Linear and planar molecules formed by coupled P donors in silicon

TL;DR

This paper develops a theoretical framework using effective mass theory to analyze the electronic structure of coupled phosphorus donors in silicon, revealing how geometry influences valley composition and binding energies.

Contribution

It introduces a novel multi-valley envelope function approach to model multi-donor configurations in silicon, accounting for valley-orbit coupling and geometrical effects.

Findings

Valley composition depends strongly on dopant geometry and orientation.

Triangular donor arrangements have higher binding energies than linear chains.

Planar donor molecules show valley polarization increasing with atom number.

Abstract

Using the effective mass theory and the multi-valley envelope function representation, we have developed a theoretical framework for computing the single-electron electronic structure of several phosphorus donors interacting in an arbitrary geometrical configuration in silicon taking into account the valley-orbit coupling. The methodology is applied to three coupled phosphorus donors, arranged in a linear chain and in a triangle, and to six donors arranged in a regular hexagon. The results of the simulations evidence that the valley composition of the single-electron states strongly depends on the geometry of the dopant molecule and its orientation relative to the crystallographic axes of silicon. The electron binding energy of the triatomic linear molecules is larger than that of the diatomic molecule oriented along the same crystallographic axis, but the energy gap between the ground state and the first excited state is not significantly different for internuclear distances from 1.5 to 6.6 nm. Three donor atoms arranged in a triangle geometry have larger binding energies than a triatomic linear chain of dopants with the same internuclear distances. The planar donor molecules are characterized by a strong polarization in favor of the valleys oriented perpendicular to the plane of the molecule. The polarization increases with number of atoms forming the planar molecule.