Linearly graded pn junctions

kn336a

Hi, my question is:

Given a linearly graded on-junction with the following doping conditions a=10^21

I have to calculate Emax, Vbi, W and the junction capacitance with Va=0.2V and Vr=-5V

This is for Silicon @ T=300k

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From what I understand, I have to use an iterative method but I don't think I'm getting the correct answer.

I'm using this equation Vbi=Vt*ln((a*Xo)/(ni))^2


Vt=0.0259
ni=1.5x10^10
a=10^21

where Xo= depletion region width

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Since i'm not given Vbi or Xo, I tried using an iterative method and Vbi and Xo converge at 20.202

I'm not quite sure what to do with this number or which value it pertains to. I would make the assumption that the potential barrier would be around 0.65-0.7V

Can anyone lead me to the right direction? Thanks.