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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

http://my.ece.ucsb.edu/mhwong/documents/thesis_app2.pdf

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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