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.
Issue Section:
Heat and Mass Transfer
References
1.
Ho
, C. S.
, Liou
, J. J.
, and Chen
, F.
, 2000
, “An Analytical MOSFET Breakdown Model Including Self-Heating Effect
,” Solid-State Electron.
, 44
(1
), pp. 125
–131
.2.
Liao
, M.
, and Gan
, Z.
, 2014
, “New Insight on Negative Bias Temperature Instability Degradation With Drain Bias of 28 nm High-K Metal Gate p-MOSFET Devices
,” Microelectron. Reliab.
, 54
(11
), pp. 2378
–2382
.3.
Rhew
, J.-H.
, Ren
, Z.
, and Lundstrom
, M. S.
, 2002
, “A Numerical Study of Ballistic Transport in a Nanoscale MOSFET
,” Solid-State Electron.
, 46
(11
), pp. 1899
–1906
.4.
Cheng
, M.-C.
, Yu
, F.
, Jun
, L.
, Shen
, M.
, and Ahmadi
, G.
, 2004
, “Steady-State and Dynamic Thermal Models for Heat Flow Analysis of Silicon-on-Insulator MOSFETs
,” Microelectron. Reliab.
, 44
(3
), pp. 381
–396
.5.
Jagadesh Kumar
, M.
, and Orouji
, A. A.
, 2006
, “Investigation of a New Modified Source/Drain for Diminished Self-Heating Effects in Nanoscale MOSFETs Using Computer Simulation
,” Physica E
, 33
(1
), pp. 134
–138
.6.
Agaiby
, R.
, Yang
, Y.
, Olsen
, S. H.
, O'Neill
, A. G.
, Eneman
, G.
, Verheyen
, P.
, Loo
, R.
, and Claeys
, C.
, 2007
, “Quantifying Self-Heating Effects With Scaling in Globally Strained Si MOSFETs
,” Solid-State Electron.
, 51
(11–12), pp. 1473
–1478
.7.
O'Neill
, A.
, Agaiby
, R.
, Olsen
, S.
, Yang
, Y.
, Hellstrom
, P.-E.
, Ostling
, M.
, Oehme
, M.
, Lyutovich
, K.
, Kasper
, E.
, Eneman
, G.
, Verheyen
, P.
, Loo
, R.
, Claeys
, C.
, Fiegna
, C.
, and Sangiorgi
, E.
, 2008
, “Reduced Self-Heating by Strained Silicon Substrate Engineering
,” Appl. Surf. Sci.
, 254
(19
), pp. 6182
–6185
.8.
Alatise
, O. M.
, Kwa
, K. S. K.
, Olsen
, S. H.
, and O'Neill
, A. G.
, 2010
, “The Impact of Self-Heating and SiGe Strain-Relaxed Buffer Thickness on the Analog Performance of Strained Si nMOSFETs
,” Solid-State Electron.
, 54
(3
), pp. 327
–335
.9.
Liu
, W.
, and Asheghi
, M.
, 2004
, “Thermal Modeling of Self-Heating in Strained-Silicon MOSFETs
,” The Ninth Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITHERM
), Las Vegas, NV, June 1–4, Vol. 2
, p. 605
.10.
Fixel
, D. A.
, and Hitchon
, W. N. G.
, 2007
, “Convective Scheme Solution of the Boltzmann Transport Equation for Nanoscale Semiconductor Devices
,” J. Comput. Phys.
, 227
(2
), pp. 1387
–1410
.11.
Sabry
, M. N.
, Fikry
, W.
, Abdel Salam
, Kh.
, Awad
, M. M.
, and Nasser
, A. E.
, 2001
, “A Lumped Transient Thermal Model for Self-Heating in MOSFETs
,” Microelectron. J.
, 32
(10–11), pp. 847
–853
.12.
Marek
, J.
, Chvála
, A.
, Donoval
, D.
, Príbytný
, P.
, Molnár
, M.
, and Mikolášek
, M.
, 2014
, “Compact Model of Power MOSFET With Temperature Dependent Cauer RC Network for More Accurate Thermal Simulations
,” Solid-State Electron.
, 94
, pp. 44
–50
.13.
Yang
, R.
, Chen
, G.
, Laroche
, M.
, and Taur
, Y.
, 2005
, “Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation
,” ASME J. Heat Transfer
, 127
(3
), pp. 298
–306
.14.
Ghazanfarian
, J.
, and Abbassi
, A.
