Strong vibration nonlinearity in semiconductor-based nanomechanical systems

TL;DR

This paper investigates how electron-phonon interactions in semiconductor nanomechanical systems induce strong nonlinear vibrational behaviors, influenced by strain and electron redistribution among energy valleys, with implications for silicon-based devices.

Contribution

It reveals the mechanism of mode nonlinearity caused by valley degeneracy lifting and provides quantitative analysis for silicon micro-systems, highlighting mode and orientation dependence.

Findings

Electron-phonon coupling causes strong vibrational mode nonlinearity.

The nonlinearity varies with electron density, temperature, and crystal orientation.

Quartic strain terms determine amplitude-dependent mode frequencies.

Abstract

We study the effect of the electron-phonon coupling on vibrational eigenmodes of nano- and micro-mechanical systems made of semiconductors with equivalent energy valleys. We show that the coupling can lead to a strong mode nonlinearity. The mechanism is the lifting of the valley degeneracy by the strain. The redistribution of the electrons between the valleys is controlled by a large ratio of the electron-phonon coupling constant to the electron chemical potential or temperature. We find the quartic in the strain terms in the electron free energy, which determine the amplitude dependence of the mode frequencies. This dependence is calculated for silicon micro-systems. It is significantly different for different modes and the crystal orientation, and can vary nonmonotonously with the electron density and temperature.