Electron-phonon scattering rates for quantum wires composed of one com
pound semiconductor material within another are calculated rigorously
for arbitrary wire shapes within the dielectric continuum approach for
the optical phonons and the effective-mass approximation for the elec
trons. No approximations are used for the boundary conditions satisfie
d by the phonons or by the electrons. Detailed results are given for t
he intrasubband and intersubband scattering rates as functions of the
initial electron energy and of wire size for wires of rectangular cros
s section. An interesting maximum in the intersubband scattering rate
as a function of wire size is found. We find that interface phonons gi
ve important contributions to the scattering rates, especially for sma
ll (less than or similar to 100 angstrom) wire widths or high electron
energies. We also give a quantitative appraisal of the rates obtained
from simple separable approximations used previously for the phonons.