Analysis of potential function in cylindrical nanowires

This paper presents extracted closed-form expressions for the potential function in cylindrical nanowires in presence of extrinsic charge distribution term, arising from doping. These expressions are derived from the solution to Poisson-Boltzmann ordinary differential equation. This ODE has been solved in terms of intrinsic carrier concentration, temperature and the distance from the central axis of the nanowire in each point inside the wire. Considering extrinsic charge distribution is an innovation in this paper as there assumed to be no external charge in the potential function analysis in previous works. Finally, some simulations have been used to verify the closed-form expressions. These simulations illustrate the potential function of the silicon-based cylindrical nanowire in terms of the distance from its axes and the environmental temperature.