Band Structure Characteristics of Two-Dimensional Si-A (Ge, Pb, Sn) Alloy-Air Holes Thermal Crystals

This paper designs the thermal crystals composed of alloy materials with air holes and analyzes their properties of band structures, heat transmission, and flux spectra. Thermal crystals composed of Si-A (A=Ge, Sn, Pb) alloys as background materials and air holes with square array are used to construct an elastic-constant periodic structure and their high-frequency phononic band is calculated by deploying finite element methods. Moreover, this paper investigates heat transmission through a finite array of thermally excited phonons and presents the thermal crystal with maximum heat transport. The results show that a wider bandgap could be achieved by increasing the air hole radius and decreasing the lattice constant. In the alloy materials, with increasing atomic radius and thus atomic mass (Ge, Sn, Pb), the frequency range (contributed to thermal conductivity) shifts towards lower frequency. Hence, the bandgap frequencies also shift toward low frequency, but this decreasing rate is not constant or in order, so former may have a faster or slower decreasing rate than the later. Thus, the frequency range for the contribution of heat transportation overlaps with the bandgap frequency range. The development of thermal crystals is promising for managing heat and controlling the propagation of the thermal wave.