J. Semicond. > Volume 36 > Issue 6 > Article Number: 065001

Propagation delay and power dissipation for different aspect ratio of single-walled carbon nanotube bundled TSV

Tanu Goyal 1, , Manoj Kumar Majumder 2, and Brajesh Kumar Kaushik 2,

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Abstract: Through-silicon vias (TSVs) have provided an attractive solution for three-dimensional (3D) integrated devices and circuit technologies with reduced parasitic losses and power dissipation, higher input-output (I/O) density and improved system performance. This paper investigates the propagation delay and average power dissipation of single-walled carbon nanotube bundled TSVs having different via radius and height. Depending on the physical configuration, a comprehensive and accurate analytical model of CNT bundled TSV is employed to represent the via (vertical interconnect access) line of a driver-TSV-load (DTL) system. The via radius and height are used to estimate the bundle aspect ratio (AR) and the cross-sectional area. For a fixed via height, the delay and the power dissipation are reduced up to 96.2% using a SWCNT bundled TSV with AR = 300 : 1 in comparison to AR = 6 : 1.

Key words: carbon nanotubethrough-silicon viasequivalent RLC circuit modelpropagation delaypower-delay productarea-delay product

Abstract: Through-silicon vias (TSVs) have provided an attractive solution for three-dimensional (3D) integrated devices and circuit technologies with reduced parasitic losses and power dissipation, higher input-output (I/O) density and improved system performance. This paper investigates the propagation delay and average power dissipation of single-walled carbon nanotube bundled TSVs having different via radius and height. Depending on the physical configuration, a comprehensive and accurate analytical model of CNT bundled TSV is employed to represent the via (vertical interconnect access) line of a driver-TSV-load (DTL) system. The via radius and height are used to estimate the bundle aspect ratio (AR) and the cross-sectional area. For a fixed via height, the delay and the power dissipation are reduced up to 96.2% using a SWCNT bundled TSV with AR = 300 : 1 in comparison to AR = 6 : 1.

Key words: carbon nanotubethrough-silicon viasequivalent RLC circuit modelpropagation delaypower-delay productarea-delay product



References:

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Kaushik B K, Majumder M K, Kumar V R. Carbon nanotube based 3-D interconnects-a reality or a distant dream[J]. IEEE Circuits Syst Mag, 2014, 14(4): 16.

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Kumar V R, Majumder M K, Kaushik B K. Graphene based on-chip interconnects and TSVs-prospects and challenges[J]. IEEE Nanotechnol Mag, 2014, 8(4): 14.

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Wei Zhen, Li Xiaochun, Mao Junfa. An accurate RLGC circuit model for dual tapered TSV structure[J]. Journal of Semiconductors, 2014, 35(9): 095008.

[15]

Wu Heng, Tang Zhen'an, Wang Zhu. Simulation of through via bottom-up copper plating with accelerator for the filling of TSVs[J]. Journal of Semiconductors, 2013, 34(9): 096001.

[16]

Leung L L W, Chen K J. Microwave characterization and modeling of high aspect ratio through-wafer interconnect vias in silicon substrates[J]. IEEE Trans Microw Theory Tech, 2005, 53(8): 2472.

[17]

Li H, Banerjee K. High-frequency analysis of carbon nanotube interconnects and implications for on-chip inductor design[J]. IEEE Trans Electron Devices, 2009, 56(10): 2202.

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Pu S N, Yin W Y, Mao J F. Crosstalk prediction of single-and double-walled carbon nanotube (SWCNT/ DWCNT) bundle interconnects[J]. IEEE Trans Electron Devices, 2009, 56(4): 560.

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Xu C, Li H, Suaya R. Compact AC modeling and performance analysis of through-silicon vias in 3-D ICs[J]. IEEE Trans Electron Devices, 2010, 57(12): 3405.

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Burke P J. Lüttinger liquid theory as a model of the gigahertz electrical properties of carbon nanotubes[J]. IEEE Trans Nanotechnol, 2010, 1(3): 129.

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Andriotis A N, Menon M, Froudakis G E. Various bonding configurations of transition-metal atoms on carbon nanotubes: Their effect on contact resistance[J]. Appl Phys Lett, 2000, 76(26): 3890.

[22]

Majumder M K, Kaushik B K, Manhas S K. Analysis of delay and dynamic crosstalk in bundled carbon nanotube interconnects[J]. IEEE Trans Electromagnetic Compatibility, 2014.

[23]

Sarto M S, Tamburrano A. Single-conductor transmission-line model of multiwall carbon nanotubes[J]. IEEE Trans Nanotechnol, 2010, 9(1): 82.

[24]

Li H, Yin W Y, Banerjee K. Circuit modeling and performance analysis of multi-walled carbon nanotube interconnects[J]. IEEE Trans Electron Devices, 2008, 55(6): 1328.

[25]

Zhao W S, Yin W Y, Guo Y X. Electromagnetic compatibility-oriented study on through silicon single-walled carbon nanotube bundle via (TS-SWCNTBV) arrays[J]. IEEE Trans Electromagnetic Compatibility, 2012, 54(1): 149.

[1]

Xu Z, Lu J Q. High-speed design and broadband modeling of through-strata-vias (TSVs) in 3D integration[J]. IEEE Trans Compon, Packag, Manufact Technol, 2011, 1(2): 154.

