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

Tanu Goyal; Manoj Kumar Majumder; Brajesh Kumar Kaushik

doi:10.1088/1674-4926/36/6/065001

J. Semicond. > 2015, Volume 36 > Issue 6 > 065001

SEMICONDUCTOR INTEGRATED CIRCUITS

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

Tanu Goyal¹, Manoj Kumar Majumder² and Brajesh Kumar Kaushik²

+ Author Affiliations

Corresponding author: Tanu Goyal, Email: tanugoy007@gmail.com; Manoj Kumar Majumder, Email: manojbesu@gmail.com; Brajesh Kumar Kaushik, Email: bkk23fec@iitr.ac.in

DOI: 10.1088/1674-4926/36/6/065001

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 nanotube, through-silicon vias, equivalent RLC circuit model, propagation delay, power-delay product, area-delay product

References

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Fig. 1. A schematic of 3D integration.

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Fig. 2. Formation of multilayered 3D ICs.

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Fig. 3. (a) Physical configuration of a TSV pair. (b) Top view of a SWCNT bundled TSV. (c) Cross-sectional view of a closely packed SWCNT bundle.

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Fig. 4. Equivalent electrical model of SWCNT bundled TSV.

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Fig. 5. Graphical plots for (a) $N_{\rm Total}$ and $N_{\rm CNT}$,(b) $R'_{\rm TSV}$ and $L'_{\rm TSV}$,(c) $C'_{\rm Q}$ and $C'_{\rm TSV}$ at via height of 30 $\mu$m.

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Fig. 6. Graphical plots for (a) $N_{\rm Total}$ and $N_{\rm CNT}$,(b) $R'_{\rm TSV}$ and $L'_{\rm TSV}$,(c) $C'_{\rm Q}$ and $C'_{\rm TSV}$ at via height of 60 $\mu $m.

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Fig. 7. Graphical plots for (a) $N_{\rm Total}$ and $N_{\rm CNT}$,(b) $R'_{\rm TSV}$ and $L'_{\rm TSV}$,(c) $C'_{\rm Q}$ and $C'_{\rm TSV}$ at via height of 90 $\mu $m.

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Fig. 8. A driver-TSV-load system.

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Fig. 9. Propagation delay of SWCNT bundled TSVs for different via heights.

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Fig. 10. Power dissipation of SWCNT bundled TSVs for different via heights.

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Table 1. Geometrical parameters and their values.

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Table 2. Percentage reduction in delay and power dissipation of SWCNT bundled TSVs for AR D 300 : 1

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Table 3. Percentage reduction in power delay product of SWCNT bundled TSVs for AR $=$ 300 : 1.

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Table 4. Percentage reduction in area delay product of SWCNT bundled TSVs for AR $=$ 300 : 1.

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Table 5. Variation of cross-sectional area of bundled SWCNT TSVs with different aspect ratio.

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Received: 20 October 2014 Revised: Online: Published: 01 June 2015

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.

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

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

DOI: 10.1088/1674-4926/36/6/065001

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