Propagation of terahertz elastic longitudinal waves in piezoelectric semiconductor rods

Terahertz elastic waves travelling in piezoelectric semiconductors (PSs) with the deformation-polarization-carrier coupling have a huge potential application in elastic wave-based devices. To reveal wave propagation characteristics of terahertz elastic waves in rod-like PS structures, we present three typical rod models based on the Hamilton principle and the linearization of the nonlinear current, which are extensions of the classical, Love, and Mindlin-Herrmann rod models for elastic media to those for PS materials. Using the derived equations, the analytical dispersion relations of the elastic longitudinal waves propagating in an n-type PS rod are obtained, which can be reduced to those for piezoelectric and elastic rods by sequentially dropping the corresponding electron- and piezoelectricity-related terms. The Mindlin-Herrmann rod model is more accurate for analysis of terahertz elastic longitudinal wave in rod-like PS structures. The effects of the interaction between the piezoelectricity and semiconducting properties on the dispersion behaviors of terahertz elastic longitudinal waves are investigated in detail. Numerical results show that both phase and group velocities have a 50%-60% reduction in the terahertz range in comparison with those in the low frequency range, and the effective tuning range of the initial electron concentration is different for longitudinal waves with different frequencies. It lays the theoretical foundations for the design of terahertz elastic wave-based devices.