Energy-band distortion in highly doped silicon

A plausible model for the doping dependences of the conduction-and valence-band shifts, and of the concomitant narrowings of the optical and electrical energy gaps, caused by high doping concentrations in silicon is developed by refining, extending, and combining previously described theories. A meaningful link is thereby established between the fundamental solid-state physics that underlies the energy-band distortion and the silicon device physics that describes the pragmatic ramifications of it. The important many-body effects, which produce actual rigid shifts in the conduction and valance bands, are identified and characterized, and are shown to exclusively narrow the optical energy gap. The electrical energy-gap narrowing comprises additional effective shifts defined by the band tails due to the randomness of the dopant distribution, which are described. Predictions of the optical and electrical energy-gap narrowings, the difference between which is explained physically for the first time, are shown to agree well with measurements from several independent experiments.