Eigenfrequencies and vibration nonlinearity of p-doped semiconductor nanomechanical resonators

Electron-phonon coupling can strongly affect eigenmodes of semiconductor-based nano- and micromechanical resonators. Doping semiconductors, and thus changing the density of electrons or holes, can lead to a change of phonon frequencies and their temperature dependence. Of particular importance for applications of nano- and microresonators, doping can change the phonon nonlinearity and thus significantly modify the dependence of the frequencies of the eigenmodes on their amplitude. The effect is rooted in the typically large values of the deformation potential. We extend the previous analysis [1,2] to study the effect of doping for p-doped resonators based on semiconductors with diamond structure and for A₃B₅ semiconductors. The underlying mechanism is the strain-induced redistribution of holes between and within the nonparabolic hole energy bands. The backaction of this redistribution can lead to a nonmonotonic dependence of the modes' eigenfrequencies on temperature and to a strong mode nonlinearity that also nonmonotonically depends on temperature. Unexpectedly, we find that the nonlinearity can nonmonotonically depend on the hole density. We also discuss the counterintuitive effect of doping on the decay rates of low-frequency eigenmodes. The results are compared with the experiment.

[1] R. W. Keyes, The electronic contribution to the elastic properties of germanium, IBM J. Res. Dev. 5, 266 (1961).

[2] F. S. Khan and P. B. Allen, Temperature dependence of the elastic constants of p⁺ silicon, Phys. Status Solidi B 128, 31 (1985).