Ceramics of composition Ba(Ti1-xZnx)O3-x: 0.00003 <= x <= 0.01 exhibit modest semiconductivity, whose value is increased by up to two orders of magnitude under the action of a small dc bias voltage. The effect, which is not observed in undoped BaTiO3, occurs in both grain and grain boundary regions and is attributed to the nature of the defect structure, which contains highly polarized clusters. It is proposed that internal electron transfer within the clusters under the action of a dc bias voltage leads to a more conductive excited state, which gradually returns to the ground state when the dc bias is removed.