  Energy carrier transport and recombination in emerging semiconductors can be
directly monitored with optical microscopy, leading to the measurement of the
diffusion coefficient (D), a critical property for design of efficient
optoelectronic devices. D is often determined by fitting a time-resolved
expanding carrier profile after optical excitation using a Mean Squared
Displacement (MSD) Model. Although this approach has gained widespread
adoption, its utilization can significantly overestimate D due to the
non-linear recombination processes that artificially broaden the carrier
distribution profile. Here, we simulate diffusive processes in both excitonic
and free carrier semiconductors and present revised MSD Models that take into
account second-order (i.e. bimolecular) and third-order (i.e. Auger) processes
to accurately recover D for various types of materials. For perovskite thin
films, utilization of these models can reduce fitting error by orders of
magnitude, especially for commonly deployed excitation conditions where carrier
densities are > 5x10$^1$$^6$ cm$^-$$^3$. In addition, we show that
commonly-deployed MSD Models are not well-suited for the study of films with
microstructure, especially when boundary behavior is unknown and feature sizes
are comparable to the diffusion length. Finally, we find that photon recycling
only impacts energy carrier profiles on ultrashort time scales or for materials
with fast radiative decay times. We present clear strategies to investigate
energy transport in disordered materials for more effective design and
optimization of electronic and optoelectronic devices.
