Modeling Semiconductors using Poisson's Equation & PDE Equation Toolbox

I am looking for suggestions on the best way to model the following equation using MATLAB, I am not sure if I should be using the PDE Toolbox or other methods. It is a relatively simple 1D problem, and I can do it on paper. But I am struggling with implementing it in MATLAB.

I am solving for E (electric field). q, episoln_s, N_D(x), n(x), N_A(x), and p(x) are known.

Answer 1

[Torsten]

If you have boundary conditions on both ends, use bvp4c.

Else use one of the ODE solvers (e.g. ode45).

Set

y(1) = psi_i, y(2) = psi_i_dot 

and solve

dy(1)/dx = y(2)
dy(2)/dx = -rho(x)/eps*(...)

with appropriate boundary conditions.