Semiconductor thermochemistry in density functional calculations

Abstract

The local-density and generalized gradient approximations ͑LDA and GGA͒ to density functional theory ͑DFT͒ exhibit incomplete error cancellation when energy differences are taken between chemically dissimilar systems. This energy inconsistency is manifested, e.g., in the tendency to underestimate the heat ͑enthalpy͒ of formation of semiconducting and insulating compounds in LDA and, even more so, in GGA. Considering a set of 61 compounds that can be formed from 14 elements ͑cations: Cu, Mg, Ca, Zn, Cd, Al, Ga, and In; anions: N, P, As, O, S, and Se͒, optimized elemental reference energies are determined by least-squares error minimization of an overdetermined set of linear equations. These elemental energies are "optimally consistent" with the DFT energies of the semiconductor compounds and imply corrections of up to 1 eV compared to the respective LDA or GGA energies. While these "corrections" are not to be understood to yield the correct absolute total energies of the elements, they are proposed to give appropriate bounds for the chemical potentials for thermodynamic processes in semiconductors and insulators, such as, e.g., defect formation, surface reconstruction, or catalytic processes. The present model allows to evaluate thermodynamic processes using DFT energy differences taken only between systems that are expected to show good error cancellation.

Thermodynamic Routes to Novel Metastable Nitrogen-Rich Nitrides

“…DFT calculations of formation energies typically require correction schemes when one of the elemental end-members is a diatomic molecule at standard state, which is the case for nitrides. We benchmarked two correction schemes for computing nitride formation energies: the fitted elemental reference energies (FERE), 54,55 as used in the NREL Materials Database, 50 and a gas-fit correction scheme, 56 as used in the Materials Project database. 49 Both schemes aim to minimize formation energy errors using a linear least-squares fit on elemental reference energies, but in the FERE scheme, the fit is performed on all elemental-phase chemical potentials, whereas in the gas-fit scheme, only the N 2 gas chemical potential is fitted.…”

“…We found the discrepancy between schemes to originate primarily from their different treatments of nitride electronic structures, which can vary from metallic subnitrides to semiconducting nitrogen-rich nitrides. The FERE scheme was originally designed for semiconducting or insulating metal−nonmetal compounds 54,55 and uses GGA+U for transition metal cations. In metallic subnitrides, this approach can lead to unphysical positive formation energies that are inconsistent with experiment.…”

Inverse design approach to hole doping in ternary oxides: Enhancingp-type conductivity in cobalt oxide spinels

“…[24]. The Hall effect was measured at room temperature using a Van der Pauw method [25] and a variable magnetic field up to 15 Tesla with a 1.7 Hz alternating current source using lock-in techniques, and averaging four up-and-down magnetic field sweeps of both polarities. The data between 0 and 1 T have been removed as they represent purely instrumental noise.…”

Hydrogen-surfactant-assisted coherent growth of GaN on ZnO substrate

“…However, there exists an intrinsic difficulty to correctly estimate the formation energy of the possible secondary phase of Zn3N2 near the interfaces, which is positive, for both our calculations and previous works, due to the intrinsic problems of exchange correlation functional [85]. And the calculated formation energies of compounds, such as Ⅱ-Ⅵ or Ⅲ-Ⅴ, are always significantly different from experimental ones [86], which are important to our further discussions. Therefore, we applied and strictly followed the fitted elemental-phase reference energies (FERE) method [86][87][88] to achieve relatively accurate formation energies.…”

“…And the calculated formation energies of compounds, such as Ⅱ-Ⅵ or Ⅲ-Ⅴ, are always significantly different from experimental ones [86], which are important to our further discussions. Therefore, we applied and strictly followed the fitted elemental-phase reference energies (FERE) method [86][87][88] to achieve relatively accurate formation energies. In the FERE method, for GGA, totally 12 elements and 44 compounds were included; for HSE, totally 9 elements and 24 compounds were included.…”