Experimental bounds on band-gap narrowing set by high open circuit voltage silicon solar cells

It has commonly been reported that the energy band gap in heavily doped silicon is smaller than in lightly doped silicon. The very high open circuit voltages recently achieved in metal-insulator-n-type-p-type (MINP) solar cells, in excess of 680 mV (AM1, 300 K), can be used to put constraints upon the magnitude of such band-gap narrowing. It was determined that most recombination in high open circuit voltage MINP cells occurred in the base region. An exact numerical analysis was then performed of the emitter region. To achieve this, a critical review of the literature was undertaken to determine the values of various material parameters in heavily doped silicon. The review of the literature on hole minority carrier lifetimes and mobilities revealed that some recent studies may be seriously in error. The result of the numerical analysis was that most published models of band-gap narrowing, or extrapolations from band-gap narrowing models, are inconsistent with the open circuit voltage achieved in MINP solar cells. The conclusion is that most band-gap narrowing models overestimate band-gap narrowing at the surface of phosphorus doped MINP solar cell emitters by 60 meV or more.