Effects of WidePhononic Bandgaps on Thermal Conductancein Silicon Nanomeshes

We investigate the effects of wide phononic bandgaps, which are distinct from electronic bandgaps, on thermal conductance in phononic crystals. To obtain a wide phononic bandgap model, the shape and the cross-sectional area of ligaments in planar lattice structures for silicon nanomeshes are determined using a gradient-based design optimization method. Nonequilibrium molecular dynamics simulations are performed in the low-temperature range of 10–50 K, where the impact of the phononic bandgap is expected to be significant. Thermal conductance is analyzed by applying the method of mode-by-mode quantum correction. The obtained bandgap model shows the largest difference in thermal conductance at 25 K when compared with a thin-undulated mode. Also, the dominant phonon approximation of the frequency at 25 K falls within the bandgap region of the obtained model, which indicates that the wide phononic bandgap plays a major role in reducing thermal conductance. Furthermore, by analyzing the spectral thermal conductance of the bandgap model, it turns out that heat transfer is significantly reduced in the bandgap region and its vicinity. Compared with other models, the thermal conductance in the bandgap model is reduced by less than one-fifth for a straight lattice model and by less than half for a thin-undulated model. By investigating the length dependence of both classical and quantum-corrected thermal conductivities, it is revealed that long-wavelength phonons appear near the bandgap frequency, exhibiting a wave-based behavior and demonstrating the bandgap effect effectively.