Built-in electric fields in InAs/GaAs quantum dots: Geometry dependence and effects on the electronic structure

Abstract

Built-in electrostatic fields in zincblende quantum dots originate mainly from-(1) the fundamental crystal atomicity and the interfaces between two dissimilar materials, (2) the atomistic strain relaxation, and (3) the piezoelectric polarization. In this paper, using the atomistic NEMO 3-D simulator, we study the origin and nature of various internal fields in InAs/GaAs quantum dots having three different geometries, namely, box, dome, and pyramid. We then calculate and delineate the impact of the internal fields on the one-particle electronic states in terms of shift in the conduction band energy states, anisotropy and twofold degeneracy in the P level, and formation of mixed excited bound states. A list of models and approaches used in this study is as follows: (1) Valence force field (VFF) with strain-dependent Keating potentials for atomistic strain relaxation; (2) 20-band nearest-neighbor sp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> s* tight-binding model for the calculation of single-particle energy states; and (3) For piezoelectricity, for the first time within the framework of sp <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> d <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</sup> s* tight-binding theory, four different recently-proposed polarization models (linear and non-linear) have been considered in this study. In contrast to recent studies of similar quantum dots, our calculations yield a non-vanishing net piezoelectric contribution to the built-in electrostatic field. We also demonstrate the importance of full three-dimensional (3-D) atomistic material representation and the need for using realistically-extended substrate and cap layers (systems containing millions of atoms) in the numerical modeling of these reduced-dimensional quantum dots.