  We calculate the critical temperature below which an excitonic insulator
exists at the pressure-induced semiconductor-semimetal transition. Our approach
is based on an effective-mass model for valence and conduction band electrons
interacting via a statically screened Coulomb potential. Assuming pressure to
control the energy gap, we derive, in the spirit of a BEC-BCS crossover
scenario, a set of equations which determines, as a function of the energy gap
(pressure), the chemical potentials for the two bands, the screening wave
number, and the critical temperature. We (i) show that in leading order the
chemical potentials are not affected by the exciton states, (ii) verify that on
the strong coupling (semiconductor) side the critical temperatures obtained
from the linearized gap equation coincide with the transition temperatures for
BEC of non-interacting bosons, (iii) demonstrate that mass asymmetry strongly
suppresses BCS-type pairing, and (iv) discuss in the context of our theory
recent experimental claims for exciton condensation in ${\rm
TmSe_{0.45}Te_{0.55}}$.
