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Impurity optical absorption and magnetic susceptibility in silicon and germanium

University of British Columbia

The eigenvalue problem for the two-electron system of a donor pair in germanium and silicon was solved. Using the Heitler-London method the 1s-1s electron energy spectra were calculated as a function of the separation between the two donors in the crystal. Also the widths of bands of closely spaced 1s-2p donor molecular levels were calculated as a function or interdonor separation. In this study the many-valley nature of the conduction band as well as the discrete structure of the crystal medium of the host semiconductor were taken into account. It was observed that all donor pairs in a germanium crystal can be divided into three classes; any two donor pairs belonging to the same class have identical electron energy spectra if their interdonor separations are equal. As an application of this study of the donor-donor interaction, the linewidths of B and E infra-red absorption lines in silicon and germanium were estimated as a function of donor concentration and compared with experimental results. A random distribution of donors in the crystal was assumed. It was supposed that optical absorption takes place through excitation of the electron system of a donor pair from an occupied state to a higher lying excited state. The agreement between theory and experiment was very good. In another application of the results of the study of the donor-donor interaction, the magnetic susceptibility of weakly interacting donors in germanium was studied as a function of donor concentration (10¹⁶ cm ⁻³ ≲N[sub d] ≲ 10¹⁷ cm ⁻³) and temperature (1°K ≲ T ≲ 5°K). The system of interacting donors was treated as a system of isolated donor pairs. A random distribution of donors in the crystal was assumed. The spin paramagnetic and orbital diamagnetic susceptibilities were calculated and an upper limit to the Van Vleck paramagnetic susceptibility was calculated. The results were compared to results of experimental measurements, and again a good agreement was observed. Special attention was paid to the behaviour of antimony-doped germanium for which case the Sonder and Schweinler theory breaks down.

Text

2011-03-23

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http://hdl.handle.net/2429/32793

Physics

University of British Columbia

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