, 2012
, “Investigation of 2D Transient Heat Transfer Under the Effect of Dual-Phase-Lag Model in a Nanoscale Geometry
,” Int. J. Thermophys.
, 33
(3
), pp. 552
–566
.15.
Ghazanfarian
, J.
, and Shomali
, Z.
, 2012
, “Investigation of Dual-Phase-Lag Heat Conduction Model in a Nanoscale Metal-Oxide-Semiconductor Field-Effect Transistor
,” Int. J. Heat Mass Transfer
, 55
(21–22), pp. 6231
–6237
.16.
Nasri
, F.
, Echouchene
, F.
, Ben Aissa
, M. F.
, Graur
, I.
, and Belmabrouk
, H.
, 2015
, “Investigation of Self-Heating Effects in a 10-nm SOI-MOSFET With an Insulator Region Using Electrothermal Modeling
,” IEEE Trans. Electron Devices
, 62
(8
), pp. 2410
–2415
.17.
Romano
, V.
, and Rusakov
, A.
, 2010
, “2D Numerical Simulations of an Electron–Phonon Hydrodynamical Model Based on the Maximum Entropy Principle
,” Comput. Methods Appl. Mech. Eng.
, 199
(41–44), pp. 2741
–2751
.18.
Dong
, Y.
, and Guo
, Z. Y.
, 2011
, “Entropy Analyses for Hyperbolic Heat Conduction Based on the Thermomass Model
,” Int. J. Heat Mass Transfer
, 54
(9–10), pp. 1924
–1929
.19.
Tzou
, D. Y.
, 1989
, “On the Thermal Shock Wave Induced by a Moving Heat Source
,” ASME J. Heat Transfer
, 111
(2
), pp. 232
–238
.20.
Tzou
, D. Y.
, 1995
, “A Unified Field Approach for Heat Conduction From Macro- to Micro Scales
,” ASME J. Heat Transfer
, 117
(1
), pp. 8
–16
.21.
Tzou
, D. Y.
, 1995
, “The Generalized Lagging Response in Small-Scale and High-Rate Heating
,” Int. J. Heat Mass Transfer
, 38
(17
), pp. 3231
–3240
.22.
Tzou
, D. Y.
, 1995
, “Experimental Support for the Lagging Behavior in Heat Propagation
,” J. Thermophys. Heat Transfer
, 9
(4
), pp. 686
–693
.23.
Han
, P.
, Tang
, D.
, and Zhou
, L.
, 2006
, “Numerical Analysis of Two-Dimensional Lagging Thermal Behavior Under Short-Pulse-Laser Heating on Surface
,” Int. J. Eng. Sci.
, 44
(20
), pp. 1510
–1519
.24.
Akbarzadeh
, A. H.
, and Pasini
, D.
, 2014
, “Phase-Lag Heat Conduction in Multilayered Cellular Media With Imperfect Bonds
,” Int. J. Heat Mass Transfer
, 75
, pp. 656
–667
.25.
Dai
, W.
, Han
, F.
, and Sun
, Z.
, 2013
, “Accurate Numerical Method for Solving Dual-Phase-Lagging Equation With Temperature Jump Boundary Condition in Nano-Heat Conduction
,” Int. J. Heat Mass Transfer
, 64
, pp. 966
–975
.26.
Ghazanfarian
, J.
, and Abbassi
, A.
, 2009
, “Effect of Boundary Phonon Scattering on Dual-Phase-Lag Model to Simulate Micro- and Nano-Scale Heat Conduction
,” Int. J. Heat Mass Transfer
, 52
(15–16), pp. 3706
–3711
.27.
Lee
, H.-L.
, Chen
, W.-L.
, Chang
, W.-J.
, Wei
, E.-J.
, and Yang
, Y.-C.
, 2013
, “Analysis of Dual-Phase-Lag Heat Conduction in Short-Pulse Laser Heating of Metals With a Hybrid Method
,” Appl. Therm. Eng.
, 52
(2
), pp. 275
–283
.28.
Al-Nimr
, M. A.
, Naji
, M.
, and Arbaci
, V. S.
, 2000
, “Nonequilibrium Entropy Production Under the Effect of the Dual-Phase-Lag Heat Conduction Model
,” ASME J. Heat Transfer
, 122
(2
), pp. 217
–223
.29.
Shomali
, Z.
, and Abbassi
, A.
, 2014
, “Investigation of Highly Non-Linear Dual-Phase-Lag Model in Nanoscale Solid Argon With Temperature-Dependent Properties
,” Int. J. Therm. Sci.
