Widening the frequency bandgap and reducing thermal conductivity in phononic crystals by tuning structural parameters using a novel computational simulation method

Abstract This paper introduces and models a phononic structure based on single-crystal silicon, aiming to investigate the width of its frequency bandgap and the impact of key parameters on thermal conductivity. The modeled phononic crystal structure features a periodic arrangement of cylindrical holes in a silicon matrix. This research holds the potential to enhance thermal management performance of thermal metamaterials. Utilizing a 3D finite element method (FEM) model in COMSOL, we have computed phonon dispersion to estimate thermal conductivity. The study systematically has explored the influence of phononic crystal parameters—specifically, porosity, lattice constant, and thickness—along with their interactions on both thermal conductivity and frequency bandgap width. A comprehensive investigation of these parameters has been conducted for their optimization to achieve the maximum frequency bandgap width and minimum thermal conductivity using the response surface method model. Eigenfrequencies and wave vector parameters are extracted from the finite element model using a MATLAB script. Subsequently, thermal conductivity is calculated through the Callaway–Holland model, a simplification of the Boltzmann transport equation (BTE). Our results indicate that the frequency bandgap begins to form at approximately 43% porosity for a lattice constant and thickness of 100 nm each. Furthermore, adjusting the parameters led to a significant reduction in thermal conductivity, decreasing from 43.89 W m −1 K −1 to 0.39 W m −1 K −1 . The novelty of our research lies in thermal conductivity control of phononic crystal metamaterials through their parameter variations, or a predictive method of thermal conductivity and its parameter sensitivity. This study advances the state of the art in phononic crystal metamaterial research, contributing to improved thermal management performance by enlarging frequency bandgaps. Overall, our findings deepen the understanding of how porosity, lattice constant, and thickness influence thermal conductivity and frequency bandgap width. They offer valuable insights into optimizing phononic crystal parameters, enhancing thermal management performance, and designing more efficient and effective phononic crystal structures.