Empirical determination of the energy band gap narrowing in highly doped n+ silicon

Highly doped regions in silicon devices should be analyzed using Fermi-Dirac statistics, taking into account energy band gap narrowing (BGN). An empirical expression for the BGN as a function of dopant concentration is derived here by matching the modeled and measured thermal recombination current densities J0 of a broad range of n+ dopant concentration profiles prepared by phosphorus diffusion. The analysis is repeated with Boltzmann statistics in order to determine a second empirical expression for the apparent energy band gap narrowing, which is found to be in good agreement with previous work.