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Microscopic theory of resonant tunneling of charge carriers in semiconductor heterostructures
Domoratskii E. V.
1, Zakharchenko M. V.
2, Glinskii G. F.
2
1ITMO University, St. Petersburg, Russia
2St. Petersburg State Electrotechnical University “LETI", St. Petersburg, Russia
2St. Petersburg State Electrotechnical University “LETI", St. Petersburg, Russia
Email: evdomoratskii@gmail.com, mikhailvzakh@gmail.com, genaglinskii@mail.ru
A general approach to the study of resonant tunneling of charge carriers in semiconductor heterostructures has been developed. The tunneling problem is solved by introducing the Green's operator for the corresponding Schrodinger equation within the framework of the biorthogonal formalism of quantum theory. As an example, model heterostructures based on one-dimensional crystals are considered, for which it is possible to construct an accurate microscopic theory of tunneling. The exact results following from the proposed theory are compared with approximate data obtained by the method of smooth envelope functions, as well as the effective mass method. It is shown that the main contribution to the difference between microscopic theory and existing approximate methods is due to the nonparabolicity of the law of dispersion of charge carriers, whereas short-range interface fields play a secondary role in the tunneling process. Keywords: effective mass method, Greens function, biorthogonal quantum mechanics, resonant tunneling effects.
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