  The laser cooling of vibrational states of solids has been achieved through
photoluminescence in rare-earth elements, optical forces in optomechanics, and
the Brillouin scattering light-sound interaction. The net cooling of solids
through spontaneous Raman scattering, and laser refrigeration of indirect band
gap semiconductors, both remain unsolved challenges. Here, we analytically show
that photonic density of states (DoS) engineering can address the two
fundamental requirements for achieving spontaneous Raman cooling: suppressing
the dominance of Stokes (heating) transitions, and the enhancement of
anti-Stokes (cooling) efficiency beyond the natural optical absorption of the
material. We develop a general model for the DoS modification to spontaneous
Raman scattering probabilities, and elucidate the necessary and minimum
condition required for achieving net Raman cooling. With a suitably engineered
DoS, we establish the enticing possibility of refrigeration of intrinsic
silicon by annihilating phonons from all its Raman-active modes simultaneously,
through a single telecom wavelength pump. This result points to a highly
flexible approach for laser cooling of any transparent semiconductor, including
indirect band gap semiconductors, far away from significant optical absorption,
band-edge states, excitons, or atomic resonances.
