Fundamentally new approaches to solving thermophysical problems in the field of nanoelectronics

Abstract

Currently, there is a rapid development of thermophysics of solids associated with the need of creating models with a high degree of predictive reliability. This paper presents new approaches to solving relevant issues related to the study of heat transfer in semiconductors and dielectrics, mainly concerning nano-structures. The first of the considered tasks is the creation of a statistical model of the processes of interaction of heat carriers – phonons – with rough surfaces of solids. For the first time authors proposed a method based on the statistics of the slopes of the profile of a random surface. The calculation results are the mean free paths of phonon between the opposite boundaries of the sample, which are necessary for calculating the effective thermal conductivity in ballistic and diffusion-ballistic regime of heat transfer, depending on the roughness parameters. The second task is to develop methods for calculating the processes of heat transfer through the contact surfaces of solids. We were able to show that, taking into account the phonon dispersion and the corresponding restrictions on the frequency values, the modified acoustic mismatch model for calculating Kapitsa resistances can be extended to temperatures above 300 K. Previously, the limit of applicability of this method was considered to be a temperature of 30 K. Moreover, the proposed method is also generalized to the case of rough interfaces. The third task is a new approach to determining the thermal conductivity of solids. The authors have developed a method of direct Monte Carlo simulation of phonon kinetics with strict consideration of their interaction due to the direct use of the laws of conservation of energy and quasi-momentum. The calculations of the thermal conductivity coefficient for pure silicon in the temperature range from 100 to 300 K showed good agreement with the experiment and ab initio calculations of other authors, and also allowed us to consider in detail the kinetics of phonons.