Doping effects and compositional grading in AlxGa1-xAs/GaAs heterojunction bipolar transistors

First-order analytical calculations were made for the energy-band diagrams for n-AlxGa1-xAs/p-GaAs heterojunctions for x = 0.15, 0.3, and 0.5 employing different compositional gradings and doping densities specifically for heterojunction-bipolar-transistor (HBT)applications. In the calculations most recently determined, conduction-band discontinuity ΔECof 65 percent of the bandgap difference ΔEgbetween the AlxGa1-xAs and GaAs, and the donor activation energies in n-AlxGa1-xAs of 60 and 160 meV for x = 0.3 and 0.5, respectively, were used. The results show that the position of the heterojunction spike barrier, and the depth and width of the notch in the conduction-band edge for a compositionally abrupt heterointerface depend on the respective doping densities on the p and n sides of the heterojunction. Also, for an abrupt heterointerface the difference in barrier heights for electron and hole injections varies between ΔEgand ΔEV(the valence-band discontinuity), depending on the doping densities and the applied bias, and is not necessarily the generally accepted value of ΔEV. Analytical expressions and curves were obtained to estimate the minimum compositional grading L for eliminating the spike barrier and the notch as a function of the doping densities and the applied bias.