Influence of Fermi-Dirac Statistics on Collector Current of npn SiGe HBT at Low Temperatures

Abstract
The doping concentration in the base of npn SiGe HBTs operating at low temperatures should be high to prevent carrier freeze-out and to assure low base resistance. As a consequence, the majority carrier concentration in the base is determined with Fermi-Dirac statistics. The influence of Fermi-Dirac statistics on collector current of npn SiGe HBTs at low temperatures is analyzed in this work. It is shown that taking Fermi-Dirac statistics into account instead of Boltzmann statistics results in lower collector current. Therefore, Fermi-Dirac statistics should be taken into account for analysis and optimization of these devices. Analytical modelling of effects induced by consideration of Fermi-Dirac statistics is investigated. Based on proposed effective Ge-induced bandgap narrowing with approximately linear dependence on Ge fraction, the accurate analytical modelling of electron transport in degenerately doped base with trapezoidal Ge profile is presented for the first time.