  Ion beam irradiation has recently emerged as a versatile approach to
functional materials design. We show in this work that patterned defective
regions generated by ion beam irradiation of silicon can create a phonon glass
electron crystal (PGEC), a longstanding goal of thermoelectrics. By controlling
the effective diameter of and spacing between the defective regions, molecular
dynamics simulations suggest a reduction of the thermal conductivity by a
factor of $\approx$20 is achievable. Boltzmann theory shows that the
thermoelectric power factor remains largely intact in the damaged material. To
facilitate the Boltzmann theory, we derive an analytical model for electron
scattering with cylindrical defective regions based on partial wave analysis.
Together we predict a figure of merit of ZT$\approx$0.5 or more at room
temperature for optimally patterned geometries of these silicon metamaterials.
These findings indicate that nanostructuring of patterned defective regions in
crystalline materials is a viable approach to realize a PGEC, and ion beam
irradiation could be a promising fabrication strategy.
