Obtaining the Charge Carrier Diffusion Length in Disordered Semiconductors from Photoconductivity Transients

Long diffusion lengths of photo-excited charge carriers are crucial for high power conversion efficiencies of photoelectrochemical and photovoltaic devices. In ordered materials, the diffusion length is usually determined from the product of charge carrier lifetime and mobility, which both can be measured by time-resolved photoconductance measurements.<br/>However, in disordered or defect-rich materials effects such as (multiple-)trapping, carrier localization and polaron formation can lead to time-varying mobilities and lifetimes that are not accounted for in the conventional analysis.<br/>Therefore, here, a generalized analysis is presented that is valid for time-dependent mobilities and time-dependent lifetimes. It determines the diffusion length directly from the integral of a photoconductivity transient, regardless of the nature of carrier relaxation.<br/>This approach is presented on amorphous silicon, a prototype of disordered materials, and BiVO₄, one of the most studied photoanode materials for solar water splitting. To this end, photoconductivity transients are measured from 100 fs to 100 µs by the combination of time-resolved terahertz (TRTS) and microwave spectroscopy (TRMC). Our generalized analysis allows monitoring the temporal evolution of the charge carrier displacement, which converges for both materials after ~100 ns to a diffusion length of a few tens of nanometers. For BiVO₄, the obtained diffusion length is significantly shorter than the typical thin film thickness, which rationalizes the photocurrent loss in the corresponding photoelectrochemical device.<br/>Our novel analysis significantly simplifies the determination of the diffusion length and will allow a robust comparison between material classes subject to different relaxation processes.