Comparison of the performances between the gray and non-gray media approaches of thermal transport in silicon-tin

We have compared the performances of the gray and non–gray media approaches of thermal transport in Silicon – Tin using Monte Carlo Simulation. The Boltzmann Transport Equation (BTE) for phonons was used to describe the heat flow and ballistic conduction in semiconducting alloy systems. In this work, we have attempted solving the BTE using Monte Carlo (MC) simulation Computational domains for both gray and non-gray media approaches are modeled and the geometry and dimensions of unit cell and sub-cells in the domain are determined. In addition, the computational performances of the gray and non-gray media approaches are compared. The results revealed that when compared to non- gray approach, the gray media approach has more errors in the sub-cells. The maximum relative error is about 3.5%. The results also show that the non–gray media approach of thermal transport in Silicon – Tin exhibited numerical predictions with a very close match to experimental data.