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

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