it should have band -gap comparable with the solar energy of the solar energy spectrum (approximately 1.2 eV) and also have large extinction coefficient.
Based on our recent combined theoretical and experimental works, there are many factors that should be focused on before considering semiconductor "x" as light absorber in solar cell, including absorption cross section, HOMO & LUMO, size distribution, emitting states, ground states etc. (Ref: http://pubs.rsc.org/en/content/articlelanding/2013/cp/c3cp52858h)
Dear Saifful, you are absolutely right but the properties that are you talking about is the properties of the device not the particular semiconductor. If you want to use a semiconductor as an active layer in the device, band- gap, extinction coefficient are the important factors. If these properties are satisfied by the semiconductor, after that we are worrying about those properties that you are talking about.
There is a number of properties that can easily be derived from the process a solar cells works - efficient absorption, conversion of energy into separated charges, charge extraction. The answer needs to be based on this process understanding - then it is also clear WHAT the main properties are. So, start with high absorption coefficient in the sun light spectrum, match the bandgap(s) with the spectrum to minimize loss due to plain heating, have low defect concentration and high mobility to extract charges effectively.
As a starter for the process understanding, I suggest this: http://en.wikipedia.org/wiki/Theory_of_solar_cells
Best method to check an inorganic semiconductor for solar cell application is to make a metallurgical junction with another thin semiconductor or metal layer with different work function and then measure current voltage characteristic under illumination with visible light. For solar grade semiconductor some open circuit voltage will be obtained.
Basically you need a band gap between 1.0 and 1.5eV, decent absorption, good mobility (or carrier diffusivity, the two are related) and high minority carrier lifetime.
There's a tradeoff between absorption coefficient and the mobility-lifetime product: the latter determines how far excited carriers can travel before recombining; if this is high, a worse absorption coefficient can be tolerated as you can just make the cell thicker (as is done for silicon). Similarly if your absorptivity is high you can make the cell thinner and tolerate a worse mobility or lifetime.
For absorber layer the band gap should be very small so that it can absorb maximum light. At the same time material also have very high absorption coefficient so that even thin layer can be used.