Shallow-deep transitions of impurities in semiconductor nanostructures

Abstract

We study the hydrogenic impurity in a quantum dot (QD). We employ the effective mass theory with realistic barrier and variable effective mass. The model is simple, but it predicts features not previously observed. We observe that the shallow hydrogenic impurity becomes deeper as the dot size (R) is reduced and with further reduction of the dot size it becomes shallow and at times resonant with the conduction band. Such a shallow-deep (SHADE) transition is investigated and a critical size in terms of the impurity Bohr radius (aI*) is identified. A relevant aspect of a QD is reduction in the dielectric constant, ε, as its size decreases. Employing a size dependent ε(R), we demonstrate that the impurity level gets exceptionally deep in systems for which aI* is small. Thus, carrier “freeze out” is a distinct possibility in a wide class of materials such as ZnS, CdS, etc. The behavior of the impurity level with dot size is understood on the basis of simple scaling arguments. Calculations are presented for III–V (AlGaAs) and II–VI (ZnS, CdS) QDs. We speculate that the deepening of the impurity level is related to the high luminescence efficiency of QDs. It is suggested that quantum dots offer an opportunity for defect engineering.