A Si/Si3N4 high contrast grating mirror has been designed for a VCSEL integration in mid-infrared (λ = 2.65 µm). The use of an optimization algorithm which maximizes a VCSEL mirror quality factor allowed the adjustment of the grating parameters while keeping large and shallow grating pattern. The robustness with respect to fabrication error has been enhanced thanks to a precise study of the grating dimension tolerances. The final mirror exhibits large high reflectivity bandwidth with a polarization selectivity and several percent of tolerance on the grating dimensions.