# Method for characterizing bulk recombination using photoinduced absorption

## TL;DR

This paper clarifies how reaction order and trap-assisted recombination influence photoinduced absorption measurements, enabling differentiation between trap distributions and recombination mechanisms through temperature, intensity, and frequency dependence analysis.

## Contribution

It introduces analytical and numerical methods to distinguish trap distributions and recombination types in photoinduced absorption data based on characteristic signal dependencies.

## Key findings

- Different trap distributions produce distinct temperature-dependent signal features.
- Recombination mechanisms can be identified by analyzing intensity and frequency dependencies.
- Characteristic exponents relate to trap energy distributions and are temperature independent for direct recombination.

## Abstract

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.