Phase transformation in Si from semiconducting diamond to metallicβ-Snphase in QMC and DFT under hydrostatic and anisotropic stress

Abstract

Silicon undergoes a phase transition from the semiconducting diamond phase to the metallic ␤-Sn phase under pressure. We use quantum Monte Carlo calculations to predict the transformation pressure and compare the results to density-functional calculations employing the local-density approximation, the generalizedgradient approximations PBE, PW91, WC, AM05, PBEsol, and the hybrid functional HSE06 for the exchangecorrelation functional. Diffusion Monte Carlo predicts a transition pressure of 14.0Ϯ 1.0 GPa slightly above the experimentally observed transition pressure range of 11.3-12.6 GPa. The HSE06 hybrid functional predicts a transition pressure of 12.4 GPa in excellent agreement with experiments. Exchange-correlation functionals using the local-density approximation and generalized-gradient approximations result in transition pressures ranging from 3.5 to 10.0 GPa, well below the experimental values. The transition pressure is sensitive to stress anisotropy. Anisotropy in the stress along any of the cubic axes of the diamond phase of silicon lowers the equilibrium transition pressure and may explain the discrepancy between the various experimental values as well as the small overestimate of the quantum Monte Carlo transition pressure.

Simulation and understanding of atomic and molecular quantum crystals

“…Nevertheless, the description of longranged and very weak interactions poses a serious challenge to some families of first-principles methods (also known as ab initio because do not rely on any predetermined knowledge of the atomic forces) as the analytical expression of the corresponding electronic exchange and correlation energies are intricate and difficult to approximate for computational purposes (Klimeš and Michaelides, 2012;Cazorla, 2015). This circumstance converts quantum solids into an ideal playground in which to perform benchmark calculations for assessing the performance of standard and advanced electronic band-structure first-principles methods like, for instance, density functional theory (DFT) and electronic quantum Monte Carlo (eQMC) [Driver et al, 2010;Henning et al, 2010;Clay III et al, 2014;Clay III et al, 2016] (see Sec. III.A).…”

Magnetic states and optical properties of single-layer carbon-doped hexagonal boron nitride

“…One such functional is the HeydScuseria-Ernzerhof (HSE) functional, 20 which we have successfully used to study important properties of technologically important semiconductors. [21][22][23][24][25] Here we present a comprehensive HSE study for electronic structure of C clusters embedded in the single-layer h-BN. Given the large gap value in h-BN, it is commonly assumed as a sort of electronic "vegetable"…”

Quantum Monte Carlo study of pressure-inducedB3−B1phase transition in GaAs

“…The tendency of DMC calibrations over DFT for the present GaAs case is consistent with those for Si bulk properties and the transition pressure. 18,19,37 The shift by DMC calibration is established as resulting from the larger correction for the energy of metallic phase (higher density phase) than that of lower density phase, making the common tangent on the dependence of free energies on system volumes steeper. We have investigated the phonon contributions to the prediction.…”

“…A possible way to calibrate XC tendencies is to perform QMC evaluations. QMC, more specifically difussion Monte Carlo (DMC), provides more reliable evaluation of electron interactions not depending on XC functionals and also recently DMC has been used to calibrate transition pressures [16][17][18][19][20] too.…”