Modified band alignment method to obtain hybrid functional accuracy from standard DFT: Application to defects in highly mismatched III-V:Bi alloys

This paper provides an accurate theoretical defect energy database for pure and Bi-containing III-V (III-V:Bi) materials and investigates efficient methods for high-throughput defect calculations based on corrections of results obtained with local and semilocal functionals. Point defects as well as nearest-neighbor and second-nearest-neighbor pair defects were investigated in charge states ranging from $-5$ to 5. Ga-V:Bi systems (GaP:Bi, GaAs:Bi, and GaSb:Bi) were thoroughly investigated with significantly slower, higher fidelity hybrid Heyd-Scuseria-Ernzerhof (HSE) and significantly faster, lower fidelity local density approximation (LDA) calculations. In both approaches, spurious electrostatic interactions were corrected with the Freysoldt correction. The results were verified against available experimental results and used to assess the accuracy of a previous band alignment correction. Here, a modified band alignment method is proposed to better predict the HSE values from the LDA ones. The proposed method allows prediction of defect energies with values that approximate those from the HSE functional at the computational cost of LDA (about $20\times$ faster for the systems studied here). Tests of selected point defects in In-V:Bi materials resulted in corrected LDA values having a mean absolute error (MAE) $=0.175$ eV for defect levels versus HSE. The method was further verified on an external database of defects and impurities in $\mathrm{Cd}X$ ($X$=S, Se, Te) systems, yielding a MAE $=0.194$ eV. These tests demonstrate the correction to be sufficient for qualitative and semiquantitative predictions, and may suggest transferability to many semiconductor systems without significant loss in accuracy. Properties of the remaining In-V:Bi defects and all Al-V:Bi defects were predicted with the use of the modified band alignment method.

Figure 1

Point defect formation energies as a function of Fermi level for all considered III-V:Bi materials. Panels (d)–(i) (Ga-V:Bi and In-V:Bi) were calculated with the HSE functional and (a)–(c) (Al-V:Bi) were obtained with LDA corrected with the modified band alignment correction (MBA) and, therefore, are marked with an asterisk. (a)–(c) correspond to AlP:Bi, AlAs:Bi, and AlSb:Bi, (d)–(f) to GaP:Bi, GaAs:Bi, and GaSb:Bi, and (g)–(i) to InP:Bi, InAs:Bi, and InSb:Bi, respectively. Chemical potentials corresponding to intermediate growth conditions were used. Results for group V- and group III-rich conditions are available in Sec. IV C, Figs. S1– S3 and S7– S9. Here we assume the MBA is sufficient for quantitative comparison, therefore, this figure serves as a presentation of the results for point defects in all studied systems, and not for assessing the method, for which we direct the reader to Figs. 3 and 4.

Figure 2

Binding energies for pair defects in Ga-V:Bi compounds, calculated with the HSE functional. (a)–(c), (d)–(f), and (g)–(i) correspond to GaP:Bi, GaAs:Bi, and GaSb:Bi respectively. Each material has been separated into three columns for clarity, where the first column includes the nearest-neighbor-pair defects, the second contains second-nearest-neighbor-pair defects with Bi-related defects, and the third contains the remaining second-nearest-neighbor defects.

Figure 3

Accuracy comparison of different approaches with hybrid functional (HSE) results on Ga-V:Bi data set. First row: Baseline LDA versus HSE; second row: band alignment (BA) correction; third row: modified band alignment (MBA) correction. First column: Formation energies of stable defects (precision and recall pertain to whether a defect in a certain charge state is predicted to be stable); second column: charge-state transition levels (precision and recall pertain to whether a charge-transition is properly predicted inside the band gap); third column: binding energies (precision and recall pertain to whether a binding energy is properly predicted as positive or negative). Red, blue, and green points correspond to defects in GaP:Bi, GaAs:Bi, and GaSb:Bi, respectively.

Figure 4

Validation of the correction methods for In-V:Bi point defects and a test set of $\mathrm{Cd}X$ ($X$=S, Se, Te) defects and impurities [46], optimized on Ga-V:Bi data set. First row: Baseline LDA/GGA versus HSE; second row: band alignment (BA) correction; third row: modified band alignment (MBA) correction. First column: Formation energies of stable defects (precision and recall pertain to whether a defect in a certain charge state is predicted to be stable); second column: charge-state transition levels (precision and recall pertain to whether a charge-transition is properly predicted to be stable and inside the band gap). Red, blue, and green points correspond to defects in InP:Bi, InAs:Bi, and InSb:Bi (CdS, CdSe, CdTe), respectively. Grey and yellow are CdSSe and CdSeTe alloys.

Figure 5

Binding energies obtained with the modified band alignment method (MBA) for pair defects in Al-V:Bi compounds. (a)–(c), (d)–(f), and (g)–(i) correspond to AlP:Bi, AlAs:Bi, and AlSb:Bi, respectively. The asterisk indicates that the results were obtained with LDA, corrected with the modified band alignment correction (MBA).

Figure 6

Binding energies obtained with the modified band alignment method (MBA) for pair defects in In-V:Bi compounds. (a)–(c), (d)–(f), and (g)–(i) correspond to InP:Bi, InAs:Bi, and InSb:Bi, respectively. The asterisk indicates that the results were obtained with LDA, corrected with the modified band alignment correction (MBA).