Ionized donor impurity in a semiconductor quantum well

Abstract
We present the results of a variational calculation of the ground state energy of a (D⁺,X) complex in a quantum well with finite potential barriers as a function of the depth and the width of the well as well as the ratio [MATH] of the electron and hole effective masses. We use the envelope function approximation. We apply Our results to the system GaAs/Ga_1-xAl_xAs with x = 0.15 and x = 0.30. It appears that the coulombic correlation energy goes through a minimum for a well thickness in the order of 50 Angströms. This minimum is comprized between the values obtained in the 2D and 3D limit cases. Furthermore, it appears that only the heavy hole states give rise to a stable binding energy for all values of the well thickness. The light hole states give rise to stable binding only in the case of large thicknesses.