THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Pei-Ling Zhang

,

Kang-Jia Wang

A NEW FRACTIONAL THERMAL MODEL FOR THE CU/LOW-K INTERCONNECTS IN NANOMETER INTEGRATED CIRCUIT

ABSTRACT
In this paper, the Cu/Low-k interconnects in a nanoscale integrated circuit are considered. A new fractal conventional heat transfer equation is suggested using He's fractal derivative. The two-scale transform method is applied for solving the equation approximately. The new findings, which the traditional differential models can never reveal, shed a bright light on the optimal design of a nanoscale integrated circuit.
KEYWORDS
He’s fractal derivative, fractional thermal model, interconnects, Two-scale transform method
PAPER SUBMITTED: 2020-06-08
PAPER REVISED: 2021-10-01
PAPER ACCEPTED: 2021-10-01
PUBLISHED ONLINE: 2022-07-16
DOI REFERENCE: https://doi.org/10.2298/TSCI2203413Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 3, PAGES [2413 - 2418]
REFERENCES
  1. Banerjee, K., Mehrotra, A., Global (interconnect) Warming, Circuits & Devices Magazine IEEE, 17 (2001), 5, pp. 16-32
  2. Banerjee, K., et al., 3-D ICs: A Novel Chip Design for Improving Deep-Submicrometer Interconnect Performance and Systems-on-Chip Integration, Proceedings of the IEEE, 89 (2001), 5, pp. 602-633
  3. Loh, G. H., et al., Processor Design in 3D Die-Stacking Technologies, IEEE Micro, 27 (2007), 3, pp. 31-48
  4. Lin, S. H., Yang, H. Z., Analytical Thermal Analysis of On-chip Interconnects. Communications, Pro-ceedings, International Conference on Communications, Circuits and Systems, Guilin, China, 2006, pp. 2776-2780
  5. Mohamad-Sedighi, H., et al., Microstructure-Dependent Dynamic Behavior of Torsional Nano-Varactor, Measurement, 111 (2017), Dec., pp. 114-121
  6. Ouakad, H. M., et al., One-to-One and Three-to-One Internal Resonances in MEMS Shallow Arches, ASME. J. Comput. Nonlinear Dynam., 12 (2017), 5., 051025
  7. Wang, K. J., et al., Thermal Optimization of a 3-D Integrated Circuit, Thermal Science, 24 (2020), 4, pp. 2615-2620
  8. Wang, K. J., et al. Thermal Management of the Through Silicon vias in 3-D Integrated Circuits, Thermal Science, 23 (2019), 4, pp. 2157-2162
  9. Wang, N. L., Zhou, R. D., A Novel Analytical Thermal Model for Temperature Estimation of Multilevel ULSI Interconnects, (in Chinese), Journal of Semiconductors, 25 (2004), 11, pp. 1510-1514
  10. Tian, Y., Wan, J. X., Exact Solutions of Space-Time Fractional 2+1 Dimensional Breaking Soliton Equation, Thermal Science, 25 (2021), 2, pp. 1229-1235
  11. Wang, K. J., et al., Application of the Extended F-Expansion Method for Solving the Fractional Gardner Equation with Conformable Fractional Derivative, Fractals, On-line first, doi.org/10.1142/ S02183 48X22501390, 2022
  12. Wang, K. J., et al., The Transient Analysis for Zero-Input Response of Fractal RC Circuit Based on Lo-cal Fractional Derivative, Alexandria Eng. J., 59 (2020), 6, pp. 4669-4675
  13. Wang, K., On a High-Pass Filter Described by Local Fractional Derivative, Fractals, 28 (2020), 3, 2050031
  14. Wang, K. J., et al., The Fractional Sallen-Key Filter Described by Local Fractional Derivative, IEEE Ac-cess, 8 (2020), Sept., pp. 166377-166383
  15. Wang, K. J., et al., A a-Order R-L High-Pass Filter Modeled by Local Fractional Derivative, Alexandria Engineering Journal, 59 (2020), 5, pp. 3244-3248
  16. Tian, D., He, C. H., A Fractal Micro-Electromechanical System and Its Pull-In Stability, Journal of Low Frequency Noise Vibration and Active Control, 40 (2021), 3,pp. 1380-1386
  17. Tian, D., et al., Fractal N/MEMS: from Pull-in Instability to Pull-in Stability, Fractals, 29 (2021), 2, 2150030
  18. Wang, K. J., A New Fractional Non-Linear Singular Heat Conduction Model for the Human Head Con-sidering the Effect of Febrifuge, Eur. Phys. J. Plus, 135 (2020), 11, pp. 1-7
  19. Wang, K. J., Wang, G. D., Variational Principle and Approximate Solution for the Fractal Generalized Benjamin-Bona-Mahony-Burgers Equation in Fluid Mechanics, Fractals, 29 (2020), 3, 2150075
  20. Wang, K, J., et al., A Fractal Modification of the Sharma-Tasso-Olver Equation and Its Fractal General-ized Variational Principle, Fractals, 30 (2022), 6, 2250121
  21. Wang, K. J., Research on the Nonlinear Vibration of Carbon Nanotube Embedded in Fractal Medium, Fractals, 30 (2022), 1, 2250016
