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Modeling Semiconductors using Poisson's Equation & PDE Equation Toolbox

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Molly McDonough
Molly McDonough 2022-3-9
回答： Torsten 2022-3-9
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.

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Torsten
Torsten 2022-3-9
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.

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