Elastic boundary conditions are shown to emerge naturally from a simpl
e unifying theory describing long-wavelength excitations in bulk semic
onductors. Their application to the cases of a freely vibrating layer
and to a layer enclosed by an infinitely rigid medium (roughly approxi
mated by a GaAs layer in vacuum and by a GaAs/AlAs quantum well respec
tively) shows that the disappearance of relevant dilational and shear
stresses in the first case and the inhibition of displacement in the s
econd case can only be obtained by s-polarized TO modes without mixing
-LO and p-polarized TO modes are forced to mix coherently. It is also
necessary for Fuchs-Kliewer interface polaritons to mix with LO modes
in order to satisfy elastic boundary conditions. The use of elastic, a
s distinct from hydrodynamic, boundary conditions brings the continuum
model much closer to the predictions of microscopic theory.