Comparison of screened hybrid density functional theory to diffusion Monte Carlo in calculations of total energies of silicon phases and defects

Abstract

Nearly quantitative agreement between density functional theory ͑DFT͒ and diffusion Monte Carlo ͑DMC͒ calculations is shown for the prediction of defect properties using the Heyd-Scuseria-Ernzerhof ͑HSE͒ screened-exchange hybrid functional. The HSE functional enables accurate computations on complex systems, such as defects, where traditional DFT may be inadequate and DMC calculation computationally unfeasible. The screened-exchange hybrid functional retains the benefits of earlier hybrid functionals in terms of treating strongly correlated insulators but unlike them it can be applied to metallic phases. This study concentrates on the DFT energetic predictions of point defects in silicon and on phase energy differences between the diamond and metallic ␤-tin phases. The prediction of energy landscapes from density functional theory ͑DFT͒ has often lacked the predictive power necessary to quantitatively anticipate experimental results such as phase diagrams and properties of point defects. This predictive capability is most needed when experiments are unable to measure desired properties directly, for example indirect probes of the existence and behavior of point defects has led to disagreements regarding the individual contributions of interstitial and vacancy defects to self-diffusion. 1,2 The first two generations of DFT functionals, the local density approximation ͑LDA͒ and the generalized gradient approximations ͑GGA͒, 3-5 yield structural properties in reasonable agreement with experiments, but the energetics of defects have been known to be poorly reproduced. For example, for both Si and Ge, two group-IV semiconductors, the LDA and GGA predict self-diffusion activation energies that are about 1.5 and 1 eV lower, respectively, than experimental measurements. 6 This is also true for the diffusion of dopants in these materials. 6 For nearly every case considered for these materials, the predicted activation energy is roughly 1 eV lower than that found by experiment. In addition, DFT with the GGA predicts the semiconductor Ge to be metallic. Without quantitative predictions of point defect properties, the modeling of larger-scale phenomena, such as dopant profiles in Si or microstructure in an irradiated material, will be inadequate.Higher computational accuracy can be achieved with the diffusion Monte Carlo ͑DMC͒ approach, although at a greater computational expense. DMC calculations have been performed on key structures, and past work 7 has shown that DMC calculations on interstitial defects in Si find formation energies that are significantly higher than those from DFT with the GGA and thus closer to experimental estimates. A computational method that combines the relative ease of DFT computations with the accuracy of DMC simulation is certainly needed in order to obtain quantitative predictive power of what would be very difficult experiments. In this vein, third-and fourth-generation density functionals have recently been developed but as yet remain untested in this energetic context. In this work two of t...

The vacancy in silicon: A critical evaluation of experimental and theoretical results

“…10 Uberuaga et al 11 predicted an activation enthalpy of 3.1 eV for Ge self-diffusion that is in excellent agreement with the experimental result of 3.09 eV reported by Werner et al 8 This agreement between experimental and theoretical results on the activation enthalpies of self-and dopant diffusion holds true for Ge and also for Si ͑see below͒ in the case an alternative functional, such as the B3YLP, is used in density functional theory ͑DFT͒ calculations, as discussed by Uberuaga et al 11 Previous DFT calculations 3-5 are known to underestimate the formation energies of defects in Si and Ge due to the lack of exact exchange in these functionals. [12][13][14][15] Although these are well converged studies employing supercells of up to 512 atoms and Brillouin-zone sampling with 2 3 k-points, the 3.17-3.29 eV values predicted for the V-formation enthalpy in Si 3,5 are a severe underestimation and are therefore not appropriate to facilitate comparison with the experimental studies that support 3.6 eV for selfdiffusion via V in Si. 1,2 This issue was pointed out in numerous previous studies of group-IV semiconductors ͑see, for example, Refs.…”

“…14,16 These techniques predict, in the case of Si, formation enthalpies of defects that are about 1 eV higher than the normal DFT predictions. 14,16 For example, the B3YLP-corrected value of the activation enthalpy of self-diffusion via V in Si is 4.56 eV ͑3.98 eV for the formation and 0.58 eV for the migration enthalpy͒, 16 which is consistent with the activation of V-mediated dopant diffusion. This demonstrates that the activation enthalpy of 3.6 eV for V-mediated self-diffusion in Si proposed by Shimizu et al 1 remains questionable.…”

CO adsorption on metal surfaces: A hybrid functional study with plane-wave basis set

“…16 For these systems, hybrid functionals are among the most accurate functionals available as far as energetics and structural properties are concerned. 17,18,19 Currently, the most popular ones are PBE0 (or PBE1PBE) 20,21 and B3LYP 22,23 . The former has been proposed by Perdew, Burke, Ernzerhof, Adamo and Barone 24,25 as a "parameter-free" functional based on the PBE exchange-correlation functional.…”

Vacancy-mediated dopant diffusion activation enthalpies for germanium

“…33,34 DFT calculations underestimate the formation energies of defects in Si and Ge due to the lack of exact exchange in the functionals. 35,36 A way to overcome this problem is the application of an alternative functional, such as the B3YLP, as previously discussed by Uberuaga et al 35 In the present study, we will use the predicted values of Uberuaga et al 35 of 2.4 and 0.7 eV for the formation and migration enthalpies, respectively, of a V in Ge. Adding these values gives an activation enthalpy of self-diffusion via V of 3.1 eV.…”