Screening in semiconductor nanocrystals: \textit{Ab initio} results and Thomas-Fermi theory

TL;DR

This paper combines first-principles calculations and Thomas-Fermi theory to analyze impurity screening in Si and Ge nanocrystals, revealing surface polarization as a key factor and proposing a simple, physically interpretable screening model.

Contribution

It introduces a simple physical model for impurity screening in nanocrystals based on ab initio results and electrostatics, linking nanoscale and bulk screening behaviors.

Findings

Surface polarization dominates local field effects.

Screening is size-independent within a bond length from the impurity.

The proposed model agrees with ab initio calculations and impurity activation energies.

Abstract

A first-principles calculation of the impurity screening in Si and Ge nanocrystals is presented. We show that isocoric screening gives results in agreement with both the linear response and the point-charge approximations. Based on the present ab initio results, and by comparison with previous calculations, we propose a physical real-space interpretation of the several contributions to the screening. Combining the Thomas-Fermi theory and simple electrostatics, we show that it is possible to construct a model screening function that has the merit of being of simple physical interpretation. The main point upon which the model is based is that, up to distances of the order of a bond length from the perturbation, the charge response does not depend on the nanocrystal size. We show in a very clear way that the link between the screening at the nanoscale and in the bulk is given by the surface polarization. A detailed discussion is devoted to the importance of local field effects in the screening. Our first-principles calculations and the Thomas-Fermi theory clearly show that in Si and Ge nanocrystals, local field effects are dominated by surface polarization, which causes a reduction of the screening in going from the bulk down to the nanoscale. Finally, the model screening function is compared with recent state-of-the-art ab initio calculations and tested with impurity activation energies.