Energy levels of hydrogenic impurity states in GaAs-Ga1−xAlxAs quantum well structures

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

“…The result in (19) shows that the relation between E b and V −1/2 0 is linear for large V 0 such that β(λ 0 ) = 0. This result agrees with the findings of Greene and Bajaj [14] for a center impurity.…”

“…In the present work, we have derived an analytical expression for the initial deviation from the binding energy of infinite confining potential. The deviation varies linearly with 1/ √ V 0 in agreement with the results of Greene and Bajaj [14] for the center impurity. It has been shown further that the sign of this deviation depends on the position of the impurity.…”

“…The general behavior of the results in Fig. 2a (center impurity) agrees with that of Greene and Bajaj [14]. The binding energy increases as L decreases until it reaches a maximum value and then it starts to decrease.…”

“…The case of finite confining 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 (373) center impurity had only been considered.…”

“…To the best of our knowledge the analytical results obtained here have not been published anywhere before. The numerical results of Greene and Bajaj [14] showed that the binding energy decreases linearly with 1/ √ V 0 for a center impurity and high values of the confining potential V 0 (V 0 is much greater than the effective Rydberg). In the present work, we have derived an analytical expression for the initial deviation from the binding energy of infinite confining potential.…”