Impact of the Regularization Parameter in the Mean Free Path Reconstruction Method: Nanoscale Heat Transport and Beyond

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.

Determining phonon mean free path spectrum by ballistic phonon resistance within a nanoslot-patterned thin film

“…Some restrictions are imposed to this convex optimization: The accumulated phonon MFP distribution 𝐹 should be smooth and increase monotonically from 𝐹(0) = 0 to 𝐹(∞) = 1. Detailed discussions of the convex optimization can be found in other studies, 13,24,[57][58][59] in which a MATLAB-based package CVX was used for this purpose. 24, 56…”

Anisotropic Thermal Conductivity of Crystalline Layered SnSe2

“…In addition, we study the effect of film thickness on the temperature-dependent k r of suspended SnSe 2 films. Finally, using the mean free path reconstruction method, − we extract the in-plane and cross-plane phonon mean free path (MFP) distribution, showing that the main contribution to the thermal transport is made by phonons with MFPs of tens to hundreds of nanometers.…”

“…To gain a further insight on how phonons contribute to the thermal conductivity, we use the MFP reconstruction model to extract the cross-plane and in-plane phonon MFP distribution (see details in Supporting Information). A detailed description of this model can be found elsewhere. − ,− Figure b displays the normalized accumulated thermal conductivity as a function of the phonon MFP. It is seen that the MFP distribution shifts to longer values for in-plane transport compared to the cross-plane.…”

Improved Capacity Retention of Lithium Ion Batteries under Fast Charge via Metal-Coated Graphite Electrodes

“…60 Conductivities of metallic thin films are also dependent on the electron scattering at the grain boundaries between crystallites and the mean free path of the electron (MFP, Cu = ∼40 nm, Ni = ∼6). 61,62 When the grain size becomes less than the MFP, the conducting electrons experience more grain boundaries and associated scattering events as they attempt to travel the MFP distance, increasing the resistivity. The size-dependence on Ni and Cu conductivities is well reported, with conductivity decreasing at and below the MFP-length particle sizes.…”