Gradient Lab · Scaling laws for thermal conductivity of nanoporous crystalline silicon using molecular dynamics simulations

Motivation

Porous crystalline silicon have received significant attention due to their wide range of applications including (i) optoelectronic devices, (ii) thermal insulator and sensor, (iii) highly energetic MEMS devices, as well as in (iv) thermoelectric devices for energy harvesting. In all these applications, knowledge of the thermal properties of these materials over a wide range of temperature is of significant importance for their practical implementation in devices. Predicting the thermal conductivity of nanoporous materials is very challenging because of the presence of nanopores presenting large matrix/pore interfacial area and resistance to energy transport through the nanostructure. Through classical molecular dynamics (MD) simulations, our study aims to provide insight into the physical phenomena controlling energy transport in nanostructured materials.

Simulation Systems and Method

Table 1. Summary of simulated crystalline nanoporous silicon systems with various porosity, pore diameter, cross-section area, system length, and pore diameter. — **Table 1.** Summary of simulated crystalline nanoporous silicon systems with various porosity, pore diameter, cross-section area, system length, and pore diameter.

Fig. 1. Structure of the nanoporous silicon systems. — **Fig. 1.** Structure of the nanoporous silicon systems.

Results and Scaling Analysis

Fig. 2. Predicted effective thermal conductivity of crystalline nanoporous silicon at 500 K as a function of system length Lz for fv=27% along with various pore diameters and simulation cell cross-section. — **Fig. 2.** Predicted effective thermal conductivity of crystalline nanoporous silicon at 500 K as a function of system length L_z for f_v=27% along with various pore diameters and simulation cell cross-section.

Fig. 3. Scaling Analysis based on the coherent potential effective medium approximation, kinetic theory, and relaxation time models — **Fig. 3.** Scaling Analysis based on the coherent potential effective medium approximation, kinetic theory, and relaxation time models

Fig. 4. Effective thermal conductivity keff as a function of (1-1.5fv)/(Ai/4+1/Lz) of all crystalline nanoporous silicon systems simulated at 500 K for fv ranging between 8% and 38%, dp between 1.74 and 5.86 nm, and Lz b — **Fig. 4.** Effective thermal conductivity k_eff as a function of (1-1.5f_v)/(A_i/4+1/L_z) of all crystalline nanoporous silicon systems simulated at 500 K for f_v ranging between 8% and 38%, d_p between 1.74 and 5.86 nm, and L_z between 13 and 130 nm.

Fig. 5. Effective bulk thermal conductivity keff as a function of (1-1.5fv)/(Ai/4) for nanoporous silicon with spherical pores (present study) at 500 K — **Fig. 5.** Effective bulk thermal conductivity k_eff as a function of (1-1.5f_v)/(A_i/4) for nanoporous silicon with spherical pores (present study) at 500 K

Fig. 6. Effective bulk thermal conductivity keff as a function of (1-1.5fv)/(Ai/4) for nanoporous silicon with cylindrical pores at 300 K. — **Fig. 6.** Effective bulk thermal conductivity k_eff as a function of (1-1.5f_v)/(A_i/4) for nanoporous silicon with cylindrical pores at 300 K.

Fig. 7. Effective bulk thermal conductivity keff as a function of (1-1.5fv)/(Ai/4) for nanoporous silicon with vacancy defects at 300 K. — **Fig. 7.** Effective bulk thermal conductivity k_eff as a function of (1-1.5f_v)/(A_i/4) for nanoporous silicon with vacancy defects at 300 K.

Conclusion

This study established that the effective thermal conductivity k_eff of crystalline nanoporous silicon predicted from non-equilibrium MD simulations is strongly affected by the pore interfacial area concentration A_i, the porosity f_v, and the system's length L_z. In addition, a modified effective medium approximation combining kinetic theory and the coherent potential approximation suggested that k_eff was proportional to (1-1.5f_v) and inversely proportional to the sum (A_i/4+1/L_z). This model agreed with MD simulation predictions for the thermal conductivity of crystalline nanoporous silicon with not only spherical pores (present study) but also with 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 for various applications including thermoelectric energy conversion.

Publications

J. Fang and L. Pilon, 2011. Scaling Laws for Thermal Conductivity of Crystalline Nanoporous Silicon Based on Molecular Dynamics Simulations, Journal of Applied Physics, Vol. 110, 064305.DOI PDF