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.

arXiv comment21 pages, 5 figures

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• Spin-orbit interaction and induced superconductivity in an one-dimensional hole gas
• Degeneracy lifting of Majorana bound states due to electron-phonon interactions
• Hole spin qubits in thin curved quantum wells
• Enhanced orbital magnetic field effects in Ge hole nanowires
• Exchange interaction of hole-spin qubits in double quantum dots in highly anisotropic semiconductors
• Electrical control of the hole spin qubit in Si and Ge nanowire quantum dots
• Valley-Free Silicon Fins Caused by Shear Strain
• Electron-phonon deformation potential interaction in core-shell Ge-Si and Si-Ge nanowires
• Microscopic analysis of proximity-induced superconductivity and metallization effects in superconductor-germanium hole nanowires
• Electron-acoustic-phonon interaction in core/shell Ge/Si and Si/Ge nanowires
• Low-energy hole subband dispersions in a cylindrical Ge nanowire: the effects of the nanowire growth direction
• Hole subband dispersions and strong `spin'-orbit coupling in a cylindrical Ge nanowire
• Acoustic phonons, spin-phonon coupling and spin relaxation via the lattice reorientation mechanism in hexagonal germanium nanowires
• Fully tunable hyperfine interactions of hole spin qubits in Si and Ge quantum dots