Ga0.5In0.5P/GaAs/Ge Solar Cell
34% efficient under concentrated sunlight
Multiple layers of semiconductors with decreasing bandgaps capture large range of photon energies.
Lattice match prevents defects or dislocations where recombination can occur.

http://www.nrel.gov/ncpv/higheff.html
http://vmsstreamer1.fnal.gov/VMS_Site_02/Lectures/colloquium/Presentations/Friedman.pdf