A double heterojunction bipolar transistor structure having desirable properties of a low base-emitter turn-on voltage and no electron blocking discontinuities in the base-collector junction. These properties are achieved by selecting base, emitter and collector materials to provide a bandgap profile that exhibits abrupt transitions at the heterojunctions, such that both abrupt transitions are due to transitions in the valence band edge of the bandgap, but not in the conductive band edge of the bandgap.