Mobility usually depends on the microstructure and grain size (if carrier scattering in grain boundaries is important). The mobility in mono-crystals could be much bigger than in poly-crystals with nanometric size grains. Annealing for re-crystallization could increase grain-size and hence improve mobility.
For solar cells application choice of material depends on the band gap which should be around 1.5 eV and absorption coefficient high, lifetime of carriers high ,I.e., defect density low and molity high. Mobility depends upon the material used. If you select material of high mobility, you may not be satisfying other conditions. There is slight increase in mobility with decrease in temperature but for solar cell applications it is not viable as one uses solar cells at room temperature.Mobility in amorphous silicon is much smaller than crystalline silicon but amorphous silicon solar cells are being used for commercial cells because of low pay back period. I suggest to make solar cells of low payback period without worrying mobility.
First you should ask: is the mobility that I measure comparable to the literature values for this material?
If the answer is yes then there is not a lot that you can do without changing materials. Strain can help increase the mobility in some cases; if the films are so thin that their thickness is comparable to the mean free path of the carriers, then increasing their thickness can improve the mobility dramatically.
If the mobility that you measure is considerably lower than what is reported in the literature then the problem is your films. First I'd consider impurities, non-stoichiometries and defects. If this is a single crystalline, epitaxial film, then you should estimate the degree of crystallinity (XRD: bragg peaks and rocking curves for start). If this is a poly-crystalline films then grain boundaries can have a considerable effect on the mobility as well.
If you could specify the material, substrate, deposition method, mobility values and how they were measured - it would be easier to give you a more detailed response.
Basically, scattering centres need to be reduced to increase the carrier mobility. Decreasing impurity content in the thin film will improve mobility. Larger grain size will also help. Surface roughness may be another factor.