Energy spectra of donors in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="normal">GaAs</mml:mi><mml:mo>−</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ga</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mi mathvariant="normal">As</mml:mi></mml:math>quantum well structures in the effective-mass approximation

Abstract

We present the results of a study of the energy spectrum of the ground state and the low-lying excited states for shallow donors in quantum well structures consisting of a single slab of GaAs sandwiched between two semi-infinite layers of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$. The effect of the position of the impurity atom within central GaAs slab is investigated for different slab thicknesses and alloy compositions. Two limiting cases are presented: one in which the impurity atom is located at the center of the quantum well (on-center impurity), the other in which the impurity atom is located at the edge of the quantum well (on-edge impurity). Both the on-center and the on-edge donor ground state are bound for all values of GaAs slab thicknesses and alloy compositions. The alloy composition $x$ is varied between 0.1 and 0.4. In this composition range, ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ is direct, and the single-valley effective-mass theory is a valid technique for treating shallow donor states. Calculations are carried out in the case of finite potential barriers determined by realistic conduction-band offsets.