We describe semiconductor cavities based on strained Ga0.85In0.15As/AlAs multilayers with permanent built-in piezoelectric fields that confine acoustic phonons in the THz range. The possible role of piezoelectric fields on the phonon lifetimes and on Raman scattering is discussed. Phonon mirrors and cavities grown along [001] (non-piezoelectric) and along [311] (piezoelectric) are studied and compared using high-resolution Raman spectra and photoelastic model calculations. The high quality of the grown [001]([311]) structures is demonstrated by the observation of up to 7(5) orders of folded acoustic phonons and the excellent agreement with theory. We observe a large broadening of the acoustic phonon peaks in the piezoelectric [311] structures upon carrier injection with near-gap excitation. Such acoustic phonon lifetime reduction evidences a strongly modified electron-acoustic phonon interaction in these structures.