1D Semiconductor Physics Equations
Equations are here (4):
This is called a drift-diffusion model and can model any semiconductor. For example pn-junctions:
or thin films of silicon, very simplified model is here:
The last two equations (and read the assumptions above that had to be made). The 3 nonlinear PDEs is a way more general and precise model, that also gives the charges at the boundaries etc.
For the 1D pn-junction, the equations are here:
it's a set of 6 nonlinear first-order ODEs. The boundary conditions are not exactly clear to me yet, but here is what I should get:
so I tried to solve it using the Euler method (for ODEs), see the attached python script. But unfortunately, p(x) explodes, but it should go to zero, as x->320nm. So either the equations are wrong, or I am setting the model constants wrong.
The constants (in the code) are:
Constants (SI units)
q: 1.6022e-19 k_b: 1.3806503e-23 eps_0: 8.854187817e-12 T: 298.0
eps_r: 12.93 mu_p: 0.045 mu_n: 0.14 D_p: 0.00115556862583 D_n: 0.00359510239146 N_A: 5e+23 N_D: 2e+24