Precise effective masses from density functional perturbation theory

Abstract

The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory. Then, we solve the latter issue by adapting the concept of "transport equivalent effective mass" to the k·p framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is ther... The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory. Then, we solve the latter issue by adapting the concept of "transport equivalent effective mass" to the k ·p framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is therefore more general, more robust, and simpler to use, which makes it especially appropriate for high-throughput computing. After validating the developed techniques, we apply them to the study of silicon, graphane, and arsenic. The formalism is implemented into the ABINIT software and supports the norm-conserving pseudopotential approach, the projector augmented-wave method, and the inclusion of spin-orbit coupling. The derived expressions also apply to the ultrasoft pseudopotential method.

An ab initio electronic transport database for inorganic materials

“…Effective mass tensors are typically evaluated from band structures by computing second derivatives at a certain k-point (e.g., the valence band maximum or conduction band minimum) along certain symmetry lines through finite differences. There are numerical challenges in doing so 32 and choosing the k-point to evaluate the effective mass is not obvious when facing band structures with important non-parabolicity, multiple degenerate bands or pockets with close energy in different part of the Brillouin zone. The conductivity effective mass can be also seen as an average over the Brillouin zone and bands of the k-dependent second derivative (equation (3)) as integration by parts leads to: $\begin{array}{}\text{(12)}& {\overline{M}}_{\mathit{\alpha }\mathit{\beta }}^{-1}=\frac{-{\sum }_i\int M_{\mathit{\alpha }\mathit{\beta }}^{-1}true(i,\mathbf{k}true)f_{\mathit{\mu }}true({\mathit{\epsilon }}_{i,\mathbf{k}},Ttrue)\frac{d\mathbf{k}}{4{\mathit{\pi }}^3}}{{\sum }_i\int f_{\mathrm{italic\mu }}\left({\mathrm{italic\epsilon }}_{i,\mathrm{boldk}},T\right)\frac{d\mathrm{boldk}}{4{\mathrm{italic\pi }}^3}}.\end{array}$ …”

Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap

“…Density-functional perturbation theory [54][55][56] has been used for the phonon frequencies, dielectric tensors, Born effective charges, effective masses, and electron-phonon matrix elements.…”

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to the full first-principles theory and the Fröhlich polaron

“…The effective masses have been computed directly using the scheme from Ref. 95. The Allen-Heine-Cardona formalism is used for the computation of the Fan and Debye-Waller self energies 44,53,58,96 .…”