Acoustic phonons and strain in core/shell nanowires

TL;DR

This paper provides a comprehensive theoretical analysis of low-energy phonons and static strain in core/shell nanowires, deriving general expressions and illustrating their impact on material properties, especially in Ge/Si systems.

Contribution

It introduces new algebraic formulas for phonon dispersion and strain in core/shell nanowires with arbitrary dimensions and elastic properties, extending previous models.

Findings

Dispersion relations vary with shell thickness for different vibrational modes.

Shell-induced strain significantly affects the hole spectrum in Ge/Si nanowires.

Results align with experimental data and previous theoretical work.

Abstract

We study theoretically the low-energy phonons and the static strain in cylindrical core/shell nanowires (NWs). Assuming pseudomorphic growth, isotropic media, and a force-free wire surface, we derive algebraic expressions for the dispersion relations, the displacement fields, and the stress and strain components from linear elasticity theory. Our results apply to NWs with arbitrary radii and arbitrary elastic constants for both core and shell. The expressions for the static strain are consistent with experiments, simulations, and previous analytical investigations; those for phonons are consistent with known results for homogeneous NWs. Among other things, we show that the dispersion relations of the torsional, longitudinal, and flexural modes change differently with the relative shell thickness, and we identify new terms in the corresponding strain tensors that are absent for uncapped NWs. We illustrate our results via the example of Ge/Si core/shell NWs and demonstrate that shell-induced strain has large effects on the hole spectrum of these systems.