Scaling laws for thermal conductivity of crystalline nanoporous silicon based on molecular dynamics simulations

摘要

This study establishes that the effective thermal conductivity k_(eff)of crystalline nanoporous silicon is strongly affected not only by the porosity f_v and the system's length L_z but also by the pore interfacial area concentration A,-. The thermal conductivity of crystalline nanoporous silicon was predicted using non-equilibrium molecular dynamics simulations. The Stillinger-Weber potential for silicon was used to simulate the interatomic interactions. Spherical pores organized in a simple cubic lattice were introduced in a crystalline silicon matrix by removing atoms within selected regions of the simulation cell. Effects of the (i) system length ranging from 13 to 130 nm, (ii) pore diameter varying between 1.74 and 5.86 nm, and (iii) porosity ranging from 8% to 38%, on thermal conductivity were investigated. A physics-based model was also developed by combining kinetic theory and the coherent potential approximation. The effective thermal conductivity was proportional to (1 - 1.5f_v) and inversely proportional to the sum (A_i/4+ 1/L_z). This model was in excellent agreement with the thermal conductivity of nanoporous silicon predicted by molecular dynamics simulations for spherical pores (present study) as well as for cylindrical pores and vacancy defects reported in the literature. These results will be useful in designing nanostructured materials with desired thermal conductivity by tuning their morphology.