A Green function approach to effective mass theory

Lukes, Timothy J.; Roberts, M. W.

doi:10.1088/0370-1328/92/3/327

Cited by 3 publications

(2 citation statements)

References 2 publications

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“…Also, an extension of effective mass theory to many bands following earlier qualitative work along the same lines by Keldysh (1964), was given by Lukes and Roberts (1969). Another extension of effective mass theory is the discussion of resonant states by Peterson (1964).…”

Section: (B 8)mentioning

confidence: 96%

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Scattering theory of defects in crystals

Rennie

1977

Advances in Physics

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The theory of scattering is applied here to the problem of the electronic states of impurities. The S, T and K matrices, the Lippman-Schwinger and Dyson equations are used to formulate the problem. The standard concepts, methods and results of scattering theory applied to impurities discussed include the scattering amplitude, the Fredholm determinant, dispersion relations, Regge poles, Levinson's theorem and Fadeev's equations. Physical consequences considered are the change in density of states, eigenstates and transport theory. The necessity of extending the scattering formalism to many-body theory is discussed. The relation between scattering theory and other methods of impurity theory is also mentioned.

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Section: (B 8)mentioning

confidence: 96%

“…The relation between effective mass theory and Green's functions has been discussed by Lukes and Roberts (1967). Also, an extension of effective mass theory to many bands following earlier qualitative work along the same lines by Keldysh (1964), was given by Lukes and Roberts (1969).…”

Section: (B 8)mentioning

confidence: 97%

Scattering theory of defects in crystals

Rennie

1977

Advances in Physics

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All Effective Mass Approximation for Several Bands

Lukes

Roberts

1969

Physica Status Solidi (b)

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The effective mass formalism is generalized to include the effect of several bands by constructing an approximate Green's function for the periodic lattice. Energy levels are obtained for a hydrogenic impurity in a periodic lattice described by two and three parabolic bands. In addition to the energy levels predicted by effective mass theory a deep level is found. An explicit expression for the deep level is given in terms of the band parameters and a comparison with the experimentally observed deep levels in gallium arsenide is made.Der ,,effektive Masse"-Formalismus wird verallgemeinert, indem der EinfluB verschiedener BInder durch die Aufstellung einer geniiherten Greenschen Funktion fur das periodische Gitter einbezogen wird. Energieniveaus werden fur eine wasserstoffahnliche Storstelle in einem periodischen Gitter, das durch zwei oder drei parabolische Bander beschrieben wird, erhalten. Zusatzlich zu den Energieniveaus, die durch die ,,effektive Masse"-Theorie gegeben werden, wird ein ,,tiefed' Niveau gefunden. Ein expliziter Ausdruck fur das tiefe Niveau wird durch die Bandparameter gegeben und es wird ein Vergleich mit den experimentell beobachteten tiefen Zustanden in Galliumarsenid durchgefuhrt.

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