Nonlocal orbital-free kinetic energy density functional for semiconductors

We propose a nonlocal kinetic energy density functional (KEDF) for semiconductors based on the expected asymptotic behavior of its susceptibility function. The KEDF’s kernel depends on both the electron density and the reduced density gradient, with an internal parameter formally related to the material’s static dielectric constant. We determine the accuracy of the KEDF within orbital-free density functional theory (DFT) by applying it to a variety of common semiconductors. With only two adjustable parameters, the KEDF reproduces quite well the exact noninteracting KEDF (i.e., Kohn-Sham DFT) predictions of bulk moduli, equilibrium volumes, and equilibrium energies. The two parameters in our KEDF are sensitive primarily to changes in the local crystal structure (such as atomic coordination number) and exhibit good transferability between different tetrahedrally-bonded phases. This local crystal structure dependence is rationalized by considering Thomas-Fermi dielectric screening theory.

Figure 1

OF-DFT and KS-DFT total energy versus volume curves for CD and $\beta$-tin silicon. For CD silicon, the optimal KEDF parameters are used ($\lambda =0.01$ and $\beta =0.65$). For $\beta$-tin silicon, the optimal $\lambda =0.0055$ is used with $\beta =0.65$ (optimal for CD silicon).

Figure 2

OF-DFT and KS-DFT total energy versus volume curves for ZB GaAs. The OF-DFT curve is calculated with optimal $\lambda =0.013$ and $\beta =0.783$.

Figure 3

Variation in CD silicon bulk modulus, equilibrium volume per atom, and total energy per atom with different $\lambda$.

Figure 4

(Color online) The electron density of CD silicon along the [111] direction. Black solid line: KS-DFT. Red dashed line: OF-DFT with $\lambda =0.0$. Blue dotted line: OF-DFT with $\lambda =0.01$ and $\beta =0.65$. Vertical axis is electron density in $1/{\text{bohr}}^3$; horizontal axis represents the grid.

Figure 5

(Color online) The electron density of ZB GaAs along the [111] direction. Black solid line: KS-DFT. Red dashed line: OF-DFT with $\lambda =0.0$. Blue dotted line: OF-DFT with $\lambda =0.013$ and $\beta =0.783$. Vertical axis is electron density in $1/{\text{bohr}}^3$; horizontal axis represents the grid.

Figure 6

OF-DFT and KS-DFT relative energy differences between CD silicon and ZB semiconductors (per primitive cell). OF-DFT results using an averaged $\lambda =0.01177$ and $\beta =0.7143$ closely match the energy ordering from KS-DFT (see Table ).

Figure 7

Gallium BLPS in real space. Coulombic tail is enforced beyond 3.5 bohr.

Figure 8

Indium BLPS in real space. Coulombic tail is enforced beyond 4.0 bohr.

Figure 9

Phosphorus BLPS in real space. Coulombic tail is enforced beyond 3.5 bohr.

Figure 10

Arsenic BLPS in real space. Coulombic tail is enforced beyond 4.0 bohr.

Figure 11

Antimony BLPS in real space. Coulombic tail is enforced beyond 4.0 bohr.