Callaway approximation to the Boltzmann equation fails to predict phonon hydrodynamics

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Physics

Background:

• The Callaway approximation to the linearized Peierls-Boltzmann equation (LPBE) is computationally efficient for simulating phonon dynamics in high thermal conductivity materials.
• Its accuracy, especially under cryogenic conditions and in comparison to the full LPBE solution, remains poorly established due to a lack of direct quantitative studies.

Purpose of the Study:

• To quantitatively compare the steady-state and transient thermal transport predictions of the Callaway approximation against the full LPBE solution.
• To investigate the applicability of the Callaway approximation in different heat transfer regimes, including Fourier-diffusive, quasiballistic, and hydrodynamic flow, at temperatures below 200 K.

Main Methods:

• First-principles calculations of the linearized Peierls-Boltzmann equation (LPBE) for 20 semiconductor materials.
• Implementation and comparison of the Callaway approximation with the full LPBE solution for steady-state thermal conductivity (κ) and transient temperature dynamics.
• Analysis of heat transfer regimes based on the relative strengths of Umklapp (U) and Normal (N) phonon processes.

Main Results:

• The Callaway approximation accurately predicts heat transfer in Fourier-diffusive and quasiballistic regimes where Umklapp processes are comparable to or stronger than Normal processes.
• As temperatures decrease and Normal processes dominate over Umklapp processes, indicating the onset of phonon hydrodynamics, the Callaway approximation significantly deviates from the full LPBE solution.
• A strong correlation was found between the failure of the Callaway approximation and the emergence of phonon hydrodynamic heat flow at low temperatures.

Conclusions:

• The Callaway approximation is reliable for phonon dynamics at cryogenic temperatures only when momentum-dissipative Umklapp processes are sufficiently strong.
• The study identifies the onset of phonon hydrodynamics as the critical factor limiting the accuracy of the Callaway approximation.
• Provides essential guidelines for determining the appropriate use of the Callaway approximation in low-temperature thermal transport studies.