Charge transport in low mobility materials

The collection of photogenerated charge carriers in a solar cell prepared from those materials has either to be achieved 

For reasonable functioning of these low cost, low mobility semiconductor solar cells, a considerable amount of the photogenerated chemical potential epc — fv of the electron hole ensemble must be used for carrier transport. An acceptable charge collection may be achieved if the extraction times for electrons and/or holes are smaller than their recombination lifetimes, i.e., 

We introduce carrier mobilities /xe and /ih and multiply by the corresponding gradients of the quasi-Fermi levels to write the velocities in the form 

We then translate them into times for extraction across the distances t d to the n-mombraiie for the electrons and (1 — )d to the p-membrane for the holes. With (4.88), the conditions for the recombination lifetime are 

Finally, after introducing the Einstein relation iie hkT = eDe,h we find 

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