Heat transport in silicon from first principles calculations

Abstract: Using harmonic and anharmonic force constants extracted from density-functional calculations within a supercell, we have developed a relatively simple but general method to compute thermodynamic and thermal properties of any crystal. First, from the harmonic, cubic, and quartic force constants we construct a force field for molecular dynamics (MD). It is exact in the limit of small atomic displacements and thus does not suffer from inaccuracies inherent in semi-empirical potentials such as Stillinger-Weber's. By using the Green-Kubo (GK) formula and molecular dynamics simulations, we extract the bulk thermal conductivity. This method is accurate at high temperatures where three-phonon processes need to be included to higher orders, but may suffer from size scaling issues. Next, we use perturbation theory (Fermi Golden rule) to extract the phonon lifetimes and compute the thermal conductivity $\kappa$ from the relaxation time approximation. This method is valid at most temperatures, but will overestimate $\kappa$ at very high temperatures, where higher order processes neglected in our calculations, also contribute. As a test, these methods are applied to bulk crystalline silicon, and the results are compared and differences discussed in more detail. The presented methodology paves the way for a systematic approach to model heat transport in solids using multiscale modeling, in which the relaxation time due to anharmonic 3-phonon processes is calculated quantitatively, in addition to the usual harmonic properties such as phonon frequencies and group velocities. It also allows the construction of accurate bulk interatomic potentials database.

• The paper introduces a dual-method framework combining DFT, GK formalism, and RTA to predict silicon's thermal conductivity.
• It employs first principles calculations with molecular dynamics and perturbation theory to derive phonon properties and lifetimes.
• Experimental comparisons and detailed analysis of phonon scattering underscore its potential for advancing thermal management in semiconductors.

Heat Transport in Silicon from First Principles Calculations

The paper under discussion tackles the complex problem of heat transport in crystalline silicon by leveraging first principles calculations. The authors, K. Esfarjani, G. Chen, and H.T. Stokes, innovate by combining density functional theory (DFT) with both Green-Kubo (GK) formalism and the relaxation time approximation (RTA) to predict thermal conductivity. The study provides a robust framework that could be crucial for advancing the fundamental understanding of phonon-mediated thermal transport in semiconductors.

Methodology and Approach

The paper delineates a method to compute the thermodynamic and thermal properties of crystalline solids using harmonic and anharmonic force constants derived from DFT. These force constants are utilized to create a force field suitable for molecular dynamics (MD) simulations. The approach is comprehensive, accounting for three-phonon interactions critical at elevated temperatures.

The study employs two primary methods to estimate the thermal conductivity ($\kappa$). First, the GK formalism is used in conjunction with MD simulations to extract bulk thermal conductivity, particularly suitable at high temperatures where three-phonon processes are significant. The second method involves perturbation theory to calculate phonon lifetimes, which, under the relaxation time approximation, facilitates the estimation of $\kappa$. This dual-method approach allows for cross-validation and highlights the distinct temperature regimes where each method excels.

Numerical Results and Validation

Application of the methodology to bulk silicon shows promising agreement with experimental data. The study presents a detailed band structure analysis and density of states (DOS) calculations, affirming the ability of the extracted force constants to replicate experimental phonon dispersion relations accurately. It is noteworthy that the study emphasizes potential inaccuracies due to neglecting higher-order phonon processes and finite size effects, especially in MD simulations. This acknowledgment reflects the intricacies involved in precise thermal conductivity predictions from first principles.

The authors further contribute to the understanding of phonon scattering processes by dissecting phonon lifetimes into normal and umklapp processes. Their findings suggest that the umklapp processes, especially for optical phonons, are major contributors to thermal resistivity at higher temperatures.

Implications and Future Directions

This study has substantial implications for both theoretical and applied physics. By rigorously modeling atomic interactions, the derived framework enhances the predictive capabilities for thermal management in semiconductor devices. The ability to reliably compute $\kappa$ expands the potential for thermal optimization in microelectronics and thermoelectric applications.

Looking forward, the methodology sets a foundation for multiscale modeling of heat transport in complex materials, including nanostructures where size effects become pronounced. Future developments could focus on incorporating higher-order phonon interactions and addressing the limitations imposed by finite-size simulations more comprehensively. Additionally, extending the approach to other semiconductor materials could pave the way for generalized models of thermal conductivity, aiding in the design of next-generation materials.

In conclusion, the paper represents a significant stride in computational materials science, enabling an enhanced understanding of heat transport at the atomic scale. The integration of DFT with MD and perturbation theory offers a powerful toolkit for researchers exploring thermal phenomena in solid-state physics.