, 83
, pp. 56
–67
.30.
Hajizadeh
, M.
, Ghalichi
, F.
, and Mirzakouchaki
, B.
, 2016
, “Optimization of Orthodontic Bracket Base Geometry for Planar Enamel Surface Teeth: A Finite Element Study
,” Orthod. Waves
, 75
(3
), pp. 64
–75
.31.
Della Bona
, Á.
, Borba
, M.
, Benetti
, P.
, Duan
, Y.
, and Griggs
, J. A.
, 2013
, “Three-Dimensional Finite Element Modelling of All-Ceramic Restorations Based on Micro-CT
,” J. Dent.
, 41
(5
), pp. 412
–419
.32.
Liao
, L.-L.
, Hung
, T.-Y.
, Liu
, C.-K.
, Li
, W.
, Dai
, M.-J.
, and Chiang
, K.-N.
, 2014
, “Electro-Thermal Finite Element Analysis and Verification of Power Module With Aluminum Wire
,” Microelectron. Eng.
, 120
, pp. 114
–120
.33.
Sullivan
, B. J.
, 2010
, “The Finite Element Method and Earthquake Engineering: The 2006 Benjamin Franklin Medal in Civil Engineering Presented to Ray W. Clough
,” J. Franklin Inst.
, 347
(4
), pp. 672
–680
.34.
Cremonesi
, M.
, and Frangi
, A.
, 2016
, “A Lagrangian Finite Element Method for 3D Compressible Flow Applications
,” Comput. Methods Appl. Mech. Eng.
, 311
, pp. 374
–392
.35.
Garegnani
, G.
, Fiori
, V.
, Gouget
, G.
, Monsieur
, F.
, and Tavernier
, C.
, 2016
, “Wafer Level Measurements and Numerical Analysis of Self-Heating Phenomena in Nano-Scale SOI MOSFETs
,” Microelectron. Reliab.
, 63
, pp. 90
–96
.36.
Le Borgne
, B.
, Salaün
, A.-C.
, and Pichon
, L.
, 2016
, “Electrical Properties of Self-Aligned Gate-All-Around Polycrystalline Silicon Nanowires Field-Effect Transistors
,” Microelectron. Eng.
, 150
, pp. 32
–38
.37.
Park
, S. J.
, Jeon
, D.-Y.
, Montès
, L.
, Barraud
, S.
, Kim
, G.-T.
, and Ghibaudo
, G.
, 2014
, “Impact of Channel Width on Back Biasing Effect in Tri-Gate MOSFET
,” Microelectron. Eng.
, 114
, pp. 91
–97
.38.
Lee
, C.-C.
, Hsieh
, C.-P.
, Huang
, P.-C.
, Cheng
, S.-W.
, and Liao
, M.-H.
, 2016
, “Ge1-xSix on Ge-Based n-Type Metal-Oxide Semiconductor Field-Effect Transistors by Device Simulation Combined With High-Order Stress-Piezoresistive Relationships
,” Thin Solid Films
, 602
, pp. 78
–83
.39.
Lee
, C.-C.
, Cheng
, H.-C.
, Hsu
, H.-W.
, Chen
, Z.-H.
, Teng
, H.-H.
, and Liu
, Ch.-H.
, 2014
, “Mechanical Property Effects of Si1-xGex Channel and Stressed Contact Etching Stop Layer on Nano-Scaled n-Type Metal-Oxide-Semiconductor Field Effect Transistors
,” Thin Solid Films
, 557
, pp. 316
–322
.40.
Chen
, P.-Y.
, Shao
, Y.-L.
, Cheng
, K.-W.
, Hsu
, K.-H.
, Wu
, J.-S.
, and Ju
, J.-P.
, 2007
, “Three-Dimensional Simulation Studies on Electrostatic Predictions for Carbon Nanotube Field Effect Transistors
,” Comput. Phys. Commun.
, 177
(9
), pp. 683
–688
.41.
Saghatchi
, R.
, and Ghazanfarian
, J.
, 2015
, “A Novel SPH Method for the Solution of Dual-Phase-Lag Model With Temperature-Jump Boundary Condition in Nanoscale
,” Appl. Math. Modell.
, 39
(3–4), pp. 1063
–1073
.42.
Xu
, M.
, and Wang
, L.
, 2005
, “Dual-Phase-Lagging Heat Conduction Based on Boltzmann Transport Equation
,” Int. J. Heat Mass Transfer
, 48
(25–26), pp. 5616
–5624
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