Differential surface charging is often a serious drawback in application of plasma techniques to defining high aspect ratio structures, necessary for the manufacturing of modern microelectronic devices. It is well established that charges can accumulate on the exposed insulating surfaces of patterned structures during plasma exposure, due to the directionality differences between impinging ions and electrons. This, in turn, gives rise to electric fields which can alter the trajectory, flux, and kinetic energy of incident ions, often resulting in undesirable side effects in the plasma-assisted processes. Earlier theoretical studies have focused on describing the mean behavior of surface charge densities and potential distributions on patterned dielectric surfaces at the micronscale or larger. However, as device feature sizes shrink into the nanometer scale regime, the influence of an individual charge transferred to the surface will be larger, leading to an increase in the variability of potentials within the charging area. This leads to the question of whether a true steady-state-like behavior will be reached for high aspect ratio dielectric structures with small absolute dimension or will large oscillations in potential lead to essentially stochastic behavior. In this presentation, we will show our simulation results of plasma bombardment of high aspect ratio dielectric structures, which demonstrate stochastic charging behavior arising as absolute dimension decreases from 500 nm to 50 nm. We will also discuss how the stochastic changing influences charging damage and feature profile evolution during plasma etching and ashing.