THERMAL SCIENCE

International Scientific Journal

Kang-Jia WangORCID

,

Chu-Xia Hua

,

Yan-Hong Liang

THERMAL OPTIMIZATION OF A 3-D INTEGRATED CIRCUIT

ABSTRACT
In a 3-D integrated circuit the heat source distribution has a huge effect on the temperature distribution, so an optimal heat source distribution is needed. This paper gives a numerical approach to its thermal optimization, the result can be used for 3-D integrated circuit optimal design.
KEYWORDS
thermal, 3-D integrated circuit, thermal optimization
PAPER SUBMITTED: 2019-02-20
PAPER REVISED: 2019-10-26
PAPER ACCEPTED: 2019-10-28
PUBLISHED ONLINE: 2020-06-21
DOI REFERENCE: https://doi.org/10.2298/TSCI2004615W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE No. 4, PAGES [2615 - 2620]
REFERENCES
[1] Zhao, Y., et al., Thermal and Wirelength Optimization With TSV Assignment for 3-D-IC, IEEE Transactions On Electron Devices, 66 (2019), 1, pp. 625-632, 10.1109/ted.2018.2875933
[2] Wang, K. J., et al., An Analytical Thermal Model for Three-dimensional Integrated Circuits with Integrated Microchannel Cooling, Thermal Science, 21 (2017), 4, pp. 1601-1606, 10.2298/tsci160716041w
[3] Yan, H. X., et al., Thermal Aware Placement in 3D ICs Using Quadratic Uniformity Modeling Approach, The VLSI Journal, 42 (2009), 2, pp. 175-180, 10.1016/j.vlsi.2008.06.001
[4] Hou, L. G., A Method to Alleviate Hot Spot Problem in 3D IC, Microelectronic Engineering, 190 (2018), Apr., pp. 19-27, 10.1016/j.mee.2018.01.004
[5] Wang, K. J., et al., Integrated Microchannel Cooling in a Three Dimensional Integrated Circuit a Thermal Management, Thermal Science, 20 (2016), 3, pp. 899-902, 10.2298/tsci1603899w
[6] Lu, T., et al., TSV-based 3d ICs: design methods and tools, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 36 (2017), 10, pp. 1593-1619, 10.1109/tcad.2017.2666604
[7] Liu, S., Thermal-WLP: A Transient Thermal Simulation Method Based on Weighted Laguerre Polynomials for 3-D ICs, IEEE Transactions on Components Packaging & Manufacturing Technology, 7 (2017), 3, pp. 405-411, 10.1109/tcpmt.2017.2656244
[8] Wang, K. J., et al., Thermal Management of The Hotspots In 3-D Integrated Circuits, Thermal Science, 22 (2018), 4, pp. 1685-1690, 10.2298/tsci1804685w
[9] Feng, Z., Li, P., Fast Thermal Analysis on GPU for 3D ICs With Integrated Microchannel Cooling, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 21 (2013), 8, pp. 1526-1539, 10.1109/iccad.2010.5653869
[10] Kandlikar, S. G., Review and Projections of Integrated Cooling Systems for Three-Dimensional Integrated Circuits, Journal of Electronic Packaging, 136 (2014), 2, pp. 456-463, 10.1115/1.4027175
[11] Wang, K. J., et al., A Micro-Channel Cooling Model for a Three-Dimensional Integrated Circuit Considering Through-Silicon Vias, Micro and Nanosystems, On-line first, 66200123154001, 2020, 10.2174/1876402912666200123154001
[12] Yoon, J. K., et al., Thermal Characterization Of Interlayer Microfluidic Cooling Of Three-Dimensional Integrated Circuits With Nonuniform Heat Flux, Journal of Heat Transfer, 132 (2010), 4, pp. 041009-041018, 10.1115/1.4000885
[13] Banerjee, K., Mehrotra, A., Global (interconnect) warming, IEEE Circuits Devices Mag., 17 (2001), 5, pp. 16-32, 10.1109/101.960685
[14] Choobineh, L., Jain, A., Analytical Solution for Steady-State and Transient Temperature Fields in Vertically Stacked 3-D Integrated Circuits, IEEE Transactions on Components Packaging & Manufacturing Technology, 2 (2012), 12, pp. 2031-2039, 10.1109/tcpmt.2012.2213820
[15] Bagnall, K. R., et al., Analytical Solution for Temperature Rise in Complex Multilayer Structures with Discrete Heat Sources, IEEE Transactions on Components Packaging & Manufacturing Technology, 4 (2014), 5, pp. 817-830, 10.1109/tcpmt.2014.2299766
[16] Koo, J.-M., et al., Integrated Microchannel Cooling for Three-Dimensional Electronic Circuit Architectures, Journal of Heat Transfer, 127 (2005), 1, pp. 49-58, 10.1115/1.1839582
[17] Samal, S. K., Adaptive Regression-Based Thermal Modeling and Optimization for Monolithic 3-D ICs, IEEE Transactions On Computer-Aided Design Of Integrated Circuits And Systems, 35 (2005), 10, pp. 1707-1720, 10.1109/tcad.2016.2523983
[18] Muzychka, Y. S., et al., Thermal Spreading Resistance and Heat Source Temperature in Compound Orthotropic Systems with Interfacial Resistance, IEEE Transactions on Components Packaging & Manufacturing Technology, 3 (2013), 11, pp. 1826-1841, 10.1109/tcpmt.2013.2269273
