Tight binding formulation of the dielectric response in semiconductor nanocrystals

TL;DR

This paper develops a tight-binding theoretical framework to analyze the dielectric response of semiconductor nanocrystals, efficiently incorporating local field effects and surpassing traditional continuum models.

Contribution

It introduces a localized orbital-based method for dielectric response calculations in nanocrystals, extending bulk approaches to nanoscale systems with improved accuracy.

Findings

Results match well with experimental data and first-principles calculations.

The scheme reveals limitations of the continuum dielectric model for nanocrystals.

It shows the importance of surface polarization effects in dielectric response.

Abstract

We report on a theoretical derivation of the electronic dielectric response of semiconductor nanocrystals using a tight-binding framework. Extending to the nanoscale the Hanke and Sham approach [Phys. Rev. B 12, 4501 (1975)] developed for bulk semiconductors, we show how local field effects can be included in the study of confined systems. A great advantage of this scheme is that of being formulated in terms of localized orbitals and thus it requires very few computational resources and times. Applications to the optical and screening properties of semiconductor nanocrystals are presented here and discussed. Results concerning the absorption cross section, the static polarizability and the screening function of InAs (direct gap) and Si (indirect gap) nanocrystals compare well to both first principles results and experimental data. We also show that the present scheme allows us to easily go beyond the continuum dielectric model, based on the Clausius-Mossotti equation, which is frequently used to include the nanocrystal surface polarization. Our calculations indicate that the continuum dielectric model, used in conjunction with a size dependent dielectric constant, underestimates the nanocrystal polarizability, leading to exceedingly strong surface polarization fields.