Optoelectronic Device Simulation Homework 2
Homework 2 Due: 4/29
(discussion in 4/29)
Coding of homework, code needs to be returned with the result. Submit your homework
electronically. No paper returned is accepted! (You can use any language including
Matlab, c, Fortran, python, … etc.). Late returned can only get maximum score 86 (A).
1. In the class and previous homework, you have finished the non-linear Poisson solver. In
the solver, you solve
−
𝐸𝑓𝑛 − 𝐸𝑐
1 𝑑 2 𝐸𝑐 𝑞
= (𝑁𝑐 exp (
) − 𝑁𝐷 )
2
𝑞 𝑑𝑥
𝜖
𝑘𝐵 𝑇
But the boundary condition was not set. We will continue the work
(1) Setup the boundary condition of nonlinear Poisson solver. If we define the bias on the left side is V1
and right hand side is V2. Then the boundary condition on the left and right hand side at –qV1 and
– qV2 . Each contact has a barrier of ϕ1 and ϕ2 . If we have want to include this into the code. Ec0
and EcN+1 = −qV1 + 𝜙1 and −qV2 +ϕ2 . Nc=1.0 × 1018 𝑐𝑚−3, T=300K
Please plot the result if
(a) V1 = 0 𝑉2 = 0, 𝜙1 = 1.5𝑒𝑉, 𝜙2 = 0𝑒𝑉. And the doping through the hole region (200nm) is
ND = 5e17 cm−3 .
(b) V1 = 0 𝑉2 = 0, 𝜙1 = 1.0𝑒𝑉, 𝜙2 = 0.5𝑒𝑉. And the doping through the hole region (200nm) is
ND = 5e17 cm−3 .
2. Two heterojunctions: If we have two materials with different bandgap Eg1 and Eg2. The electron
affinities are 𝜒1 and 𝜒2 . Please write the modified non linear Poisson solver to address this problem.
The testing would be:
V1 = 0 𝑉2 = 0, 𝜙1 = 1.5𝑒𝑉, 𝜙2 = 0𝑒𝑉. Eg1=3.0eV and Eg2=2.0eV. 𝜒1 and 𝜒2 are 3.5eV and 4.0eV.
And the doping through the hole region (200nm) is ND = 1e17 cm−3.
3. The previous case (a) is like a typical Schottky diode. But since we didn’t solve drift-diffusion
equation, we cannot model this Schottky diode. So we need to solve drift-diffusion equation. There
were two options to solve drift-diffusion equations. If we want to use Slotboom variable, we can solve
the problem by
dJn
d
−𝐸𝑐 𝑑
= (μNc 𝑘𝐵 𝑇 exp (
) (Φ))
dx dx
𝑘𝐵 𝑇 𝑑𝑥
We assume the boundary condition, where Efn(0) = −qV1 and Efn(N + 1) = −qV2 . Please finish the
coding of above equations.
For the P1 (a) condition, If V2 = 0, V1 = −5𝑉 to 5V, step V < 0.2V, Please plot the J versus V. Please
check if this is similar to Schottky diode equations. μ = 200cm2 /𝑉𝑠.
Please also try the condition P1(b) if V1 also from 𝐕𝟏 = −𝟓𝑽 to 5V.