Energy-gap reduction in heavily doped silicon: Causes and consequences

The authors review briefly the existing theoretical treatments of the various effects that contribute to the reduction of the energy gap in heavily doped Si, namely electron-electron and electron-impurity interactions and the effect of disorder in the impurity distribution. They then turn to the longstanding question why energy-gap reductions extracted from three different types of experiments have persistently produced values with substantial discrepancies, making it impossible to compare with theoretical values. First, they demonstrate that a meaningful comparison between theory and experiment can indeed be made if theoretical calculations are carried out for actual quantities that experiments measure, e.g. luminescence spectra, as recently done by Selloni and Pantelides. Then, they demonstrate that, independent of any theoretical calculations, the optical absorption spectra are fully consistent with the luminescence spectra and that the discrepancies in the energy-gap reductions extracted from the two sets of spectra are caused entirely by the curve-fitting procedures used in analyzing optical-absorption data. Finally, they show explicitly that, as already believed by many authors, energy-gap reductions extracted from electrical measurements on transistors do not correspond to true gap reductions. They identify two corrections that must be added to the values extracted from the electrical data in order to arrive at the true gap reductions and show that the resulting values are in good overall agreement with luminescence and absorption data. They, therefore, demonstrate that the observed reduction in emitter injection efficiency in bipolar transistors is not strictly due to a gap reduction, as generally believed, but to three very different effects.