Callaway approximation to the Boltzmann equation fails to predict phonon hydrodynamics
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View abstract on PubMed
Summary
This summary is machine-generated.The Callaway approximation accurately models heat transfer in semiconductors at low temperatures, but fails when phonon hydrodynamics emerge. This study provides guidelines for its use in cryogenic conditions.
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.
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