Band gaps and built-in electric fields in InAlN/GaN short period superlattices: Comparison with (InAlGa)N quaternary alloys

The general trends in the behavior of the band gaps in short period superlattices (SLs) composed from InAlN and GaN layers and grown along the wurtzite $c$ axis have been analyzed for different alloy compositions and several thicknesses of quantum wells and barriers. The composition dependence of the gaps is compared to that of the quaternary alloys $\mathrm{I}{\mathrm{n}}_y\mathrm{A}{\mathrm{l}}_{1\ensuremath{-}x\ensuremath{-}y}\mathrm{G}{\mathrm{a}}_x\mathrm{N}$ with the same effective contents of In, Al, and Ga as the SLs. The differences in the gaps are explained mainly by the built-in electric fields in the SLs caused by spontaneous and piezoelectric polarizations. Other factors, such as internal strain caused by lattice mismatch between wells and barriers and wave function hybridization, are taken into account. A simplified approach to determine the built-in electric fields directly from the dielectric properties of the constituent materials has been applied and verified by comparison to ab initio calculations for selected SLs. The calculated band gaps are compared with existing experimental data.