Extracting semiconductor band gap zero-point corrections from experimental data

We describe an improved method for extracting semiconductor band gap zero-point corrections from experimental data. We propose two extrapolation schemes and use first-principles calculations to show that they are up to an order of magnitude more accurate than existing schemes. We apply our schemes to diamond, extracting a value of the zero-point correction of $-0.41$ eV, in better agreement with first-principles results than previous estimates. Finally, we consider the low-temperature limit of the class of observables that includes the electronic band gap, obtaining a $T^4$ dependence in three dimensions, $T^2$ in two dimensions, and $T^{3/2}$ in one dimension.

Figure 1

Upper: Temperature dependence of the thermal band gap of diamond. The experimental data (black squares, from Ref. [6]) are compared to the first-principles results (gray solid line) that have been shifted to match the experimental data at zero temperature. The high-temperature linear extrapolation is also shown (black dashed line). Lower: ZP correction to the thermal band gap of diamond obtained with the linear extrapolation scheme, using the most accurate models listed in Table 1. The horizontal dashed line in the lower part of the figure labeled “ZP” denotes the value obtained from the first-principles calculations.

Figure 2

Upper: Temperature dependence of the thermal band gap of LiH. We show first-principles results (gray solid line) and the high-temperature linear extrapolation (black dashed line). Lower: ZP correction to the thermal band gap of LiH obtained with the linear extrapolation scheme, using the most accurate models listed in Table 1. 2 BE denotes double BE.