Increasing the efficiency of photovoltaic power cells Given that solar cells use one or more semiconductor materials to convert light to electricity, and that the efficiency of that conversion is dependent on the material and the wavelength of the light, why can't a more optimal solar cell be designed like this?


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*Choose the cheapest semiconductor material possible.

*For all incoming light, split the wavelengths apart using a prism.

*Pass the light with a wavelength range that converts to electricity most efficiently (given the material chosen) directly to the semiconductor junctions.

*"Convert" all the remaining light to a wavelength that is more appropriate before passing it to the junctions.


I have no idea how to "Convert" light, but it seems like it might be possible if the photons were passed through a particular medium first in which the speed of light is different.  More specifically then, is there a common way to convert light with a small wavelength to a higher wavelength?  If so, that seems like a reasonable design.
 A: You raise 4 very good points. 
Without exploiting temperature gradients or fission/fusion of photogenerated charge carriers, spectral splitting and spectral modification are the only routes to very high efficiency solar cells.
Tailoring the cell to the spectrum
Spectral splitting can be achieved in two ways:


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*Selective reflectors (which split light like a prism) that bounce photons towards a matched solar cell,

*Multiple junction solar cells. 
Both approaches tailor the design of the solar cell to solar spectrum.
The latter is the most common approach and in essence you are using the spatial arrangement and the band gap property (which is different for each cell or "junction") of each material to split the spectrum across multiple cells.
The former approach is also currently being explored but require very optically efficient selective reflectors and are inherently more bulky and (probably) expensive.
Multijunction solar cells are the only real near term approach to very high efficiencies. The design of real cells is constrained because they can only be grown with materials that share the same lattice constant. There are other "mechanical stack" approaches which allows materials of different lattice constants to be stacked but this introduces many technological challenges.
In principle these approaches can achieve an 86% efficient device (with an infinite number of junctions or spectral slices). One reason why you don't see cells this efficient is because of the effect of diminishing returns. For example, you can jump from 30% to 55% efficient device when going from one junction to three. However, to get from 55% to 86% infinitely many more junctions are needed! Moreover, every time a new junction is added it contributes less to the overall efficiency enhancement. Furthermore, the technological difficult increases much faster as more and more junctions are added. At some point a limit will be reached beyond which there is little point in adding more layers.
Tailoring the spectrum to the solar cell
Your #4 is an example of the inverse, where the the spectrum is modified to better match the solar cell. These approaches are usually called photon up-conversion and down-conversion.
This can be achieved by utilising a three level system. Let's recap. Normal solar cell, and semiconductor in general, are two level systems meaning that there is a single dominant optical transition between the lower and upper level. However, with a three level system it's possible to use the additional optical transitions to change the energy of the absorbed photons.
In up-conversion one low energy photon causes a transition from energy level 1 (the lowest energy level) to level 2. Then a second low energy photon can cause a transition from level 2 to level 3 (the upper most level). Finally, the electron that has been promoted to level 3 can fall directly to level 1 in a single step. The two low energy photons have been converted to one high energy photon.
In down-conversion one high energy photon promotes an electron from 1 to 3, and by falling to energy level 2 and then 1, two photons can be emitted. Thus one high energy photon in and two low energy photons out.
Of course the next step would be to use a solar cell to collect the converted photons. The up and down converters themselves don't generate power.
Other approaches
There are other approaches to reaching higher efficiency. In specially engineered materials high energy photons can generate multiple electron-hole pairs which provides more current per photon than normal solar cells.
Then there are the hot-carrier approaches. If a material and maintain a thermal gradient then this provides an additional thermodynamic potential allowing higher efficiencies to be achieved.
You can even use hot-carrier materials as a spectral converters! I've worked on this approach over the last few years.
