Electronic structures of free-standing nanowires made from indirect bandgap semiconductor gallium phosphide

TL;DR

This study provides a theoretical analysis of the electronic structures of freestanding GaP nanowires with various orientations and cross sections, revealing band crossing behaviors, symmetry properties, and confinement energy formulas.

Contribution

It introduces a detailed tight binding model analysis of GaP nanowires, including symmetry analysis and empirical formulas for confinement energies, which is novel for indirect bandgap semiconductor nanowires.

Findings

Band structures show anti-crossings for [001]-oriented wires.

Conduction band minima are at two points, valence maximum at Gamma.

Empirical formulas for electron and hole confinement energies.

Abstract

We present a theoretical study of the electronic structures of freestanding nanowires made from gallium phosphide (GaP)--a III-V semiconductor with an indirect bulk bandgap. We consider [001]-oriented GaP nanowires with square and rectangular cross sections, and [111]-oriented GaP nanowires with hexagonal cross sections. Based on tight binding models, both the band structures and wave functions of the nanowires are calculated. For the [001]-oriented GaP nanowires, the bands show anti-crossing structures, while the bands of the [111]-oriented nanowires display crossing structures. Two minima are observed in the conduction bands, while the maximum of the valence bands is always at the $\Gamma$-point. Using double group theory, we analyze the symmetry properties of the lowest conduction band states and highest valence band states of GaP nanowires with different sizes and directions. The band state wave functions of the lowest conduction bands and the highest valence bands of the nanowires are evaluated by spatial probability distributions. For practical use, we fit the confinement energies of the electrons and holes in the nanowires to obtain an empirical formula.