Effects of sulfur isotopic composition on the band gap of $\mathrm{PbS}$

Low temperature photoluminescence spectra of synthetic $\mathrm{PbS}$ crystals having the natural isotopic abundance (95% ${}^{32}S$) are compared with crystals grown using 99% ${}^{34}S$. An anomalous decrease in the band gap energy of $6.5\pm 2{\mathrm{cm}}^{-1}$ with increasing $S$ mass was observed. The unusual sign of this isotope shift can be related to the temperature dependence of the band gap energy, which opposite to the behavior seen for most common semiconductors, increases strongly between $2\mathrm{K}$ and $320\mathrm{K}$. This temperature dependence was measured with improved accuracy using absorption spectroscopy, and a fit to this data suggests that there should be virtually no net renormalization of the band gap energy due to zero point motion at low temperatures. This must result from a cancellation of the contributions from $S$ and Pb, but the predicted “normal” isotope shift of the band gap energy with Pb mass is too small to be measured.

Figure 1

Low temperature photoluminescence spectra of $\mathrm{PbS}$ samples grown using natural $S$ $(\sim 95\%{}^{32}S)$ and highly enriched ${}^{34}S$ are compared. The measured value of the peak shift is $6.5\pm 2{\mathrm{cm}}^{-1}$.

Figure 2

The temperature dependence of the band gap of natural $\mathrm{PbS}$ as determined by absorption spectroscopy is plotted from 2 to $320\mathrm{K}$. The solid line is a fit to the data using a three oscillator model as described in the text. The dashed line, which has a slope of $\sim 0.45\mathrm{meV}∕°\mathrm{K}$, is an extrapolation of a linear fit to the model in the high temperature limit. The near-agreement of this extrapolation and the observed $T\approx 0$ band gap energy indicates that there is essentially no net zero-point renormalization of the band gap energy at low temperature in $\mathrm{PbS}$.