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I am trying to understand Space-Charge-Limited-Current (SCLC) and the resulting Mott-Gurney Law.

My main problem is conceptual; I don't get why SCLC doesn't produce Ohm's law (j $\propto$ V).

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Semiconductors are complicated, nonlinear materials so there's no reason to assume a particular simple relationship between any two inequivalent quantities. They're not just conductors with resistance - the non-Ohmic relationship between current and voltage is really what they're famous for and good for. I think that a better approach to similar questions is to look at a derivation of the Mott-Gurney law (yes, Mott was my uncle) such as

and ask about particular assumptions of the derivation rather than directly about the final result. One can't see what the result is or is not without actually deriving it.

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