I have read one journal where it states that with the thickness of the i-layer (0.5, 0.8,1, 2, 2.5 microns), the current density initially increases up to 1 micron and gets saturated. What is the reason for saturation?
The i-layer thickness becomes larger than the drift length of carriers. Basically, even though you're absorbing more photons, the electron-hole pairs created in the middle of the absorber all recombine before they can reach the p- or n-layers, and only the carriers generated near the boundaries of the i-layer are collected.
Also, carriers in p-i-n cells are collected by drift in the inbuilt field, which is Vbi/d, where d is the thickness, so the drift length itself decreases as the i-layer becomes thicker. All the theory is explained in Löper 2013 APL and the references therein.
It's going to depend on what material you're talking about, but the saturation is most likely due to >95% of the incident photon flux being absorbed in the first few absorption lengths. Eventually adding more i-region gives diminishing returns in current increase because it doesn't lead to much increase in photon absorption.
Also, to add to Manuel Schnabel's answer, the carrier drift length depends on the drift velocity at the built-in electric field strength and on the carrier lifetime. Both of these are functions of the material's properties and quality. For high quality materials, the drift length is tens of microns. For amorphous Si, I wouldn't be surprised if it wasn't much shorter, and thus might be the limiting factor.
If you want to do some further reading on the subject, in addition to Manuel's suggestion, you might want to have a look at an older paper that discusses bias voltage-dependent photocurrents and is quite "didactic" (I think :-): R .S . CRANDALL . Modeling of thin film solar cells: Uniform field approximation. J. Appl. Phys. 54(12) 7176-7186 (1983).
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