Comparison of models of the built-in electric field in silicon at high donor densities

The built-in electric field for holes due to donor-density gradients in n-type silicon is calculated at 300 K for donor densities between 1×1018 and 1×1020 cm−3. The calculation is based upon a recent model of band-gap narrowing that includes the effects of ionized impurities, many-body interactions, and an estimate of spatial fluctuations of the band-gap edge caused by the random distribution of donor atoms in the silicon crystal. This model of band-gap narrowing differs significantly from a number of other band-gap narrowing models currently in use in that it agrees with the band-gap narrowing measured optically at 35 and 300 K rather than that inferred from electrical measurements. The built-in electric field based on this model, which also differs significantly from the results of most previous models, decreases significantly above a donor density of 1×1019 cm−3 with a reversal of the field above 7×1019 cm−3. The implications of this work for photodiodes are discussed.