Application of an improved band-gap narrowing model to the numerical simulation of recombination properties of phosphorus-doped silicon emitters

The commonly used band-gap narrowing (BGN) models for crystalline silicon do not describe heavily doped emitters with desirable precision. One of the reasons for this is that the applied BGN models were empirically derived from measurements assuming Boltzmann statistics. We apply a new BGN model derived by Schenk from quantum mechanical principles and demonstrate that carrier degeneracy and the new BGN model both substantially affect the electron–hole product within the emitter region. Simulated saturation current densities of heavily phosphorus-doped emitters, calculated with the new BGN model, are lower than results obtained with the widely used empirical BGN model of del Alamo.