Impact of the regularization parameter in the Mean Free Path reconstruction method: Nanoscale heat transport and beyond

TL;DR

This paper investigates how the regularization parameter affects the reconstruction of mean free path distributions in nanoscale heat transport, emphasizing the importance of optimal parameter selection for accurate physical insights.

Contribution

The study revises the MFP reconstruction method and demonstrates the critical impact of the regularization parameter on the resulting distributions using the L-curve criterion.

Findings

Optimal regularization parameter significantly influences MFP distribution accuracy.

Using the L-curve criterion yields a more reliable regularization parameter.

Incorrect parameter choice can lead to misleading physical interpretations.

Abstract

The understanding of the mean free path (MFP) distribution of the energy carriers in materials (e.g. electrons, phonons, magnons, etc.) is 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.