How absorption coefficient determines which material is used to make solar cells? Does the knowledge of the material absorption coefficients aids engineers in determining which material to use in their solar cell designs? If yes, how?
 A: The solar spectrum hitting the earth corresponds to black body radiation (apart from some absorption lines due to gasses in our atmosphere and inherent to the sun). In principle, one wants to harvest an as large as possible fraction of this spectrum.
Solar cells can be optimized by increasing the absorption at a certain wavelength (which mostly depends on the bandgap of the semiconductor material used). On the other hand, they can also be optimized by joining several layers, which convert different wavelengths into an electrical voltage. I admit that multi-junction solar cells are more at a research stage at the moment, but they present an interesting approach.
Another problem, which is somewhat related is the incoupling efficiency. A significant part of the incident light is reflected and never makes it into the active material. Therefore one has to engineer anti-reflection layers, which also need to be optimized to be either broadband or work for certain wavelength ranges. In the simplest case this can be done by roughening the surface of silicon chips by etching them with KOH.
A: Ideally, the absorption coefficient $\alpha$ of a material should be large enough that all of the incident photons are absorbed and converted into electrons. According to the Beer-Lambert Law, the intensity of the incident light beam as a function of distance is $I(z)=I_0 e^{-\alpha z}$. So in a good cell of thickness $h$, you should have $e^{-\alpha h} \approx 0$. This is especially important in thin-film cells, in which the cell may not be thick enough to absorb all of the incident light. You can imagine using this equation to figure out how thick a very simplistic solar cell, consisting of a single layer of amorphous Silicon, should be. These days, the best solar cells use several layers of different materials, with each layer optimized to absorb a specific portion of the spectrum. 
A: Absorption coefficient determines the the thickness of the material of the solar cells.
For example organic solar cells has very high absorption coefficient and that' s why the thickness of the organic solar cell is very less.
In opposite to it Si solar cell has very low absorption coefficient that's why it' s thickness is kept very high.
More importantly while designing a solar cell the absorption coefficient plays an important role in determining the type of material to be used.The material which has a very high absorption coefficient will absorb effectively or completely a range of incoming spectrum so more electron hole pairs are generated and more electrical energy is produced.
