Theory of one and two donors in Silicon

TL;DR

This paper provides a comprehensive modeling framework for silicon nano-devices with one or two group V donors, analyzing different approximation methods and connecting theoretical results with recent experimental data.

Contribution

It introduces a detailed modeling approach for donor pairs in silicon, comparing various approximation techniques and their validity, including multivalley effective mass and analytical models.

Findings

Quantitative results within multivalley effective mass model.

Assessment of analytical approximations like LCAO, Huckel, and Hubbard.

Discussion of the connection between models and recent experiments.

Abstract

We provide here a roadmap for modeling silicon nano-devices with one or two group V donors (D). We discuss systems containing one or two electrons, that is, D^0, D^-, D_2^+ and D_2^0 centers. The impact of different levels of approximation is discussed. The most accurate instances -- for which we provide quantitative results -- are within multivalley effective mass including the central cell correction and a configuration interaction account of the electron-electron correlations. We also derive insightful, yet less accurate, analytical approximations and discuss their validity and limitations -- in particular, for a donor pair, we discuss the single orbital LCAO method, the Huckel approximation and the Hubbard model. Finally we discuss the connection between these results and recent experiments on few dopant devices.