See these lecture slides (42 pages) Light Absorption and Thermalization:
http://oasis.mechse.illinois.edu/me432/ME432_L12_Sept21.pdf
Page 15 Thermal Efficiency vs Band Gap
For small band
gaps, efficiency is
limited by
thermalization
losses
For large band
gaps, efficiency is
limited by losses
due to non-
absorption of the
solar spectrum
The tradeoff between thermalization and non-absorption losses results in the optimal band gap of a semiconductor of approximately 1.2 eV, and a maximum theoretical efficiency of close to 30%.
Page 36:
Light absorption in a direct semiconductor requires only photons
Light absorption in an indirect semiconductor requires a photon and a phonon, and is statistically less likely to occur.
Page 38:
Solar cells made from indirect semiconductors need to be thicker
because we need to provide more opportunities for the transition to take
place.
Page 39:
Absorption in indirect semiconductors is temperature-dependent, because phonons are needed and phonon population depends on temperature.
The direct materials may seem to have an advantage, however, the economics and design tradeoff in a given application are not discussed in the reference.