Determination of absorption coefficients and Urbach tail depth of ZnO below the bandgap with two-photon photoluminescence

Abstract

In this article, we demonstrate a novel approach to determine the absorption coefficient of ZnO below the bandgap via measuring the self-absorption (SA) effect on the two-photon luminescence (TPL) spectrum of the ZnO bulk crystal rod at cryogenic temperature. Under a geometric configuration of side-excitation and front-detection, the intensities of several major spectral components of TPL spectra of ZnO can be decisively tuned by precisely varying the transmitting distance of luminescence signal, so that the absorption coefficients at different wavelengths can be determined on the basis of Beer-Lambert law. Furthermore, the peak position of donor bound exciton luminescence exhibits a unique redshift tendency with increasing the transmitting distance. Starting from the product of Lorentzian lineshape function and exponential absorption edge of Urbach tail, an analytical formula is derived to quantitatively interpret the experimental redshift characteristic with the transmitting distance. The energy depth of Urbach tail of the studied ZnO crystal is deduced to be ∼13.3 meV. In principle, this new approach can be used to determine absorption coefficient of any luminescent solids as long as the SA effect happens.