Binding Energy of an Off-Center Hydrogenic Donor Impurity in a Finite Confining Potential Quantum Well

Abstract

Low dimensional semiconductor heterostructures such as quantum wells, wires, boxes, and dots have gained a great importance in the last two decades due to their fundamental properties and their wide range of applications. Special care has been given to investigate these quantum systems in the presence of shallow impurities [1{9]. The problem of calculating the binding energy of hydrogenic impurity in a quantum well has been considered in the pioneering work of Bastard [10]. He studied the case of center and ofi-center impurity but in an inflnite conflning potential quantum well. He applied a variational approach that was based on modifying the exact wave function of an inflnite quantum well by adding a term that represents the hydrogenic impurity. The resulting trial wave function depends on one variational parameter. The case of flnite conflning potential quantum well was dealt with by using a similar approach by Chaudhuri and Bajaj [11] and Elabsy [12]. Jia-Lin Zhu [13] and Greene and Bajaj [14, 15] applied more complicated variational methods. However, in all these treatments the case of a