Phonon-induced band gap renormalization by dielectric dependent global hybrid density functional tight-binding
Physical Review B(2024)
Abstract
Accurate electronic bandstructures of solids are indispensable for a wide
variety of applications and should provide a sound prediction of phonon-induced
band gap renormalization at finite temperatures. We employ our previously
introduced formalism of general hybrid functionals within the approximate
density functional method, DFTB, to present first insights into the accuracy of
temperature dependent band gaps obtained by a dielectric-dependent global
hybrid functional. The work targets the prototypical group-IV semiconductors
diamond and silicon. Following Zacharias et al. [Phys. Rev. Lett. 115, 177401
(2015)], we sample the nuclear wave function by stochastic Monte-Carlo
integration as well as the deterministic one-shot procedure [Phys. Rev. B 94,
075125 (2016)] derived from it. The computational efficiency of DFTB enables us
to further compare these approaches, which fully take nuclear quantum effects
into account, with classical Born-Oppenheimer molecular dynamic (BOMD)
simulations. While the quantum mechanical treatments of Zacharias et al. yield
band gaps in good agreement with experiment, calculations based on BOMD
snapshots inadequately describe the renormalization effect at low temperatures.
We demonstrate the importance of properly incorporating nuclear quantum effects
by adapting the stochastic approach to normal amplitudes that arise from the
classical equipartition principle. For low temperatures the results thus
obtained closely resemble the BOMD predictions, while anharmonic effects become
important beyond 500 K. Comparisons between DFTB parametrized from
semi-local DFT, and global hybrid DFTB, suggest that Fock-type exchange
systematically yields a slightly more pronounced electron-phonon interaction,
hence stronger gap renormalization and zero-point corrections.
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