Hi Juan,
Let me start by wishing you a Happy NewYear.
I’m thrilled to implement a fast simulation of the internal electric field of the device to improve its speed.A pn junction with a one-dimensional finite depletion region has a depletion width that can be directly solved by charge neutralization conditions without involving the diffusion equation.This suggests that there’s a way to directly solve the potential equation via similar charge neutralization conditions for 2D/3D devices.Based on this, in the present solution, is it the case that solving the diffusion equation is time consuming, and if so, is it possible to realize a fast simulation of the potential and electric field inside the device without solving the diffusion equation.
Kind regards
Hi @senzhao
Happy New Year! The normal simulation procedure is to do PotentialOnly solution, which is based on solving only for the electric field with the Poisson equation and assuming a flat fermi level. This is then used as the initial guess for the full drift diffusion equation solution. Would using this initial guess solution work for your purposes?
{\nabla^2 \psi} + q \left(p -n + N_{D}^+\right) = 0
where
n = n_i \exp\left(\frac{\psi}{V_T}\right)\\
p = n_i \exp\left(\frac{-\psi}{V_T}\right)\\
additionally the following is enforced at ohmic contacts:
p - n + N_D^+ =0
I apologize for any sign mistakes in the above equations.