I. V. Bodrova¹, A. B. Dubois¹, S. I. Kucheryavyy², A. S. Safoshkin¹

¹V.F. Utkin Ryazan State Radioengineering University (Ryazan, Russian Federation)

²Obninsk Institute for Nuclear Power Engineering (OINPE) NRNU MEPhI (Obninsk, Russian Federation)

Abstract. To describe the kinetic processes occurring in a low-dimensional quantum structure (e.g., electron-electron interactions), it is necessary to calculate the potential distribution $ V \left( z \right) $ and the wave functions $ \Psi \left( z \right) $ of its conduction band. The screening potential, which includes the dielectric function of an electron gas, acts as an external perturbation. In most studies, the potential well is approximated by a rectangular profile, but attempts to apply analytical results were unsuccessful. The paper presents a joint self-consistent solution of the system of Schrodinger and Poisson differential equations for calculating wave functions and potential distribution of a single moderately doped heterojunction ${AlGaAs}\left( {Si} \right)/{GaAs}$. Solving this system is necessary to describe kinetic processes in a two-dimensional electron gas, primarily electron-electron interactions, which are dominant at low temperatures. The paper demonstrates that these equations can be conveniently solved for dimensionless potential and wave functions. Constructing a quantum well potential profile, i.e., solving the system of Schrodinger and Poisson equations, is an important task in studying graphene structures with similar geometries.

Key Words: modeling of the band structure of a heterojunction, joint solution of Schrodinger and Poisson differential equations, electron-electron interactions

For citation: I. V. Bodrova, A. B. Dubois, S. I. Kucheryavyy, A. S. Safoshkin. Modeling of the band structure of a single heterojunction. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 28:2(2026), 115–129. DOI: https://doi.org/10.15507/2079-6900.28.202602.115-129

Information about the authors:

Irina V. Bodrova, Ph.D. (Engineering), Associate Professor of the Department of Higher Mathematics, V.F. Utkin Ryazan State Radioengineering University (59/1 Gagarina St., Ryazan 390005, Russia), ORCID: http://orcid.org/0009-0003-6677-7461, bodrovamilyutina@mail.ru

Alexander B. Dubois, Ph.D. (Phys. and Math.), Associate Professor of the Department of Higher Mathematics, V.F. Utkin Ryazan State Radioengineering University (59/1 Gagarina St., Ryazan 390005, Russia), ORCID: http://orcid.org/0000-0002-5924-4128, abd- 69@mail.ru

Sergei I. Kucheryavyy, Ph.D. (Phys. and Math.), Associate Professor of the Department of General and Special Physics, Obninsk Institute for Nuclear Power Engineering (OINPE) NRNU MEPhI (1 Studgorodok, Obninsk 249039, Kaluga region, Russia), ORCID: http://orcid.org/0000-0001-6030-9286, kucheryavyy@iate.obninsk.ru

Alexey S. Safoshkin, Ph.D. (Phys. and Math.), Associate Professor of the Department of Higher Mathematics, V.F. Utkin Ryazan State Radioengineering University (59/1 Gagarina St., Ryazan 390005, Russia), ORCID: http://orcid.org/0000-0002-1419-979X, safoshkin.a.s@rsreu.ru