Wide band gap semiconductors exhibit a low electron affinity and may prove suitable for cold cathode applications. We introduce a simple closed-form analytic approximation for the stability of electrons in the electron accumulation layer of planar Low Electron Affinity (LEA) semiconducting cathodes. This analysis extends our previous results, which used Runge-Kutta numerical integration of the linearized equations of motion for the electric potential and quasi Fermi level. The model shows conditions in which the electrons in the accumulation layer form a two dimensional array of regions of higher and lower electron density. This instability could lead to field enhancement without surface roughness and could account for observed electron emission at low applied fields.