1. The emitter efficiency of a bipolar junction transistor is governed by the ratio of current densities carried across the emitter-base junction by electrons and holes, which should be as large as possible. The dominant factor in this ratio is the ratio of minority carriers at equilibrium on the two sides. This can be controlled only through the doping in a homojunction, so bipolar transistors have a heavily doped emitter and lightly doped base. Calculate the ratio np /pn, for the homojunction, where np is the minority density of electrons in p-type material and similarly for pn.
Show that the band discontinuities provide an additional degree of freedom in a heterojunction where the emitter has the wider band gap. Consider again the specific example of n-AlGaAs and p-GaAs, which is often used for the emitter-base junction of an npn heterojunction bipolar transistor (HBT). Show that the change from GaAs to AlGaAs in the emitter, keeping everything else fixed, decreases the density of minority holes there. What happens to the ratio np/pn? This in turn reduces the current density carried by holes; the electrons are unaffected.

2. Electrons are trapped in a well whose effective mass is very different from that of the barriers. What happens to the boundary condition at the heterojunction? Consider both