Acoustic phonons and strain in core/shell nanowires

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.

21 pages, 5 figures

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• One-Dimensional Hole Gas in Germanium/Silicon Nanowire Heterostructures
• Prospects for Spin-Based Quantum Computing
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Cited by in corpus (4)

• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
• Exchange interaction of hole-spin qubits in double quantum dots in highly anisotropic semiconductors
• Electron-phonon deformation potential interaction in core-shell Ge-Si and Si-Ge nanowires
• Fully tunable hyperfine interactions of hole spin qubits in Si and Ge quantum dots