Nonradiative Multiphonon Model of Deep-Level Transient Spectroscopy: Beyond Henry-Lang Model

Abstract

Deep-level transient spectroscopy (DLTS) is a key experimental method for defect characterization, yet its analysis remains controversial, and the two widely used models developed by Henry and Lang are conflicting. We show that the Henry-Lang model is valid only under the Condon approximation, as well as high-temperature and strong electron-phonon coupling approximations, which cause incorrect temperature dependence of carrier emission and capture. Here we develop a rigorous nonradiative multiphonon (NMP) model, and demonstrate that the temperature dependence is governed predominantly by effective phonons with large phonon wavefunction overlap and high thermal occupation. The effective phonons are strongly correlated with lattice relaxation.The neglect of this correlation in existing DLTS models introduces substantial errors when they are used to fit DLTS-measured emission rates. Our comparison for 21 different defects in 12 semiconductors, including Si, SiC and Ga$_2$O$_3$, shows that the Henry-Lang model gives a completely different temperature dependence of carrier capture cross section from that obtained using the rigorous NMP model, with errors reaching up to six orders of magnitude at room temperature. Our study highlights the necessity of revisiting previous DLTS analysis studies using the rigorous NMP model.