Upon some calculation I arrive to the expression:(adsbygoogle = window.adsbygoogle || []).push({});

d^{2}DPn(x)/dx^{2}= DPn(x)/Lh^{2}

Where:

DPn(x) = Pn(x) + Pno - excess minority carriers (holes) concentration in the n-type part of the pn junction.

Now the roots to the characteristic equation are +/- 1/Lh where Lh is the length of the diffusion.

Therefore the solution looks like:

DPn(x) = Ae^{-1/Lh}+ Be^{1/Lh}

I know for a fact the solution isDPn(x) = DPn(0)e^{-x/Lh}

The initial conditions would be that:

@ x = 0 we have hole concentration DPn(0)

@ x = Lh we have DPn(Lh) = 0

But I have no idea how to arrive at the solution in bold. I'm missing something and I was thinking you could help.

Thank you.

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# Second degree DE for pn-junction carrier concentration

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