solving 1D drift diffusion model for a semiconductor using FDTD. Can anyone rectify this error.

% Constants and parameters

q = 1.602e-19; % elementary charge

k = 1.38e-23; % Boltzmann constant

eps0 = 8.85e-12; % vacuum permittivity

epsr = 11.7; % relative permittivity of silicon

Na = 1e17; % doping concentration (p-type)

L = 1e-6; % length of the semiconductor

mu_e = 1000*1e-4; % electron mobility

mu_h = 1000*1e-4; % hole mobility

D_e = k*300*mu_e/q; % electron diffusion coefficient

D_h = k*300*mu_h/q; % hole diffusion coefficient

T = 300; % temperature

V = 0.1; % applied voltage

% Spatial and time parameters

nx = 100; % number of spatial grid points

dx = L/nx; % spatial step

dt = 1e-9; % time step

nt = 100; % number of time steps

% Initialize carrier densities and electric potential

n = zeros(nx, 1); % electron density

p = zeros(nx, 1); % hole density

phi = zeros(nx, 1); % electric potential

phi(1) = V; % boundary condition at x=0

% Simulation loop

for t = 1:nt

% Calculate electric field

E = -(phi(2:end) - phi(1:end-1))/dx;

% Calculate electron and hole densities

Jn = q*D_e*(n(3:end) - n(2:end-1))/dx - q*mu_e*E.*n(2:end-1);

Jp = q*D_h*(p(3:end) - p(2:end-1))/dx + q*mu_h*E.*p(2:end-1);

% Update carrier densities

n(2:end-1) = n(2:end-1) + dt*Na./(1+exp((phi(2:end-1)-V/2)/(k*T))) - dt*Jn;

p(2:end-1) = p(2:end-1) + dt*Na./(1+exp((V/2-phi(2:end-1))/(k*T))) - dt*Jp;

% Update electric potential

rho = q*(Na - n - p); % charge density

phi(2:end-1) = phi(2:end-1) + dt*1/(epsr*eps0)*rho(2:end-1);

end

Answer 1

[Star Strider]

In the ‘Jp’ and ‘Jn’ calculations, the relevant ‘n’ vectors are (98x1) while ‘E’ is(99x1). That appears to be the problem.

I leave its resolution to you.