Degenerate Germanium. II. Band Gap and Carrier Recombination

The data bearing on the band structure of degenerate germanium have been abstracted from the literature and intercompared. A variety of effects are described in terms of a voltage characteristic of each. It is found that all the voltages have essentially the same value and show a striking independence of the carrier concentrations. The conclusion is drawn that this voltage closely represents the band gap of degenerate germanium. It is shown that the thermal current at low temperature must be carried by recombination in the junction, which gives the proper barrier if the recombination centers lie near the band edge. This model of recombination explains the thermal current, the minority carrier lifetime, the excess current, and the emission spectrum. The reflectivity peak at 2.2 ev is also consistent if the bands at the [111] edge are roughly parallel to each other. The barrier found from the transition capacitance is not understood. The recombination centers lie close to the band edge. Assuming they are donors and acceptors, their capture cross section at room temperature is about ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ per neutral atom. On the basis of this model, the thermal gap of highly degenerate germanium is about 30 mv less than for the unperturbed lattice. The shrinkage is independent of temperature.