Plasmons-Enhanced Minority-Carrier Injection as a Measure of Potential Fluctuations in Heavily Doped Silicon

Well-known apparent electrical silicon bandgap narrowing in a heavily doped region of a bipolar transistor is observed by means of an enhanced minority-carrier injection experiment. In the region of interest, plasmons-induced potential fluctuations are existent in nature and hence constitute the origin of apparent bandgap narrowing. In this letter, we extract the underlying potential fluctuations directly from the enhanced minority-carrier injection experiment published in the literature. The core of the extraction lies in a combination of the two existing theoretical frameworks. First, the Gaussian distribution can serve as a good approximation of potential fluctuations. Second, no change can be made in the real bandgap between fluctuating conduction- and valence-band edges. Extracted potential fluctuations come from plasmons, as verified by our published temperature dependences of plasmons limited mobility in the inversion layer of MOSFETs as well as theoretical calculation results on bulk silicon. More importantly, this letter can deliver potential applications in the modeling and simulation area of nanoscale FETs (MOSFETs, FinFETs, and so forth) and bulk semiconductors.