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6/22/20071
Defect Modeling of CNT Interconnects for System-in-Package Application
Prof. Bruce KimDepartment of Electrical and Computer Engineering
University of Alabama
USA
6/22/20072
Outline
� Properties of carbon nanotubes (CNT)� Predicting the performance of CNT
interconnect� Circuit model of CNT interconnect.
� Fault Model of CNT interconnect.
� Fabrication of Bundle CNT-interconnect.
� Conclusion.
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Interconnect and Technology scaling
� On chip communication is a bottleneck. � Copper interconnect currently plagued by delay, noise, and
reliability problems� Electromigration also decreases reliability.
� Problem aggravated by interconnect scaling� Smaller wire dimensions� Process variations becoming an important reliability concern
6/22/20074
Resistivity changes in copper wire with Technology
� Resistivity of copper
interconnect increases as
cross-sectional dimensionsdecreases( Dimensions on
the order of mean free path
of electrons).
� Radical alternative
technology is required� ITRS 2006.
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Carbon Nanotubes for On-chip Interconnects.
� Carbon nanotubes have been proposed as a possiblereplacement for on-chipinterconnect.1. Large current density.2. Relatively low resistivity.3. Small dimensionality
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Types of Carbon Nanotube
� Single-walled carbon nanotubes (SWCNTs).1. Rolled single sheet of graphene.
2. Typical diameter: 0.4 nm to 4.0 nm.
� Multi-walled carbon nanotubes (MWCNTs).1. Nested SWCNTs.2. Distance between layers: 0.34 nm.3. Typical diameter: up to 100 nm.
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Single Walled CNT: Electrical Properties.
� SWCNTs exhibit either metallic or semiconducting behavior.
– Chirality dependent.
– 1/3 of possible SWCNT is Metallic.
� Strong carbon-carbon bonds allow large current densities ~ 109 A/cm2 .
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Carbon nanotube Bundles
� Bundles of Carbon nanotubes have been proposed for interconnect applications.
� Why Bundles?– High Current carrying capabilites
– Reduced resistance ( Single SWCNT has effective resistance of ~6.5K).
� Bundles of SWCNT have reduced resistance and effective inductance.
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System in Package
6/22/200710
SiP Integration Levels
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Circuit model of SWCNT
� Equivalent circuit model for SWCNT bundles1. Based on model for a single SWCNT from Burke [4].2. Captures experimentally verified resistance as well as
theoretically predicted capacitive and inductive effects.
/ 2CNTR / 2CNTR
ECEC
4 QC 4 QC
/ 4M KL L+ / 4M KL L+
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Electrostatic Capacitance
� To date, there is no accurate model to describe the electrostatic capacitive and inductive coupling between different CNT-bundles.
� The electrostatic capacitive and inductive couplings between CNT-bundles are strongly dependent on geometry, placement and distance of separation between individual CNT-bundle. They are also affected by permittivity and permeability of materials in different layers of SiP substrate in which these bundles are placed.
� Three Different models for determining Electrostatic capacitance between CNT-bundles.
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PROPOSED CNT BUNDLE MODEL
183
2
5
4
76
G r o u n d
E LCE RC
E MCE MC
E GC
R i g h t C N T -
b u n d l e
L e f t C N T -b u n d l e
F i g . 1 : T h r e e C N T b u n d l e s i n p a r a l l e l w i t h g r o u n d p l a n e ( g e o m e t r y I ) .
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EDC
EDCEDC
EDC
Stacked CNT Bundle Model
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Power Plane CNT-Bundle Model
ELCERC
EMCEMC
EMCEMC
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Defects in CNT-bundle Interconnect
� CNT-bundle interconnects in nano scale SiP design is affected by various parametric variations, manufacturing defects and process variations .
� Types of Defects
� Short Defects.� Open Defects.
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Shorts Defect Model
� A short defect is a connection between the two CNT-bundles that are merged and it forms a single bundle at a defective point.
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OPEN DEFECTS
� An open defect is a break in the connection in the CNT-bundle. Two major types of open defects that are important from nano interconnects point of view are
– Complete Open– Partial Open
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Physical Open Defects
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OPEN DEFECT MODEL
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Latency variation in CNT-bundles
# CNT BUNDLE
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variation of effective resistance
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Effective inductance
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Effective Capacitance
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CONCLUSIONS
� We proposed three different CNT-bundle architectures for nano scale interconnect applications in system-in-package.
� We compared the latency of the three architectures.
� We provided defect models of the CNT interconnects for open and shorts defects.
� Increase in resistance and inductance as the defect sizes increases whereas the effective capacitance decreases.
6/22/200726
REFERENCES
� [1] S. Iijima, “Helical Microtubules of Graphitic Carbon,” Nature, Vol. 354, pp. 56-58, 1991.
� [2] K. Banerjee, “Are Carbon Nanotube the future of VLSI interconnects?”Design Automation Conference, 2006 43rd ACM/IEEE 24-28 July 2006 Page(s):809 – 814.
� [3] N. Srivastava, R.V. Joshi and K. Banerjee, “Carbon Nanotube Interconnects: Implications for Performance, Power Dissipation and Thermal Management,”IEDM, 2005, pp. 257-260.
� [4] Burke, P.J. “An RF circuit model for carbon nanotubes,” Nanotechnology, IEEE Transactions, Volume 2, Issue 1, March 2003, Page(s):55 – 58.
� [5] International Technology Roadmap for Semiconductors, 2006.� [6] Luigi Dilillo, Patrick Girard, Serge Pravossoudovitch, Arnaud Virazel
“Comparison of open and resistive open defect test conditions in address decoders,” Proceedings of the 12th Asian Test Symposium (ATS’03).
6/22/200727
Acknowledgement
•National Science Foundation
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