Abstract
The understanding of the mean free path (MFP) distribution of the energy carriers in materials (e.g., electrons, phonons, magnons, etc.) provides a key physical insight into their transport properties. In this context, MFP spectroscopy has become an important tool to describe the contribution of carriers with different MFP to the total transport phenomenon. In this work, we revise the MFP reconstruction technique and present a study on the impact of the regularization parameter on the MFP distribution of the energy carriers. By using the L-curve criterion, we calculate the optimal mathematical value of the regularization parameter. The effect of the change from the optimal value in the MFP distribution is analyzed in three case studies of heat transport by phonons. These results demonstrate that the choice of the regularization parameter has a large impact on the physical information obtained from the reconstructed accumulation function, and thus cannot be chosen arbitrarily. The approach can be applied to various transport phenomena at the nanoscale involving carriers of different physical nature and behavior.
Highlights
In solid-state materials there is a variety of scattering mechanisms for energy carriers involved in different transport phenomena, such as impurities, boundaries, and collisions with other particles/quasi-particles
By normalizing and integrating this spectral function we obtain the accumulation function, which describes the contribution of carriers with different mean free path (MFP) below a certain MFP cut off to the total transport property, being very intuitive to identify which MFPs are the most relevant to the transport phenomenon under study by plotting this function
We apply this criterion to the thermal conductivity and the phonon-MFP distribution and we present a study of the impact that the choice of its value has in the reconstructed accumulation
Summary
In solid-state materials there is a variety of scattering mechanisms for energy carriers involved in different transport phenomena, such as impurities, boundaries, and collisions with other particles/quasi-particles. The average distance that a moving particle (photon, electron, etc.) or quasi particle (phonon, magnon, etc.) travels before being absorbed, attenuated, or scattered is defined as the mean free path (MFP). It is possible to quantitatively describe how energy carriers with a specific MFP contribute to the total transport property by an MFP spectral function or MFP distribution [3], which contains the information of the specific transport property associated with the energy carriers with a certain MFP. By normalizing and integrating this spectral function we obtain the accumulation function, which describes the contribution of carriers with different MFPs below a certain MFP cut off to the total transport property, being very intuitive to identify which MFPs are the most relevant to the transport phenomenon under study by plotting this function
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