While much progress has been made towards improved energy resolution in STJ detectors recently, results are still more than an order of magnitude worse than the theoretical limit. Several factors have been identified as contributing to degradation of energy resolution in STJ devices: recombination losses, parasitic quasiparticle trapping and quasiparticle diffusion into current leads. In addition, STJ detectors tend to have poor photon capture efficiency. Semiconducting detectors achieve their near theoretical energy resolutions and high efficiencies via doping and/or applying an external field to a pure substance. These methods are ineffective for STJ detectors, therefore engineered materials (consisting of multiple materials artificially patterned on the microscopic level) should be considered. The most common engineered structures in use are quasiparticle trapping configurations which alleviate lead diffusion and detection efficiency problems, and we have proposed a multilayered approach which addresses parasitic trapping along with diffusion and efficiency. We now propose the possibility of a engineered structure which will alleviate quasiparticle recombination losses via the existence of a phononic band gap which overlaps the 2Δ energy of phonons produced during recombination of quasiparticles. We will present a 1D Kronig-Penny model for phonons normally incident to the layers of a multilayered superconducting tunnel junction as an idealized example.