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We present a novel experimental protocol using Cathodoluminescencemeasurements as a function of the electron incident energy to study bothexciton diffusion in a directional way and surface exciton recombination. Ourapproach overcomes the challenges of anisotropic diffusion and the limitedapplicability of existing methods to the bulk counterparts of 2D materials. Theprotocol is then applied at room and at cryogenic temperatures to four bulkhexagonal boron nitride crystals grown by different synthesis routes. Theexciton diffusivity depends on the sample quality but not on the temperature,indicating it is limited by defect scattering even in the best qualitycrystals. The lower limit for the diffusivity by phonon scattering is 0.2cm$^{2}$.s$^{-1}$. Diffusion lengths were as much as 570 nm. Finally, thesurface recombination velocity exceeds 10$^{5}$ cm$^{2}$.s$^{-1}$, at a levelsimilar to silicon or diamond. This result reveals that surface recombinationcould strongly limit light-emitting devices based on 2D materials.

Surface recombination and out of plane diffusivity of free excitons in hexagonal boron nitride