High current electron emission and injection in a gap with both vacuum and solid

A model to account for SCL current injection in a gap consists of both free space (vacuum) and solid dielectric is presented. The SCL electron current density J is solved numerically to obtain the voltage scaling of J~VGⁿ, and n is found to be between n=3/2 (vacuum gap) and n=2 (dielectric diode). The dependence of n is calculated as a function of dielectric constant, electron mobility, and the relative length scale between the free space and dielectric solid. The model has been used to explain a recent STM experiment.