The ability of energy carriers to move within and between atoms and molecules underlies virtually all biochemical and material function. 1 Understanding and controlling energy flow, however, requires observing it on ultrasmall and ultrafast spatiotemporal scales, where energetic and structural roadblocks dictate the fate of energy carriers. 2,3 We therefore developed a universal, noninvasive optical scheme that leverages non-resonant interferometric scattering 4,5 to track tiny changes in material polarizability created by energy carriers. Our approach enables mapping energy transport trajectories in four dimensions of spacetime with few-nanometer precision and directly correlating them to material morphology. We visualize exciton, charge, and heat transport in polyacene, silicon and perovskite semiconductors and elucidate how disorder affects energy flow. As one example, we show that grain boundaries in polycrystalline metal halide perovskites possess lateral-and depth-dependent resistivities that lead to highly anisotropic 3D transport that can help to bias carrier motion toward charge extraction layers. We furthermore reveal new strategies to interpret energy transport in disordered environments that will direct the design of defect-tolerant materials for the semiconductor industry of tomorrow.Energy flow is a ubiquitous phenomenon, central to the function of all biological, chemical and material systems. Elucidating how distinct macroscopic system functions emerge from different structural arrangements of atoms and molecules is a longstanding goal of scientific research, and one that necessarily relies on understanding how energy is transduced and transported between the system's building blocks 1 . Materials science, for example, is undergoing a revolution with a recent burst of new high-performing semiconductors made from a vast diversity of molecular building blocks that can be readily tuned for specific functions 6-8 . Nevertheless, a fundamental understanding of why some semiconductors perform better than others remains elusive 9 , inhibiting the rational design of future materials. The difficulty in gaining such predictive power is compounded by often-encountered nanoscale spatio-energetic disorder, manifested in defects, impurities, and grain boundaries (GBs), that give rise to complex and spatiotemporally heterogeneous energy transport behavior. Elucidating how the microscopic details of a material relate to its emergent optoelectronic function will therefore require the ability to individually, systematically, and easily correlate nanoscale structure to energy flow across a wide range of systems.Supplementary information for: Imaging material functionality through 3D nanoscale tracking of energy flow

Although sulfide perovskites usually require high-temperature syntheses, we demonstrate that organosulfides can be used in the milder syntheses of halide perovskites. The zwitterionic organosulfide, cysteamine (CYS; +NH3(CH2)2S–), serves as both the X– site and A+ site in the ABX3 halide perovskites, yielding the first examples of 3D organosulfide-halide perovskites: (CYS)PbX2 (X– = Cl– or Br–). Notably, the band structures of (CYS)PbX2 capture the direct bandgaps and dispersive bands of APbX3 perovskites. The sulfur orbitals compose the top of the valence band in (CYS)PbX2, affording unusually small direct bandgaps of 2.31 and 2.16 eV for X– = Cl– and Br–, respectively, falling in the ideal range for the top absorber in a perovskite-based tandem solar cell. Measurements of the carrier dynamics in (CYS)PbCl2 suggest carrier trapping due to defects or lattice distortions. The highly desirable bandgaps, band dispersion, and improved stability of the organosulfide perovskites demonstrated here motivate the continued expansion and exploration of this new family of materials, particularly with respect to extracting photocurrent. Our strategy of combining the A+ and X– sites with zwitterions may offer more members in this family of mixed-anion 3D hybrid perovskites.

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