Method for characterizing bulk recombination using photoinduced absorption

The influence of reaction order and trap-assisted recombination on continuous-wave photoinduced absorption measurements is clarified through analytical calculations and numerical simulations. The results reveal the characteristic influence of different trap distributions and enable distinguishing between shallow exponential and Gaussian distributions as well as systems dominated by direct recombination by analyzing the temperature dependence of the in-phase and quadrature signals. The identifying features are the intensity dependence of the in-phase at high intensity, $\textit{PA}_\text{I}\propto I^{\gamma_\text{HI}}$, and the frequency dependence of the quadrature at low frequency, $\textit{PA}_\text{Q}\propto \omega^{\gamma_\text{LF}}$. For direct recombination $\gamma_\text{HI}$ and $\gamma_\text{LF}$ are temperature independent, for an exponential distribution they depend on the characteristic energy $E_\text{ch}$ as $\gamma_\text{HI}=1/(1+E_\text{ch}/kT)$ and $\gamma_\text{LF}=kT/E_\text{ch}$ while a Gaussian distribution shows $\gamma_\text{HI}$ and $\gamma_\text{LF}$ as functions of $I$ and $\omega$, respectively.