  Understanding energy transport in semiconductors is critical for design of
electronic and optoelectronic devices. Semiconductor material properties such
as charge carrier mobility or diffusion length are measured in bulk crystals
and determined using models that describe transport behavior in homogeneous
media, where structural boundary effects are minimal. However, most emerging
semiconductors exhibit microscale heterogeneity. Therefore, experimental
techniques with high spatial resolution paired with models that capture
anisotropy and domain boundary behavior are needed. We develop a diffusion
tensor-based framework to analyze experimental photoluminescence (PL) diffusion
maps accounting for material microstructure. Specifically, we quantify both
carrier transport and recombination in single crystal and polycrystalline lead
halide perovskites by globally fitting diffusion maps, with spatial, temporal,
and PL intensity data. We reveal a 29% difference in principal diffusion
coefficients and alignment between electronically coupled grains for CH3NH3PbI3
polycrystalline films. This framework allows for understanding and optimizing
anisotropic energy transport in heterogeneous materials.
