition in a direct-gap semiconductor neglecting the Coulomb interaction between electron and hole and calculate the absorption spectrum for a dipole-allowed and a dipole-forbidden transition, i.e. for a transition with a matrix element varying linearly with \(\varvec{k}\).

21.3

Consider the \(n_{\text {B}} = 1\) A\(\Gamma _{5}\)-polariton resonances in CdS (Fig. 21.3b) and determine for a light beam incident at 45\(^\circ \) to the surface (\(\varvec{E} \perp \varvec{c}\), \(\varvec{k}\perp \varvec{c}\)) the length and direction of the wave vectors of the propagating modes in the sample and their phase and group velocities. Select a few characteristic photon energies. Explain the term “spatial dispersion”.

21.4

Explain the differences between the concepts of polaritons with spatial dispersion and of birefringence.

21.5

Can the transition energy of a dipole-allowed intra-excitonic transition 1s \(\rightarrow \) 2p coincide with the energy of a dipole-allowed TO phonon?

21.6

Consider Fig. 21.8e for \(\varvec{E}\) perpendicular to \(\varvec{c}\). In the low temperature limit the A and B excitons are resolved, at 295 K no longer due to their increasing homogeneous broadening.

(a) Deduce the exciton binding energy in ZnO from the 4.2 K spectra and mark then the position of the bandgap at 295 K.

(b) Use equations like a square root absorption edge or an equation for the Tauc regime e.g., from [10K1] to fit the low energy tail of the absorption spectrum. Convince yourself that such a fit works only over a limited range of absorption coefficients \(\alpha (\hbar \omega )\) and verify that the extrapolation of this fit to \(\alpha (\hbar \omega )=0\) does give the correct value of the bandgap. Demonstrate also that the maximum of the derivative \(\mathrm{d}\alpha (\hbar \omega ) /\mathrm{d}\hbar \omega \) does not coincide with the gap.

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Kalt, H., Klingshirn, C.F. (2019). Optical Properties of Intrinsic Excitons in Bulk Semiconductors. In: Semiconductor Optics 1. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-24152-0_21

Download citation

Publish with us

Policies and ethics

Search

Navigation