[2]

Banerjee K, Souri S J, Kapur P. 3-D ICs: a novel chip design for improving deep-sub micrometer interconnect performance and systems-on-chip integration[J]. Proc IEEE, 2001, 89(5): 602.

[3]

Kumari A, Majumder M K, Kaushik B K. Effect of polymer liners in CNT based through silicon vias[J]. Proceedings IEEE Electronics Components and Technology Conference (ECTC), 2014: 1921.

[4]

Lu J Q. 3-D hyperintegration and packaging technologies for micro-nano systems[J]. Proc IEEE, 2009, 97(1): 18.

[5]

Knickerbocker J U, Andry P S, Colgan E. 2.5D and 3D technology challenges and test vehicle demonstrations[J]. Proceedings of IEEE 62nd International Conference on Electronic Components and Technology Conference (ECTC), 2012-1068.

[6]

Kaushik B K, Majumder M K, Kumar V R. Carbon nanotube based 3-D interconnects-a reality or a distant dream[J]. IEEE Circuits Syst Mag, 2014, 14(4): 16.

[7]

Kumar V R, Majumder M K, Kaushik B K. Graphene based on-chip interconnects and TSVs-prospects and challenges[J]. IEEE Nanotechnol Mag, 2014, 8(4): 14.

[8]

Davis W R, Wilson J, Mick S. Demystifying 3D ICs: the pros and cons of going vertical[J]. IEEE Design and Test of Computers, 2005, 22(6): 498.

[9]

Christie P, Stroobandt D. The interpretation and application of Rent's rule[J]. IEEE Trans VLSI Syst, 2000, 8(6): 1.

[10]

Naeemi A, Sarvari R, Meindl J D. Performance comparison between carbon nanotube and copper interconnects for gigascale integration (GSI)[J]. IEEE Electron Device Lett, 2005, 26(2): 84.

[11]

Li H, Xu C, Srivastava N. Carbon nanomaterials for next-generation interconnects and passives: physics, status, and prospects[J]. IEEE Trans Electron Devices, 2009, 56(9): 1799.

[12]

Hoenlein W, Kreupl F, Duesberg G S. Carbon nanotube applications in microelectronics[J]. IEEE Trans Compon Packag Technolog, 2004, 27(4): 629.

[13]

Saito R, Dresselhaus G, Dresselhaus S. Physical properties of carbon nanotubes[J]. London, UK: Imperial College Press, 1998.

[14]

Wei Zhen, Li Xiaochun, Mao Junfa. An accurate RLGC circuit model for dual tapered TSV structure[J]. Journal of Semiconductors, 2014, 35(9): 095008.

[15]

Wu Heng, Tang Zhen'an, Wang Zhu. Simulation of through via bottom-up copper plating with accelerator for the filling of TSVs[J]. Journal of Semiconductors, 2013, 34(9): 096001.

[16]

Leung L L W, Chen K J. Microwave characterization and modeling of high aspect ratio through-wafer interconnect vias in silicon substrates[J]. IEEE Trans Microw Theory Tech, 2005, 53(8): 2472.

[17]

Li H, Banerjee K. High-frequency analysis of carbon nanotube interconnects and implications for on-chip inductor design[J]. IEEE Trans Electron Devices, 2009, 56(10): 2202.

[18]

Pu S N, Yin W Y, Mao J F. Crosstalk prediction of single-and double-walled carbon nanotube (SWCNT/ DWCNT) bundle interconnects[J]. IEEE Trans Electron Devices, 2009, 56(4): 560.

[19]

Xu C, Li H, Suaya R. Compact AC modeling and performance analysis of through-silicon vias in 3-D ICs[J]. IEEE Trans Electron Devices, 2010, 57(12): 3405.

[20]

Burke P J. Lüttinger liquid theory as a model of the gigahertz electrical properties of carbon nanotubes[J]. IEEE Trans Nanotechnol, 2010, 1(3): 129.

[21]

Andriotis A N, Menon M, Froudakis G E. Various bonding configurations of transition-metal atoms on carbon nanotubes: Their effect on contact resistance[J]. Appl Phys Lett, 2000, 76(26): 3890.

[22]

Majumder M K, Kaushik B K, Manhas S K. Analysis of delay and dynamic crosstalk in bundled carbon nanotube interconnects[J]. IEEE Trans Electromagnetic Compatibility, 2014.

[23]

Sarto M S, Tamburrano A. Single-conductor transmission-line model of multiwall carbon nanotubes[J]. IEEE Trans Nanotechnol, 2010, 9(1): 82.

[24]

Li H, Yin W Y, Banerjee K. Circuit modeling and performance analysis of multi-walled carbon nanotube interconnects[J]. IEEE Trans Electron Devices, 2008, 55(6): 1328.

[25]

Zhao W S, Yin W Y, Guo Y X. Electromagnetic compatibility-oriented study on through silicon single-walled carbon nanotube bundle via (TS-SWCNTBV) arrays[J]. IEEE Trans Electromagnetic Compatibility, 2012, 54(1): 149.

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T Goyal, M K Majumder, B K Kaushik. Propagation delay and power dissipation for different aspect ratio of single-walled carbon nanotube bundled TSV[J]. J. Semicond., 2015, 36(6): 065001. doi: 10.1088/1674-4926/36/6/065001.

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Manuscript received: 20 October 2014 Manuscript revised: Online: Published: 01 June 2015

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