# Attempting to calculate the mobility from SCLC measurement (space charge limited current)

I performed an SCLC measurement on a p-type material (hole transport layer) for a solar cell. Referring to the wikipedia page:https://en.wikipedia.org/wiki/Space_charge

The relationship between $$J$$ and $$V$$ should be $$J= \frac{9\epsilon\mu V^2}{8L^3}$$ (Mott Gurney law), so $$J$$ should be proportional to $$V^2$$. From plotting $$J$$ vs $$V$$ it should therefore be possible to obtain the hole mobility.

However, in all of my results I found that this quadratic dependence is not true.

Plotting a log-log plot tells me that $$J \propto V^{1.17}$$

A student in the research group claim that this is a result of the layer being produced for this measurement being too thin, just 100$$nm$$ but I'm not so sure why this should give a completely different J-V characteristic.

So my first question is, do you have any idea why this is not a quadratic dependence, and could the small thickness of the layer explain this?

Secondly, on wikipedia I found another equation explaining the "Low Voltage Regime". It explains that for low voltages, $$J = \frac{4\pi^2 k_b T \mu \epsilon V}{qL^3}$$. I could fit a line to the very beginning of my curve (low voltage) and perhaps calculate the mobility this way. What I'm not sure about is how low is low? Are my increments small enough to get a meaningful measurement?

Thank you for any help.