Emergent formation of dynamic topographic patterns in electron beam induced etching

Spontaneous formation of geometric patterns is a fascinating, ubiquitous process that provides fundamental insights into the roles of symmetry breaking, anisotropy and nonlinear interactions in emergent phenomena. Here we report dynamic, highly ordered topographic patterns on the surface of diamond that span multiple length scales and have a symmetry controlled by the chemical species of a precursor gas used in electron beam induced etching (EBIE). This behavior reveals an underlying etch rate anisotropy and an electron energy transfer pathway that has been overlooked by existing EBIE theory. We present an etch rate kinetics model that fully explains our results and is universally applicable to EBIE. Our findings can be exploited for controlled wetting, optical structuring and other emerging applications that require nano and micro-scale surface texturing.