We show that phononic frequency conversion can be enhanced by orders of magnitude in piezoelectric systems by heterogeneous integration of high-mobility semiconductor films. A lithium niobate and indium gallium arsenide heterostructure is utilized to demonstrate efficient three-wave mixing processes at microwave frequencies, including 16% phononic power conversion efficiency for sum-frequency generation and 1% phononic power conversion efficiency for difference-frequency generation, as well as the most efficient degenerate four-wave phononic mixing to date. We present a theoretical model that accurately predicts the sum-frequency and difference-frequency generation processes and we show that the conversion efficiency can be further enhanced by the application of semiconductor bias fields. Laser Doppler vibrometry is then applied to examine many three-wave and four-wave mixing processes simultaneously in the same device. Through the use of our developed model, we show that these nonlinearities can be enhanced far beyond what is demonstrated here by confining phonons to smaller dimensions in waveguides and optimizing semiconductor material properties or using 2D semiconductors.
