Collective vs. Individual Dot Response of Quantum Dot Ensembles

Abstract

Quantum dots are microscopic, essentially zero-dimensional structures, where the confining potential can be tailored through the material parameters and the geometry of confinement. A periodic ensemble of quantum dots is created by periodic etching or periodic gating, with the objective of creating a regular lattice of identical quantum dots. In the case of self assembled quantum dots, on the other hand, the individual dots may vary in size and the interdot separations are randomly distributed. Primary experimental tools employed to study the response of quantum dot ensembles have been the far infrared (FIR) spectroscopy and single electron charging (capacitance) studies. Theoretical studies are by and large based on model confining potentials (for the individual dots) and model electronelectron interactions. We examine in this paper the FIR response of an ensemble of quantum dots where the individual dots may have different intrinsic FIR responses and where the interdot distances may be randomly distributed. This is the experimental situation for the self assembled dots. It is intuitively clear that if the interdot distances are large, the dots will respond individually at their specific frequencies, and for an ensemble of dots that span a broad frequency range, one should expect a correspondingly broadened line shape. When the interdot separations are small, and the interdot interactions are strong, the possibility arises that the whole ensemble will respond at a single (or a few) collective frequencies, with narrow line widths. We develop here a formalism to determine the transition from the individual to the collective behavior.