Theoretical analysis of incomplete ionization on the electrical behavior of radial <i>p-n</i> junction structures

In this work, we studied the electrical behavior of radial p-n junctions based on submicron Silicon (Si) and Gallium Arsenide (GaAs) structures, with a focus on the implications of incomplete ionization of atoms below 800 K. By solving the Poisson equation in a cylindrical coordinate system, we derived solutions for radial structures with a core radius of R = 0.5 μm. An analytical solution was obtained, providing the probability of ionization P(T) of dopant atoms in the range 0–800 K, as well as the variation of space charge density ρ(T), with temperature.