Heat jet approach for finite temperature atomic simulations of single-crystal silicon layers

Abstract

An accurate and efficient heat bath method plays a key role in atomic simulations of the thermal and mechanical properties of single-crystal silicon. Here, focusing on the single-crystal silicon (111) layer, which is a crucial lattice structure commonly employed as a substrate for chips, we propose a heat jet approach for finite temperature atomic simulations of silicon layers. First, we formulate the linearized dynamic equations for the silicon atoms and calculate the dispersion relation and lattice wave solutions. Then, an appropriate matching boundary condition is chosen for designing the two-way boundary condition, which allows incoming waves to inject into the lattice system while eliminating boundary reflections. Combining the two-way boundary condition and phonon heat source, the heat jet approach for the silicon (111) layer is proposed. Numerical tests illustrate the accuracy and effectiveness of the heat jet approach in simultaneously resolving thermal fluctuations and controlling temperature. Furthermore, we simulate the propagation of a Gaussian hump at a given temperature with the heat jet approach compared to the Nosé–Hoover heat bath. Numerical results demonstrate that the heat jet approach can well describe the movement of large structural deformations among thermal fluctuations without boundary reflections.