BANDGAP NARROWING IN MODERATELY TO HEAVILY DOPED SILICON

A model of bandgap reduction in silicon through the stored electrostatic energy of majority-minority carrier pairs is developed and compared with experimental results in the doping range from 3 X 107 to 1.5 X 1020,/cm3 at room temperature. An analytic expression for the bandgap reduction in nondegenerate material is obtained [formula omitted] having a square-root dependence on the majority carrier concentrat on. At room temperature this becomes [formula omitted] In degenerate material, the bandgap reduction is independent of temperature, following the relationship [formula omitted] The experimental data at room temperature are in excellent agyeen ent with this theory. Plots of bandgap narrowing as a function of doping level are presented for a number of temperatures. Copyright © 1979 by The Institute of Electrical and Electronics Engineers, Inc.