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Light-emitting transistor (LET) and transistor laser (TL) can provide the high-speed electrical and optical modulations simultaneously, advancing light-emitting diodes and diode lasers. Still, between experimental data and rate-equation modeling, there are two-order-of-magnitude uncertainties on the carrier lifetimes of quantum wells (QWs) inserted in heavily p-doped bases of these devices. In view of the importance of this timescale on the modulation speed, we provide a comprehensive approach to calculate carrier lifetimes under such circumstances. We model the Hartree potential energy with self-consistent solutions of the Schrodinger’s and Poisson’s equations. The hole distribution is obtained from real-space density of states through multiband retarded Green functions, taking the outgoing-wave features of hole quasi-bound states into account. We then estimate the carrier lifetimes based on a multiband source-radiation approach including both bound-to-bound and bound-to-continuum components of spontaneous (SP) emissions. Under low surface carrier injections, a large Hartree potential is formed, and the valence band around the QW is strongly tilted. Both bound and quasi-bound valence states are present, and quasi-bound holes may tunnel out of QW and reemerge in the base. The SP spectrum from the QW in the heavily doped base is significantly larger than that from an undoped one due to preexisting holes. At the high injection level, the screening effect significantly reduces the Hartree potential and band bending. We also include the nonradiative Auger recombination to evaluate the total carrier lifetime. Overall carrier lifetimes and small-signal ones are estimated as hundred picoseconds at a doping density of 1019 cm−3 and might be even shorter in the case of heavier doping.
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