We report on the performance of density functional theory (DFT) with the Tran–Blaha modified Becke–Johnson exchange potential and the random phase approximation dielectric function for optical constants of semiconductors in the ultraviolet–visible (UV-Vis) light region. We calculate optical bandgaps Eg, refractive indices n, and extinction coefficients k of 70 semiconductors listed in the Handbook of Optical Constants of Solids [(Academic Press, 1985), Vol. 1; (Academic Press, 1991), Vol. 2; and (Academic Press, 1998), Vol. 3] and compare the results with experimental values. The results show that the calculated bandgaps and optical constants agree well with the experimental values to within 0.440 eV for Eg, 0.246–0.299 for n, and 0.207–0.598 for k in root mean squared error (RMSE). The small values of the RMSEs indicate that the optical constants of semiconductors in the UV-Vis region can be quantitatively predicted even by a low-cost DFT calculation of this type.
References
Since n and k have rarely been measured at wavelengths completely consistent with the selected ones (300 nm, 400 nm, …, 800 nm), when calculating the RMSE, we used linearly interpolated values of n and k between two closest points only if there were valid data within eV from the selected wavelength (energy). For a semiconductor showing optical anisotropy, we employed only the xx elements of the matrices (, , or and , , or kxx) and compared them with those obtained from the DFT calculations. Note that nondiagonal elements of the dielectric tensor are ignored when calculating the n and k of monoclinic structures. When only polycrystalline samples were available for measuring optical constants of a semiconductor showing optical anisotropy (AlN, h-BN, CdGeAs2, and AgI), we used the averaged experimental values for comparison with the averaged diagonal elements of the matrices [ or ] obtained by the DFT calculation. When experimental and analytical insufficiency was mentioned in Refs. 39–41, we did not use these experimental values in the comparison (Bi12GeO20). The experimental data for seven compounds (AgGaSe2, PbSe, PbTe, LiTaO3, TlCl, TlBr, and TlI) differ from reference to reference, and the reliability of the measurements and analysis is sometimes not mentioned in Refs. 39–41. In such cases, we were not able to make a choice as to which data should be adopted for the comparison, and so these experimental data were not used when obtaining the RMSE.