[19] Wang, K. L., Wang. K. J., A Modification of the Reduced Differential Transform Method for Fractional Calculus, Thermal Science, 22 (2018), 4, pp. 1871-1875, 10.2298/tsci1804871w
[20] Park, M., et al., Evaluation of Si Liquid Cooling Structure with Microchannel and TSV for 3D Application, Microsystem Technologies, 23 (2017), 7, pp. 2609-2614, 10.1007/s00542-016-3009-x
[21] Liu, Y. Q., et al., Nanoscale Multi-Phase Flow and Its Application To Control Nanofiber Diameter, Thermal Science, 22 (2018), 1A, pp. 43-46, 10.2298/tsci160826148l
[22] Yu, W. J., et al., Fast 3-D Thermal Simulation for Integrated Circuits With Domain Decomposition Method, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems , 32 (2013), 12, pp. 2014-2018, 10.1109/tcad.2013.2273987
[23] Wang, K. J., et al., An Analytical Model for Steady-State and Transient Temperature Fields in 3-D Integrated Circuits, IEEE Transactions on Components Packaging & Manufacturing Technology, 6 (2016), 7, pp. 1028-1041, 10.1109/tcpmt.2016.2574897
[24] Wang, K. J., et al., The Thermal Management of the Through Silicon Vias in 3-D Integrated Circuits, Thermal Science, 23 (2019), 4, pp. 2157-2162, 10.2298/tsci1904157w
[25] Nagata, M., Limitations, Innovations, and Challenges of Circuits and Devices into a Half Micrometer and Beyond, IEEE Journal of Solid-State Circuits, 27 (1992), 4, pp. 465-472, 10.1109/4.126533
[26] Sridhar, A., et al., 3D-ICE: A Compact Thermal Model for Early-Stage Design of Liquid-Cooled ICs, IEEE Transactions on Computers, 63 (2014), 10, pp. 2576-2589, 10.1109/tc.2013.127
[27] He, J. H., Ji, F. Y., Taylor Series Solution for Lane-Emden Equation, Journal of Mathematical Chemistry, 57 (2019), 8, pp. 1932-1934, 10.1007/s10910-019-01048-7
[28] He, J. H., A Modified Li-He's Variational Principle for Plasma, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, , 2019, 10.1108/HFF-06-2019-0523
[29] He, J. H. Lagrange Crisis and Generalized Variational Principle for 3D unsteady flow, International Journal of Numerical Methods for Heat and Fluid Flow, On-line first, , 2019, 10.1108/HFF-07-2019-0577
[30] He, J. H., Sun, C., A Variational Principle for a Thin Film Equation, Journal of Mathematical Chemistry, 57 (2019), 9, pp. 2075-208, 10.1007/s10910-019-01063-8
[31] He, J. H., From Micro to Nano and from Science to Technology: Nano Age Makes the Impossible Possible, Micro and Nanosystems, 12 (2020), 1, pp. 1-2, 10.2174/187640291201191002101844
[32] He, J. H., Fractal Calculus and Its Geometrical Explanation, Result in physics, 10 (2018), Sept., pp. 272-276, 10.1016/j.rinp.2018.06.011
[33] Ren, Z. F., et al., He's Multiple Scales Method for Nonlinear Vibrations, Journal of Low Frequency Noise Vibration and Active Control, 38 (2019), 3-4, pp. 1708-1712, 10.1177/1461348419861450
[34] Wang, K. L., et al., Physical Insight of Local Fractional Calculus and Its Application to Fractional KdV-Burgers-Kuramoto Equation, Fractals, 27 (2019), 7, ID 1950122, 10.1142/s0218348x19501226
[35] Wang, Q. L., et al., Fractal Calculus and Its Application to Explanation of Biomechanism of Polar Bear Hairs, Fractals, 26 (2018), 6, 1850086, 10.1142/s0218348x1850086x
[36] He, J. H., et al. A Fractional Model for Dye Removal, Journal of King Saud University - Science, 28 (2016), 1, pp. 14-16, 10.1016/j.jksus.2015.07.001
[37] He, J. H., et al., A New Fractional Derivative And Its Application To Explanation Of Polar Bear Hairs, Journal of King Saud University - Science, 28 (2016), 2, pp. 190-192, 10.1016/j.jksus.2015.03.004
[38] Wang, Y., et al., A Variational Formulation for Anisotropic Wave Traveling in a Porous Medium, Fractals, 27 (2019), 4, 1950047, 10.1142/s0218348x19500476
[39] Wang, K. L., He, C. H., A Remark on Wang's Fractal Variational Principle, Fractals, 27 (2019), 8, ID 1950134, 10.1142/s0218348x19501342
[40] He, J. H., A Simple Approach to One-Dimensional Convection-Diffusion Equation and Its Fractional Modification for E Reaction Arising in Rotating Disk Electrodes, Journal of Electroanalytical Chemistry, 854 (2019), ID 113565, 10.1016/j.jelechem.2019.113565
[41] Wang, K. L., et al., A Fractal Variational Principle for the Telegraph Equation with Fractal Derivatives, Fractals, On-line first, , 2020, 10.1142/S0218348X20500589
[42] Wang, K. J., On a High-Pass Filter Described by Local Fractional Derivative, Fractals, On-line first, , 2020, 10.1142/S0218348X20500310
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Thermal optimization of a 3-D integrated circuit

© 2026 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