The equilibrium segregation of impurities at the melt–solid interface during silicon crystallization is a key factor in determining the impurity concentration and distribution in the crystal. Unfortunately, this property is difficult to measure experimentally due to the presence of complex transport physics in the melt. Here, using the Tersoff family of empirical potential models, we describe a thermodynamic integration framework for computing the interstitial oxygen and substitutional carbon segregation coefficients in silicon. Thermodynamic integration using an ideal gas reference state for the impurity atoms is shown to be an efficient and convenient pathway for evaluating impurity chemical potentials in both solid and liquid phases. We find that the segregation coefficient is captured well for substitutional carbon impurity while it is significantly underestimated for interstitial oxygen. The latter discrepancy is partially attributed to the qualitatively incorrect silicon solid-to-liquid density ratio predicted by the empirical interatomic potential.

It has long been suggested that the familiar intrinsic point defects (vacancies and self-interstitials) encountered in crystals at low temperatures ($T$) transform into extended domains characterized by a missing or excess atom compared with the same-sized region in the perfect crystal so that such extended defects may be viewed as dropletlike regions of enhanced or diminished density. However, the implications of such a transformation, or whether it even occurs in crystalline Si, remain uncertain. To address this fundamental problem, we consider a comprehensive thermodynamic analysis of the thermodynamics of vacancy and self-interstitial formation over a broad $T$ range based on thermodynamic integration with a focus on entropic contributions. In cooled liquids, it is well known that the form of the intermolecular potential can greatly influence the configurational entropy $S_c$, and correspondingly, we analyze several empirical Si potentials to determine how the potential influences both the $T$ dependence of $S_c$ and the enthalpy and entropy of defect formation. We indeed find that the $S_c$ associated with point defects increases significantly upon heating, consistent with the existence of extended defects. Moreover, each type of defect species gives a significantly different contribution to $S_c$ at elevated $T$ and to a qualitive difference in the $T$ dependence of the entropy of defect formation in the extended defect regime. We discuss some potential consequences of these thermodynamic changes of defect formation on the $T$ dependence of diffusion in heated crystals.

The significant increase in the operating temperature of solar cells has a negative effect on the electrical efficiency of photovoltaic (PV) cells. To maintain the high-power generation efficiency of the PV cells, cooling technology will be used in some PV power stations. However, common cooling technologies, such as water cooling and phase change material cooling, have the disadvantage of high costs and are unsuitable for large-scale applications in PV power stations. In this paper, a novel stair-stepping multi-layer arrangement for PV panels has been proposed to decrease the temperature of the PV panels. In contrast to the arrangement scheme of single-layer PV modules, the impact of the PV array arrangements on heat dissipation and power generation efficiency has been studied. The ground-mounted stand-alone PV modules have been investigated through computational fluid dynamics simulation. The results show that the triple-layer arrangement has better cooling performance. Under different wind speeds of 3 m/s, the triple-layer arrangement can reduce the temperature by more than 6 K, increase the photoelectric conversion efficiency by more than 0.5%, and increase the output power by 3%. The study demonstrates how novel multi-layer arrangements can enhance PV efficiency by improving the convective heat transfer of PV panels, providing a low-cost and effective alternative to PV power stations for heat dissipation.

Free energy calculation is fundamentally important in the research of physics, chemistry, and materials. Thermodynamic integration is the most common way to estimate free energies. In the research, we proposed a unified approach using atomic simulations to calculate the free energies of liquid and defective crystals. The new approach is based on thermodynamic integration using two alchemical pathways. Softcore potentials are developed for three-body interatomic potentials to realize the alchemical pathways. Employing the new approach, the free energy of the liquid can be calculated without requiring another reference system. The free energy of the defective crystal can be calculated directly at high temperatures. It avoids the singularity at the integration endpoint caused by the defect diffusion, which is a serious problem in the widely used Einstein crystal method. In addition, the new approach can capture the whole free energy of the defective crystal including the contribution of anharmonic and configurational entropy, which are particularly important at high temperatures. The new method is simple yet effective and can be extended to different materials and more complex liquid and defective crystal systems.