Dependence of Space-Charge-Limited Current Density on Electrode Thickness for A Planar Diode

Space-charge-limited current density (SCLCD) is the maximum steady-state current that can flow in a diode [1] . Understanding SCLCD is critical for many applications including high-power vacuum devices, thermionic converters, photovoltaic devices, organic field-effect transistors, and inertial confinement fusion [1] . An exact solution for SCLCD in a one-dimensional planar diode was derived by Child and Langmuir over a century ago [1] . Since then, many attempts were made to obtain analytical equations for SCLCD in two-and three-dimensional diodes [2] . We have recently used variational calculus [3] and vacuum capacitance to derive analytical equations for SCLCD in multi-dimensional planar diodes with finite electrodes [4] .