Optical Determination of the Band Gap and Band Tail of Epitaxial Ag$_2$ZnSnSe$_4$ at Low Temperature

We report on the precise determination of both the band gap E$_text{g}$, and the characteristic energy $U$ of the band tail of localized defect states, for monocrystalline Ag$_2$ZnSnSe$_4$. Both photoluminescence excitation and time-resolved photoluminescence studies lead to E$_text{g} = 1223pm3$ meV, and $U = 20pm3$ meV, at 6 K. The interest of the methodology developed here is to account quantitatively for the time-resolved photoluminescence and photoluminescence excitation spectra by only considering standard textbook density of states, and state filling effects. Such an approach is different from the one most often used to evaluate the energy extent of the localized states, namely by measuring the energy shift between the photoluminescence emission and the excitation one -- the so-called Stokes shift. The advantage of the present method is that no arbitrary choice of the low power excitation has to be done to select the photoluminescence emission spectrum and its peak energy.