Parameter‐Free Calculation for the Optical Bandgap Energies of InGaAlN

The accurate prediction of bandgap energy E g is crucial for the future development of semiconductors. Ab initio simulation studies have been undertaken to unravel the intricacies of compound semiconductors. However, traditional density functional theory estimates E g to be mostly 30–50% smaller than experimental values. To reconcile these disparities, fitting parameters such as U have been employed, albeit at the expense of violating the virial theorem's essential conditions. In our pursuit of a more accurate approach, utilizing a computational method that adheres to virial's theorem without resorting to fitting parameters is proposed. Employing the self‐consistent Green‐function vertex (GW) approximation calculation, standard phenomenological results are built upon as an initial condition. This novel methodology successfully resolves the long‐standing issue surrounding E g of InN, a nitride semiconductor InGaAlN known for blue light‐emitting diodes. The numerical results from our calculations demonstrate a remarkable alignment with experimental values across the entire In x Ga 1− x N range, with an impressive accuracy of 0.1 eV. This innovative method holds promise for application to various semiconductors, serving as a potent tool for predicting new semiconductors with small E g . This calculation method is also applied to E g of In 1− x Al x N and Ga 1− x Al x N.