Research Papers: Heat and Mass Transfer

Effect of Temperature Jump on Nonequilibrium Entropy Generation in a MOSFET Transistor Using Dual-Phase-Lagging Model

[+] Author and Article Information
Fraj Echouchene

Laboratory of Electronics and Microelectronics,
University of Monastir,
Monastir 5019, Tunisia
e-mail: frchouchene@yahoo.fr

Hafedh Belmabrouk

Department of Physics,
College of Science AlZulfi,
Majmaah University,
Al-Majma'ah 15341, Saudi Arabia
e-mail: Hafedh.Belmabrouk@fsm.rnu.tn

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 12, 2016; final manuscript received May 28, 2017; published online July 19, 2017. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 139(12), 122007 (Jul 19, 2017) (8 pages) Paper No: HT-16-1132; doi: 10.1115/1.4037061 History: Received March 12, 2016; Revised May 28, 2017

This paper investigates the effect of temperature-jump boundary condition on nonequilibrium entropy production under the effect of the dual-phase-lagging (DPL) heat conduction model in a two-dimensional sub-100 nm metal-oxide-semiconductor field effect transistor (MOSFET). The transient DPL model is solved using finite element method. Also, the influences of the governing parameters on global entropy generation for the following cases—(I) constant applied temperature, (II) temperature-jump boundary condition, and (III) a realistic MOSFET with volumetric heat source and adiabatic boundaries—are discussed in detail and depicted graphically. The analysis of our results indicates that entropy generation minimization within a MOSFET can be achieved by using temperature-jump boundary condition and for low values of Knudsen number. A significant reduction of the order of 85% of total entropy production is observed when a temperature-jump boundary condition is adopted.

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Fig. 1

Schematic drawing of device geometry and boundary conditions simulated in this paper: The nanoscale heat source embedded in the substrate, which is similar to the heat generation and transport in the MOSFET device

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Fig. 2

Quadratic rectangular element (left) and shape functions φ(x, y) on the [0 1] × [0 1] (right)

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Fig. 4

Comparison of temperature distribution obtained from the finite element method with results of Saghatchi and Ghazanfarian [41] for Kn = 0.1 at t* = 10

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Fig. 5

Comparison of transient temperature distribution at the centerline using the Boltzmann equation, the ballistic-diffusive equations, and the DPL model for Kn = 10 at t* = 1

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Fig. 6

Comparison of transient entropy production distribution at the centerline using the DPL heat conduction model without and with temperature boundary condition for Kn = 0.1 and Ω = 0.4

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Fig. 7

Comparison of transient entropy production distribution at the centerline using the DPL heat conduction model without and with temperature boundary condition for Kn = 1 and Ω = 0.4

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Fig. 8

Comparison of transient entropy production distribution at the centerline using the DPL heat conduction model with and without temperature jump boundary condition for Kn = 10 and Ω = 0.4

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Fig. 9

Transient total entropy generation inside the transistor with and without jump boundary condition for different Knudsen numbers for Ω = 0.4: (a) Kn = 0.1, (b) Kn = 1, and (c) Kn = 10

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Fig. 10

Total entropy productions as a function of Knudsen number. Two data sets are from simulation (square) and curve-fitting (line).

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Fig. 11

Distribution of total entropy generation due to heat transfer as a function of Knudsen number and Ω factor at t* = 100: (a) without a temperature-jump boundary condition and (b) with a temperature-jump boundary condition

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Fig. 12

Comparison of results of BDE, BTE, Fourier law, and present DPL model, heat flux distribution on the centerline of transistor at t = 10 ps inside the transistor

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Fig. 13

Comparison of the evolution of the total equilibrium and the nonequilibrium entropy production inside the transistor




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