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We act on the suggestion that an excitonic insulator state mightseparate---at very low temperatures---a semimetal from a semiconductor and askfor the nature of these transitions. Based on the analysis of electron-holepairing in the extended Falicov-Kimball model, we show that tuning the Coulombattraction between both species, a continuous crossover between a BCS-liketransition of Cooper-type pairs and a Bose-Einstein condensation of preformedtightly-bound excitons might be achieved in a solid-state system. The precursorof this crossover in the normal state might cause the transport anomaliesobserved in several strongly correlated mixed-valence compounds.

Electron-hole pair condensation at the semimetal-semiconductor transition: a BCS-BEC crossover scenario