Bandgap narrowing in moderately to heavily doped silicon

A theoretical model of bandgap narrowing in silicon at high doping levels has been developed. The model takes into account the electrostatic energy of interaction between a minority carrier and the majority carriers surrounding it, which reduces the thermal energy necessary for creation of an electron-hole pair. A pair energy similar to the excitonic binding energy of bound electron-hole pairs in insulators is obtained. Theoretical results are in excellent agreement with experimental results in the doping range from 3 times 10 to the 17th to 1.5 times 10 to the 20th/cu cm at room temperature. These results indicate that at high injection levels such as a transistor biased into the conductivity-modulation regime or a solar cell whose surface is established by ion implantation into an oxide layer, the bandgap narrowing is determined by the injected carrier concentration rather than by the doping level.