Question about simple PN junction using DEVICE

device
debyetailing

#1

Hello, I have a question about the electric field profile simulation using DEVICE. It’s a simple p+/n- junction with P+ layer doping of 1e18 and N- layer doping of 1e15. I used constant doping for both. But the simulation result shows a spike as below:

The electric field profile I expect should be a simple triangle, but why there are two “slopes” in the N layer? Is it because N layer is not exactly constant doping? Thanks.


#2

Hi @mengx1. The electric field in the depletion region can be calculated by solving Poisson’s equation.

In text books we neglect the contribution from the charge carriers n and p and only consider the charge in the depletion region to be due to the constant charges from the donor and acceptor atoms. Due to the constant nature of the fixed charges the electric field will be a linear function of x.

However, when you consider the n and p values in this equation, the solution is not so simple anymore and the electric field does not vary linearly with x. Specially near the boundary between the n and p region you cannot neglect the contribution from the carriers (look at the plot from DEVICE for a simple pn junction).

When DEVICE solves for the electric field it solves the full Poisson’s equation and this is why the electric field profile is not a pure straight line.


#3

Dear aalam,

Many thanks for your reply. Now I understood why I got this spike. As you said, it is down to the “depletion approximation” the text book uses, which simplify the full Poisson’s equation. And I just read a paper which is saying the “tailing effect” that electrons or holes have to penetrate into depletion region is the so called Debye tailing. And this is exactly what your figure above shows. A big thanks to you!

Regards
Xiao