V. Ranjan

Shallow-deep transitions of impurities in semiconductor nanostructures

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, e, as its size decreases. Employing a size dependent e(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.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, e, as its size decreases. Employing a size dependent e(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...

Semiconductor quantum dots: Theory and phenomenology

Research in semiconductor quantum dots (q-dots) has burgeoned in the past decade. The size (R) of these q-dots ranges from 1 to 100 nm. Based on the theoretical calculations, we propose energy and length scales which help in clarifying the physics of this mesoscopic system. Some of these length scales are: the Bohr exciton radius (αB*), the carrier de Broglie and diffusion length (λD andlD), the polaron radius (αp), and the reduction factor modulating the optical matrix element (Mx).R<αB is an individual particle confinement regime, whereas the larger ones are exciton confinement regime wherein Coulomb interaction play an important role. Similarly a size-dependent dielectric constantε(R) should be used forR<αp<αB. An examination ofMx reveals that an indirect gap material q-dot behaves as a direct gap material in the limit of very small dot size. We have carried out effective mass theory (EMT) calculations to estimate the charge density on the surface of the quantum dot. We present tight binding (TB) calculation to show that the energy upshift scales as 1/Rx, wherex is less than 2 and the exponent depends on the orientation of the crystallite.

Many electron effects in semiconductor quantum dots

Semiconductor quantum dots (QDs) exhibit shell structures, very similar to atoms. Termed as ’artificial atoms’ by some, they are much larger (1 100 nm) than real atoms. One can study a variety of manyelectron effects in them, which are otherwise difficult to observe in a real atom. We have treated these effects within the local density approximation (LDA) and the Harbola-Sahni (HS) scheme. HS is free of the self-interaction error of the LDA. Our calculations have been performed in a three-dimensional quantum dot. We have carried out a study of the size and shape dependence of the level spacing. Scaling laws for the Hubbard ‘U’ are established.