Cube-root broadening of surface-charge packets

Abstract

The width of a surface-charge packet in the proximity of a conducting sheet increases asymptotically only as the cube root of the time due to space-charge repulsion. By contrast, thermal diffusion broadens as the square root of the time, and is otherwise negligible here. The cube-root behavior is invariant over a wide range of transverse and normal electric fields, and may have significant implications for the minimum spatial variation of charge density achievable in devices.