Electron transport in bipolar transistors with biaxially strained base layers

In silicon npn bipolar junction transistors grown on (100) oriented substrate, at base doping levels in excess of 10²⁰ boron atoms/cm³, strain induced splitting of the normally sixfold degenerated conduction band minimum becomes important and needs to be considered in modeling of injection currents. The biaxial tensile strain, originating in the smaller covalent radius of boron compared to silicon, induces a lowering of two valleys with heavy effective mass in vertical direction whereas the remaining four valleys are raised in energy. Using a coupled set of equations for the electron gas systems in the twofold and fourfold degenerated valleys, emitter and collector current formulas are derived. In the relevant case of strong f-type intervalley scattering rates compared to Auger recombination rates (which holds at least up to about 10²¹ cm^-3) collector currents are described by (V_BC=0 V) j_C=-e(D_n4n_4,0+D_n2n_2,0 )/w(e^V(BE/V(th))-1) provided that the electron diffusion length is large compared to the base width w. D_n4 D _n2, and n_4,0, n_2,0 are diffusion constants and equilibrium minority carrier concentrations in the two electron gas systems, respectively. In Si/SiGe heterojunction bipolar transistors the conduction band situation in the base is similar to that in extremely heavily boron doped (homojunction) base layers as presence of Ge also causes the conduction band minimum to split (splitting is, however, of opposite sign). Thus, the transport model discussed here applies also to that kind of device