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Electronic structure and deep impurity levels in  GaAs/Al x Ga1−x As semiconductor superlattices
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3.For a review of deep level theories, see, J. D. Dow, in Highlights of Condensed Matter Theory (Proceedings of the International School of Physics “Enrico Fermi” Course 89, Varenna, 1983), edited by F. Bassani, F. Fumi, and M. P. Tosi (North‐Holland, Amsterdam, 1985), pp. 465 et seq. and references therein.
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5.J. D. Dow, S. Y. Ren, and J. Shen, in NATO Conference Proceedings, edited by C. Y. Fong (in press).
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10.A preliminary account of this work was given by J. D. Dow and S. Y. Ren, Bull. Am. Phys. Soc. 33, 630 (1988).
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14.see also W. Y. Hsu, J. D. Dow, D. J. Wolford, and B. G. Streetman, Phys. Rev. B 16, 1597 (1977) for the concepts that form the foundation of this work.
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17.We use the same impurity potential for Si in GaAs as in Ref. 4.
18.M. Chandrasekhar, H. R. Chandrasekhar, A. Kangarlu, U. Venkateswaran, F. A. Chambers, and J. M. Meese, Superlatt. Microstruct. 4, 107 (1988). These authors reported the first experimental confirmation of the Si deep impurity level in a GaAs multiquantum well, as we predicted, Ref. 4.
19.Mathematically we use the condition to find the vacancy energy levels, here is the on‐site Green’s function of the host semiconductor with a specific symmetry. Under the central cell perturbation approximation, the coefficient of a deep defect state wave function at the defect site, is determined by (Ref. 20): Because is always smaller than zero, the condition naturally is equivalent to i.e., the widely used approximation of M. Lannoo and P. Lenglart, J. Phys. Chem. Solids 38, 2409 (1969),
20.S. Y. Ren, Sci. Sinica 27, 443 (1984).
21.The reason is that at an interface of a  superlattice, either one or the other of the ‐derived and levels of the As vacancy will be within the GaAs layer; the other one will be within the As layer. But at an interface of a  superlattice, neither the nor the e As ‐detived vacancy state will be completely within the GaAs or the As layer.
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