Table 3 Energy difference \({E}_{g}=({\Gamma }_{8}^{\mathrm{v}}-{\Gamma }_{1}^{\mathrm{c}})\) obtained using FullBand simulator based on the proposed model compared with those reported earlier, with those computed from previously reported various density functional theory (DFT) techniques and with experimental results.

Material	Previously reported values of E_g	E^LDA	E^LDA-1/2	DFT^PBE	DFT^HSE	Experiments	E^{This work}
AlN	6.54⁷, 6.23¹⁰	4.50^5,7	6.06⁵	4.13⁷, 4.02²⁰	6.42⁷, 6.29²⁰	6.23⁵, 6.026¹⁷, 6.1–6.2^7,20	6.20
GaN	3.5⁷, 3.507¹⁰	2.02⁵, 2.11⁷	3.52⁵	1.69^7,20	3.55⁷, 3.55²⁰	3.507⁵, 3.35²², 3.51²⁰	3.47
InN	0.7–1.0^7,8, 0.7–1.9¹⁰	− 0.03⁵, − 0.24⁷	0.95⁵	− 0.42^7,20	0.86⁷, 0.86²⁰	0.7–1.9⁵, 0.6–0.7²⁰	0.7
Al_0.2Ga_0.8N	3.99*	2.353⁵	3.951⁵	4.570¹²	4.569¹²	3.962²⁴	3.94
In_0.2Ga_0.8N	2.72–2.78*	1.52⁵	2.76⁵	2.272⁵	1.925¹²	2.625²³	2.66
In_0.2Al_0.8N	4.7–4.76*	3.431⁵	4.409⁵	3.445¹²	2.976¹²	4.515²⁵	4.71

Here suffix represents the reference numbers.
LDA local density approximation, LDA-1/2 approximately includes the self-energy of excitations in semiconductors, PBE Perdew–Burke–Ernzerhof (PBE) exchange energy theory, HSE Heyd–Scuseria–Ernzerhof exchange–correlation functional uses an error function screened Coulomb potential to calculate the exchange portion of the energy.
*calculated from modified Vegard’s law^11,12 \({\mathrm{E}}_{\mathrm{ g}}\left(\mathrm{x}\right)=\mathrm{x}\cdot {\mathrm{E}}_{\mathrm{g}}^{\mathrm{A}}+\left(1-\mathrm{x}\right)\cdot {\mathrm{E}}_{\mathrm{g}}^{\mathrm{B}}-\mathrm{b}.\mathrm{x}.(1-\mathrm{x})\) where A and B represent band gap values for binary nitride alloys and b is bowing parameter¹².

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