Excitons in Semiconductors
The quantum mechanical problem of a single electron-hole pair in a homogeneous semiconductor leads to the Wannier equation, which, for a parabolic bandstructure is mathematically identical to the hydrogen atom Schrödinger equation . This equation can be solved analytically in three and two dimensions, which is relevant for idealized bulk or quantum-well structures. Solutions are also available for quasi-one dimensional systems, however, their treatment requires the regularization of the Coulomb interaction potential [2, 3].
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- 1.R.J. Elliott in: Polarons and Excitons, ed by C.G. Kuper, G.D. Whitefield (Oliver and Boyd 1963 ) pp 269Google Scholar
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- 3.For a textbook discussion see H. Haug, S. W. Koch: Quantum Theory of the Optical and Electronic Properties of Semiconductors, 4th ed. ( World Scientific, Singapore 2004 )Google Scholar
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