Abstract <p>An analytical and numerical study of a beam-driven multi-scale phonon-plasmon coupled mode propagating in piezoelectric semiconductor quantum plasmas is presented. Lattice shear excites phonons, and an external electron beam excites plasmons that in turn couple and become unstable. The coupled mode may resonate at different time scales depending on the corresponding frequency of the plasma species. The lattice equations, along with the quantum hydrodynamic model, are employed for dispersive analysis of the shear phonon-plasmon coupled mode. The dispersive features are elaborated in depth by numerical studies and depicted in a graphical representation. The effects of all plasma parameters on instability behavior are carefully observed in magnetically quantized GaAs semiconductor plasmas. This work seeks its modern applications in acoustic wave resonators and amplifiers, piezoelectric semiconductor devices, nanophotonics, nanomaterials, and nanotubes that have the capability to manipulate electrical signals.</p>