  We calculate the rate of acoustic phonon generation by a current-carrying,
ballistic quantum channel, defined in a two-dimensional electron gas by a
split-gate. Both uniform and nonuniform channels are considered. The generation
rate of acoustic phonons of a particular frequency and direction of propagation
is a steplike function of the applied bias voltage, with threshold voltages
that are calculated in the paper. The emitted phonons have a characteristic
angular distribution which changes significantly at the thresholds. The voltage
dependence of the generation rate is shown to be sensitive to the shape of the
channel. Thus the spectral and spatial distributions of the emitted phonons
bear information both on electron-phonon coupling in the vicinity of the device
and on characteristics of the electron spectrum.
