Vibrational Contribution to Thermal Conductivity of Silicon Near Solid-Liquid Transition

Abstract

Although thermal transport in silicon is dominated by phonons in the solid state, electrons also participate as the system approaches, and exceeds, its melting point. Thus, the contribution from both phonons and electrons must be considered in any model for the thermal conductivity, k, of silicon near the melting point. In this paper, equilibrium molecular dynamics simulations measure the vibration mediated thermal conductivity in Stillinger-Weber silicon at temperatures ranging from 1400 to 2000 K -encompassing the solid-liquid phase transition. Non-equilibrium molecular dynamics is also employed as a confirmatory study. The electron contribution may then be estimated by comparing these results to experimental measurements of k. The resulting relationship may provide a guide for the modeling of heat transport under conditions realized in high temperature applications, such as laser irradiation or rapid thermal processing of silicon substrates.

Vibrational contribution to thermal transport in liquid cooper: Equilibrium molecular dynamics study

“…8). The estimated value of K slightly decreases from 2.1 Å to 2 Å as the temperature increases from 1300 K to 1800 K. As was pointed out in [38,43], the mean free path of the vibrational modes predicted for a liquid system is useful to discuss within the framework of the Cahill-Pohl model developed for an amorphous solid [44,45]. The Cahill-Pohl model assumes that the vibrational modes have a mean free path equal to one half of their wavelength, which fits amorphous solids reasonably well [38,44,45].…”

“…11). This can be useful to compare with the vibrational contribution of about 2.76% (the absolute value is about 1.56 W/(mK)) to the total thermal conductivity of liquid Si at 1700 K (which is near its melting temperature) estimated by a similar approach in a MD study [43] using the Stillinger-Weber interatomic potential [49]. Lastly, taking into account the almost exact coincidence of the calculated and experimental values of the heat capacity at constant pressure (the electronic contribution here is shown to be very minor), the difference between the calculated and real values of the thermal diffusivity in liquid Cu can be predicted to be very similar to the case of the thermal conductivity.…”

Modeling of thermal conductivity of Si in the range from the normal to near-critical conditions

“…Fig. 3 shows the obtained temperature dependence of the phonon thermal conductivity with the experimental data [42] and the data from [29] for the Stillinger -Weber potential, as well as a theoretical estimate [44,45]. The dashed line shows the extrapolation of the phonon thermal conductivity to the critical point.…”

“…3. Temperature dependence of the phonon thermal conductivity of silicon (this work), experimental data for total thermal conductivity [42], and data from [29] for the Stillinger-Weber potential. A theoretical estimate for the solid phase is also given [44].…”

“…Despite the fact that research on the theoretical determination of the thermal conductivity of a silicon lattice has been going on for several decades, it has not been possible to obtain the temperature dependence in a wide range necessary for mathematical modeling, which confirms the complexity of the problem. The results of modeling the phonon thermal conductivity of silicon, as a rule, contain values at one, two, or three temperatures [17][18][19][20][21], either a temperature dependence, but only for the solid phase [22][23][24][25][26][27][28], or a narrow range dependence near the melting point [29].…”