Femtosecond energy relaxation of nonthermal electrons injected in p-doped GaAs base of a heterojunction bipolar transistor

Abstract

We study femtosecond relaxation of minority carriers (electrons) injected into a heavily p-doped base of a heterojunction bipolar transistor (HBT). Here, we consider the case of p-doped GaAs, to be specific. The electrons are assumed to have a peaked energy distribution at t=0, with kinetic energies a few hundred meV above the conduction band threshold. We solve the time dependent Boltzmann equation governing the dynamics of these electrons. The main feature of this work is a detailed calculation of the time dependent nonthermal, nonequilibrium electron energy distribution, that relaxes due to single particle excitations via electron–hole scattering and interaction with coupled optical phonon-hole plasmon modes in the sub and picosecond time domains. We highlight the significant role that the electron-hole scattering plays in this relaxation. The majority carriers (holes) are assumed to remain in quasiequilibrium with the lattice, taken to be at room temperature (or at 77 K). We present calculations of electron energy relaxation with the hole density varied from 1×1018 to 1×1020 cm−3. In the initial, subpicosecond stages of the relaxation, the energy distribution evolves into two major components: a quasiballistic but broad component, at energies near the injection energy, and an energy relaxed component near E=0. The latter becomes dominant in a picosecond or so. The electrons with an initial mean velocity of ∼1.5×108 cm/s attain a cooler distribution with a mean velocity of ∼4×107 cm/s within about 1 ps for p doping in excess of 1×1019 cm−3. The temporal evolution of average velocity 〈v〉 of the electrons should be useful in obtaining values of the base width suitable for effective operation of HBTs.