Investigation of non-local heat transport in two-dimensional Silicon MOSFETs

The nonlocal heat transport accompanied by time delay in two-dimensional nanomaterials is investigated. The method utilized is phenomenological nonlocal dual phase lag model. This method considers nonlocal effects in heat transfer at micro/nano scale. These phenomena, validated through experimental tests on silicon nanofilms and transient temperature variations, contribute to a better understanding of thermal behaviors at these scales. Dimensionless numerical analyses were conducted to illustrate the effects of nonlocal heat transfer and phase lags on thermal conduction. The results of analysis highlight the significance of nonlocal parameters in enhancing the comprehension of thermal behavior at nanoscale. In more detail, here, the nonlocal parameter γ is incorporated into the dual-phase lag model equation, and a temperature jump boundary condition is applied to account for the phonon scattering from the boundaries. Results are obtained for three different sizes with Knudsen numbers (Kn) of 10, 1, and 0.1 at various times. The results present good consistency with the available data derived from the Boltzmann transfer Equation (BTE). The comparisons revealed that the parameter γ is highly dependent on the Knudsen number and plays a key role in temperature distribution and heat flux profiles. It has been shown that the γ value in both x and y direction is the same for 2D silicon. More particularly, for a Knudsen number of Kn =10, the γ value is 1.5, while for Kn =1, it is 0.15, and finally for Kn=0.1, the value of γ decreases to 0.015. This is true for both x and y directions. Moreover, for a Knudsen number of 10, the value of γ is one hundred times greater than that of the Kn=0.1. Further, the value of the γ obtained for the two-dimensional silicon material, is one half of the γ obtained for the one-dimensional silicon slab. This lower value presents less non-homogeneity of the two dimensional case in comparison to the one dimensional material. It should be noted that for two cases of 1D and 2D silicon, the γ is linearly dependent on the value of the Knudsen number. The results indicate that as the characteristic length decreases, that is, as the Knudsen number increases, the effects of the nonlocal parameter become more pronounced. This research aids in better simulating and predicting complex thermal behaviors in nanoscale systems.