  Here we report on an acoustoelectric slab waveguide heterostructure for
phonon amplification using a thin Al$_{0.58}$Sc$_{0.42}$N film grown directly
on a 4H-SiC substrate with an ultra-thin In$_{0.53}$Ga$_{0.47}$As epitaxial
film heterogeneously integrated onto the surface of the
Al$_{0.58}$Sc$_{0.42}$N. The aluminum scandium nitride film grown directly on
silicon carbide enables a thin (1 micron thick) piezoelectric film to be
deposited on a thermally conductive bulk substrate (370 W/m-K for 4H-SiC),
enabling negligible self-heating when combined with the
In$_{0.53}$Ga$_{0.47}$As semiconductor parameters of large mobility (~7000
cm$^2$/V-s) and low concentration of charge carriers (~5x10$^{15}$ cm$^{-3}$).
A Sezawa mode with optimal overlap between the peak of its evanescent electric
field and the semiconductor charge carriers is supported. The high velocity of
the heterostructure materials allows us to operate the Sezawa mode amplifier at
3.05 GHz, demonstrating a gain of 500 dB/cm (40 dB in 800 microns).
Additionally, a terminal end-to-end radio frequency gain of 7.7 dB and a
nonreciprocal transmission of 52.6 dB are achieved with a dissipated DC power
of 2.3 mW. The power added efficiency and acoustic noise figure are also
characterized.
