Applicability of the Six-Band kp-Model Equations to Semiconductor Heterostructures
V. P. Zhukov1, M. P. Fedoruk1,2, A. F. Zinov’eva3, A. V. Nenashev4,5, A. V. Dvurechenskii4,5
1Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 6, Novosibirsk, 630090 Russia
2Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
3Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia
4Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, ul. Pirogova 2, Novosibirsk, 630090 Russia
5Novosibirsk State University, pr. Akademika Lavrent’eva 13, Novosibirsk, 630090 Russia
Keywords: energy spectrum, quantum dots, heterojunction, silicon, germanium, wave function
Abstract
The problem of the applicability of the six-band kp -model to heterostructures with sharp boundaries is studied by calculating the energy spectrum of holes in the Ge/Si system with quantum dots. The boundary conditions which satisfy the conditions of particle flux conservation and the wave function continuity on the heterojunction are formulated at the level of differential equations and are characterized by a single parameter µ, which depends on the heterojunction properties. It is shown that a certain choice of µ leads to nonphysical interface states that fill the entire band gap. Conditions (range of µ) for the absence of such nonphysical states are determined by considering the simplest cases – a single heterojunction and a quantum well.
|