  22. Wang, K. J., Variational Principle and Approximate Solution for the Generalized Burgers-Huxley Equa-tion with Fractal Derivative, Fractals, 29 (2020), 2, 2150044
  23. Wang, K. J., Wang, G. D., He's Variational Method for the Time-Space Fractional Non-linear Drinfeld-Sokolov-Wilson System, Mathematical Methods in the Applied Sciences，On-line first, doi.org/10.1002/mma.7200, 2021
  24. Wang, K. J., Wang, K. L., Variational Principles for fractal Whitham-Broer-Kaup Equations in Shallow Water, Fractals, 29 (2020), 2, 21500286
  25. Wang, K. L., Fractal Solitary Wave Solutions for Fractal Nonlinear Dispersive Boussinesq-Like Models, Fractals, 30 (2022), 4, ID 2250083
  26. Wang, K. L., Wang, H., Fractal Variational Principles for Two Different Types of Fractal Plasma Mod-els with Variable Coefficients, Fractals, 30 (2022), 3, ID 2250043
  27. Wang, K. J., Si, J., Investigation into the Explicit Solutions of the Integrable (2+1)-Dimensional Maccari System via the Variational Approach, Axioms, 11 (2022), 5, 234
  28. He, J. H., et al., A Fractal Modification of Chen-Lee-Liu Equation and Its Fractal Variational Principle, International Journal of Modern Physics, 35 (2021), 21B, 21502143
  29. He, J. H., et al., On a Strong Minimum Condition of a Fractal Variational Principle, Applied Mathemat-ics Letters, 119 (2021), Sep., 107199
  30. He, J. H., et al., Variational Approach to Fractal Solitary Waves, Fractals, 29 (2021), 7, 2150199
  31. Wang, K. J., Generalized Variational Principle and Periodic Wave Solution to the Modified Equal width-Burgers Equation in Non-Linear Dispersion Media, Physics Letters A, (2021), 1773
  32. Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, 1950134
  33. Liu, F. J., et al., Thermal Oscillation Arising in a Heat Shock of a Porous Hierarchy and Its Application, Facta Universitatis Series: Mechanical Engineering, On-line first, https//doi.org/ 10.22190/FUME21031 7054L, 2021
  34. Li, X. X., He, J. H., Along the Evolution Process: Kleiber's 3/4 Law Makes Way for Rubner's Surface lAw: A Fractal Approach, Fractals, 27 (2019), 2, 1950015
  35. Tian, D., et al., Hall-Petch Effect and Inverse Hall-Petch Effect: A Fractal Unification, Fractals, 26 (2018), 6, 1850083
  36. Wang, K. J., Wang, G. D., Solitary Waves of the Fractal Regularized Long Wave Equation Travelling along an Unsmooth Boundary, Fractals, 30 (2022), 1, 2250008
  37. He, C. H., et al., Low Frequency Property of a Fractal Vibration Model for a Concrete Beam, Fractals, 29 (2021), 5, 150117
  38. Feng, G. Q., He's frequency Formula to Fractal Undamped Duffing Equation, Journal of Low Frequency Noise Vibration and Active Control, 40 (2021), 4, pp. 1671-1676
  39. Han, C., et al., Numerical Solutions of Space Fractional Variable-Coefficient KdV-Modified KdV Equa-tion by Fourier Spectral Method, Fractals, 29 (2021), 8, 2150246-1602
  40. Dan, D. D., et al., Using Piecewise Reproducing Kernel Method and Legendre Polynomial for Solving a Class of the Time Variable Fractional Order Advection-Reaction-Diffusion Equation, Thermal Science, 25 (2021), 2B, pp. 1261-1268
  41. Wang, K. J., On New Abundant Exact Traveling Wave Solutions to the local Fractional Gardner Equa-tion Defined on Cantor Sets, Mathematical Methods in the Applied Sciences, 45 (2021), 4, pp. 1904-1915
  42. Wang, K. J., Zhang, P. L., Investigation of the Periodic Solution of the Time-Space Fractional Sasa-Satsuma Equation Arising in the Monomode Optical Fibers, EPL, 137 (2022), 6, 62001
  43. He, J. H., Fractal Calculus and Its Geometrical Explanation, Results Phys., 10 (2018), Sept., pp. 272-276
  44. He, J. H., Li, Z. B., Converting Fractional Differential Equations Into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
  45. Wang, K. J., Periodic Solution of the Time-Space Fractional Complex Nonlinear Fokas-Lenells Equation by an Ancient Chinese Algorithm, Optik, 243 (2021), Oct., 167461
  46. He, J. H., et al., Solitary Waves Travelling Along an Unsmooth Boundary, Results in Physics, 24 (2021), May, 104104
  47. Anjum, N., et al., Two-Scale Fractal Theory for the Population Dynamics, Fractals, 29 (2021), 7, 21501826-744
PDF VERSION [DOWNLOAD]
A new fractional thermal model for the Cu/Low-k interconnects in nanometer integrated circuit

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence