Spin and cyclotron energies of electrons in GaAs/Ga$_{1-x}$Al$_x$As quantum wells

TL;DR

This paper develops a detailed five-level { extit{Pp}} model to accurately describe the spin $g^*$-factor and cyclotron mass of electrons in GaAs/Ga$_{1-x}$Al$_x$As quantum wells, matching experimental data without adjustable parameters.

Contribution

It introduces an advanced iteration-based approach solving coupled differential equations, improving the theoretical description of electron spin and cyclotron properties in quantum wells.

Findings

Excellent agreement with experimental $g^*$-factor data across various well widths.

Accurate modeling of cyclotron masses in different quantum well structures.

Highlights the importance of bulk inversion asymmetry in spin properties.

Abstract

A five-level {\Pp} model of the band structure for GaAs-type semiconductors is used to describe the spin $g^*$-factor and the cyclotron mass $m^*_c$ of conduction electrons in GaAs/Ga$_{1-x}$Al$_x$As quantum wells in an external magnetic field parallel to the growth direction. It is demonstrated that the previous theory of the $g^*$-factor in heterostructures is inadequate. Our approach is based on an iteration procedure of solving 14 coupled differential {\Pp} equations. The applicability of the iteration procedure is verified. The final eigenenergy problem for the conduction subbands is reduced to two differential equations for the spin-up and spin-down states of consecutive Landau levels. It is shown that the bulk inversion asymmetry of III-V compounds is of importance for the spin $g^*$-factor. Our theory with no adjustable parameters gives an excellent description of experimental data on the electron spin $g^*$-factor in GaAs/Ga$_{0.67}$Al$_{0.33}$As rectangular quantum wells for different well widths between 3 and 12 nm. The same theory describes very well experimental cyclotron masses in GaAs/Ga$_{0.74}$Al$_{0.26}$As quantum wells for the well widths between 6 and 37 nm.