Optical absorption measurements of band-gap shrinkage in moderately and heavily doped silicon

Abstract

Optical absorption studies in the infra-red region around the fundamental energy gap have been carried out on both n- and p-Si samples in the range of concentrations from 3*1014 cm-3 to 7.3*1018 cm-3 for p-Si and from 6.5*1016 cm-3 to 9.2*1018 cm-3 for n-Si at room temperature (294 K). The transmission ratios were first measured for each sample in the range of wavelengths from about 0.9 mu m to 2.5 mu m. These ratios were then applied to calculate the reflectivity and the absorption coefficients for the samples. After correcting for free-carrier absorption, the band-gap shrinkage was then determined from the absorption coefficients for each sample. These results were then compared with those determined from other optical absorption studies, with those found by electrical device measurements and with those predicted from theories. It was found that even well below 3*1018 cm-3, a reduction in band-gap energy Delta Eg could be determined for both n- and p-Si, in contrast to the earlier optical absorption studies which reported that none could be detected. Between 1018 cm-3 and 1019 cm-3 the authors experimental values are consistent with those determined by other optical absorption studies. Their results also show that even in the moderately doped regime, their values of mod Delta Eg mod are less than those found by electrical device measurements and those predicted by various recent theories. This is consistent with the findings of the other optical studies in the heavily doped regime. The authors also found that the gap shrinkage mod Delta Eg mod depends on the dopant concentration as N13/. This is in agreement with the experimental results of Wagner and Vol'fson and Subashiev as well as with the theoretical results of Mahan and Berggren and Sernelius.