  We study the occurrence of excitonic superfluidity in electron-hole bilayers
at zero temperature. We not only identify the crossover in the phase diagram
from the BCS limit of overlapping pairs to the BEC limit of non-overlapping
tightly-bound pairs but also, by varying the electron and hole densities
independently, we can analyze a number of phases that occur mainly in the
crossover region. With different electron and hole effective masses, the phase
diagram is asymmetric with respect to excess electron or hole densities. We
propose as the criterion for the onset of superfluidity, the jump of the
electron and hole chemical potentials when their densities cross.
