Measured and calculated radiative lifetime and optical absorption of ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ quantum structures

We apply photoluminescence, photoluminescence excitation, and time-resolved optical spectroscopy for studying a set of ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}/\mathrm{G}\mathrm{a}\mathrm{N}$ periodic structures, which were characterized by high-resolution x-ray diffraction including x-ray mapping in reciprocal space. We found that the energy differences between the absorption edge and the photoluminescence peak (Stokes shift), and the photoluminescence decay time drastically increase with the ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{N}$ layer thickness. The decay time strongly increases with the sample temperature. We were able to quite accurately determine the radiative and nonradiative decay times of excitons in these structures by measuring the temperature dependence of the decay times, the integrated photoluminescence intensities, and the photoluminescence intensities immediately after the picosecond excitation pulse. The intrinsic radiative lifetimes, which are inversely proportional to the exciton oscillator strengths, were then calculated from the temperature dependence of the radiative lifetimes. These experimental findings are analyzed using an eight-band $\mathbf{k}\cdot \mathbf{P}$ model, which quantitatively explains both the Stokes shifts and the intrinsic radiative lifetimes. Their strong dependence on the quantum well width is due to a large (∼1 MV/cm) lattice-mismatch strain-induced piezoelectric field along the growth axis.