Multi-phonon-assisted absorption and emission in semiconductors and its potential for laser refrigeration

Laser cooling of semiconductors has been an elusive goal for many years, and while attempts to cool the narrow gap semiconductors such as GaAs are yet to succeed, recently, net cooling has been attained in a wider gap CdS. This raises the question of whether wider gap semiconductors with higher phonon energies and stronger electron-phonon coupling are better suitable for laser cooling. In this work we develop a straightforward theory of phonon-assisted absorption and photoluminescence of semiconductors that involves more than one phonon and use to examine wide gap materials, such as GaN and CdS and compare them with GaAs. The results indicate that while strong electron-phonon coupling in both GaN and CdS definitely improves the prospects of laser cooling, large phonon energy in GaN may be a limitation, which makes CdS a better prospect for laser cooling.