Optics of Semiconductors from Meta-Generalized-Gradient-Approximation-Based Time-Dependent Density-Functional Theory

We calculate the optical spectra of silicon, germanium, and zinc blende semiconductors in the adiabatic time-dependent density-functional formalism, making use of kinetic energy density-dependent [meta-generalized-gradient-approximation (GGA)] exchange-correlation functionals. We find excellent agreement between theory and experiment. The success of the theory on this notoriously difficult problem is traced to the fact that the exchange-correlation kernel of meta-GGA supports a singularity of the form $\alpha /q^2$ (where $q$ is the wave vector and $\alpha$ is a constant), whereas previously employed approximations (e.g., local-density and generalized gradient approximations) do not. Thus, the use of the adiabatic meta-GGA opens a new path for handling the extreme nonlocality of the time-dependent exchange-correlation potential in solid-state systems.

Figure 1

Dielectric function of silicon. Thin solid (red online) line is the result obtained with MGGA band structure and including the many-body interactions through $f_{\mathrm{xc}}$ of Eq. (10). Dashed (green online) line is the result obtained with MGGA band structure but with $f_{\mathrm{xc}}=0$ (RPA). Dotted (blue online) line is obtained with LDA band structure within RPA. Thick solid line is the experiment from Ref. 27.

Figure 2

The same as Fig. 1 but for germanium.