Thermal Expansion and Isotopic Composition Effects on Lattice Thermal Conductivities of Crystalline Silicon

Equilibrium molecular dynamics simulation is used to calculate lattice thermal conductivities of crystal silicon in the temperature range from 400K to 1600K. Simulation results confirmed that thermal expansion, which resulted in the increase of the lattice parameter, caused the decrease of the lattice thermal conductivity. The simulated results proved that thermal expansion imposed another type resistance on phonon transport in crystal materials. Isotopic and vacancy effects on lattice thermal conductivity are also investigated and compared with the prediction from the modified Debye Callaway model. It is demonstrated in the MD simulation results that the isotopic effect on lattice thermal conductivity is little in the temperature range from 400K to 1600K for isotopic concentration below 1%, which implies the isotopic scattering on phonon due to mass difference can be neglected over the room temperature. The remove of atoms from the crystal matrix caused mass difference and elastic strain between the void and the neighbor atoms, which resulted in vacancy scattering on phonons. Simulation results demonstrated this mechanism is stronger than that caused by isotopic scattering on phonons due to mass difference. A good agreement is obtained between the MD simulation results of silicon crystal with vacancy defects and the data predicted from the modified Debye Callaway model. This conclusion is helpful to demonstrate the validity of Klemens’ Rayleigh model for impurity scattering on phonons. INTRODUCTION Silicon is a fundamental material for semiconductor industry. The thermal conductivity of silicon is a key parameter for the design of the electronic device. With the rapid growth of the microprocessor running speed, the removal of the Joule heat becomes critical for the next generation of electronic devices. With the ready availability of isotopically purified source materials, the isotope effect has undergone reexamination over the last decade. Isotopically purified diamond [1–3] displays a room-temperature isotope effect on the order of 40% at room temperature. In a very thorough investigation of the isotope effect in germanium, Asen-Palmer et al.[4] showed that an isotopically purified sample had thermal conductivity 30% larger compared to natural abundance Ge. Ruf et al in their series papers [5,6] reported the maximum thermal conductivity of highly enriched (99.8588%) Si silicon is six times larger than that in nature silicon around 20K. At room temperature, a thermal conductivity of enhancement of 60% compared with nature silicon is measured. However, Kremer et al [7] remeasured isotopically enriched Si (enrichment better than 99.9%) in temperature range 5300K. Their measured k of isotoptically enriched Si exceeds that of nature Si by 28