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An InP/InGaAs double heterojunction bipolar transistor (DHBT) with an undoped emitter tunneling barrier and composite collector structure is fabricated and studied. Due to the mass filtering effect for holes, a thin InP tunneling barrier can be used to replace the wide-gap emitter. Experimentally, an appropriate tunneling barrier thickness of 150 Å is employed to achieve good I-V characteristics. In addition, InGaAsP compositionally step-graded layers are introduced between the p+-InGaAs base and n--InP collector. By modulating the bandgap energy of InGaAsP, the large base-collector (B-C) potential spike can be divided into several small spikes with lower barrier height. The 4000 Å InP collectors with InP/InGaAsP/InGaAs step-graded junction achieve high breakdown voltages of 14.6 V. A small offset voltage of 80 mV and a small saturation voltage of 1.8 V at the collector current level of 5 mA are obtained. Prior to the current gain fall-off caused by the self-heating effect, the step-graded DHBT has the current gain as high as 118 H at IC = 30 mA and VCE = 3V.