The Non-Local Dual Phase Lag Model of Heat Conduction in a Silicon Metal-Oxide-Semiconductor Field-Effect Transistor

TL;DR

This paper introduces a nonlocal dual phase lag model for heat conduction in silicon transistors, accounting for nanoscale effects with improved accuracy and computational efficiency, highlighting the significance of non-locality in thermal predictions.

Contribution

It develops a nonlocal DPL model incorporating a non-locality parameter, enhancing the accuracy of nanoscale heat transport analysis in silicon transistors.

Findings

Non-locality parameter {b3} depends linearly on Knudsen number.

Non-local effects are more significant at higher Knudsen numbers.

Inclusion of {b3} improves thermal behavior predictions in micro/nano systems.

Abstract

As the transistors and consequently the chips are getting smaller, the accurate investigation of heat transport at micro/nanoscale, becomes an important issue of concern. This is due to an increase in the energy consumption and the leakage currents as a result of the miniaturization which requires taking care of the thermal behavior to make sure that the device is working in the threshold temperature regime. The current work deals with a two-dimensional framework, incorporating the nonlocality in space, for more accurate investigation of the nanoscale heat transport using the lower computational cost phenomenological macroscopical Dual Phase Lag (DPL) method. The non dimensional non-locality parameter {\gamma}, which indicates the strength of the non-locality, is embedded through the modified DPL model named as nonlocal DPL. It is obtained that for the two-dimensional silicon transistor, the {\gamma} parameter in x and y direction has the same value and like its behavior at one-dimension, is linearly dependent on the Knudsen number, being 1.5 for Kn=10 and 0.015 for Kn=0.1. Also, the phase lagging ratio, B, is found to be 0.08. It should be mentioned that the non-locality effect is more pronounced for smaller systems with higher Knudsen number in which the non-Fourier behavior is more evident but contemplating the non-locality parameter in systems with lower Knudsen number, makes the results more precise. In brief, it is confirmed that taking into account the {\gamma} parameter is noteworthy for accurately predicting the thermal behavior in micro/nano scale systems using the classical macroscopical methods.