Carbon Nanomaterials for Next Carbon Nanomaterials for Next - - PowerPoint PPT Presentation

SLIDE 1

Kaustav Banerjee, UCSB KEYNOTE: 12th IEEE Workshop on Signal Propagation on Interconnects (SPI), Avignon, France, May 15th, 2008

Carbon Nanomaterials for Next Generation I nterconnects and Passives Carbon Nanomaterials for Next Generation I nterconnects and Passives

Prof.

• Prof. Kaustav

Kaustav Banerjee Banerjee

University of California, Santa Barbara University of California, Santa Barbara

kaustav@ece.ucsb.edu kaustav@ece.ucsb.edu

NSF-SRC-SIGDA-DAC Design Automation Summer School, July 25-26 2009, San Francisco, CA

SLIDE 2

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I : Part I :

• Limitations of Copper Interconnects

Limitations of Copper Interconnects

• Carbon

Carbon Nanomaterials Nanomaterials: Basics : Basics

• Circuit Elements of CNT/GNR

Circuit Elements of CNT/GNR

• Fabrication and Integration of CNT/GNR

Fabrication and Integration of CNT/GNR Interconnects Interconnects Part I I : Part I I :

• Performance Evaluation of CNT/GNR Interconnects

Performance Evaluation of CNT/GNR Interconnects

• Electro

Electro-

• thermal Analysis of CNT

thermal Analysis of CNT Vias Vias

• High

High-

• Frequency Analysis of CNT Interconnects

Frequency Analysis of CNT Interconnects

• Passives and Other Applications

Passives and Other Applications

SLIDE 3

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Part I Part I

SLIDE 4

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

I nterconnects in I Cs…. I nterconnects in I Cs….

By volume, I Cs have become “all wires”… I nterconnects have become the dominant player in circuit timing and process complexity…

SEM image of IBM’s six-level Cu interconnect technology

SLIDE 5

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Future I nterconnect Requirements: 2005 I TRS

End of the Road for Cu? End of the Road for Cu?

Red Areas: no known solutions! from 2014 onwards: Jmax > 1.06 x 107 A/ cm2

SLIDE 6

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

What is Wrong with Cu? What is Wrong with Cu?

• Size effect on Cu resistivity

Size effect on Cu resistivity

• S. Im et al., IEEE TED, Dec. 2005

1 2 3 4 5

Total

Resistivity [μΩ-cm] Technology Node [nm]

Barrier Layer Effect Surface Scattering Grain Boundary Scattering Background Scattering (ρo)

22 32 45 65 90

At 300 K

1 2 3 4 5

Total

Resistivity [μΩ-cm] Technology Node [nm]

Barrier Layer Effect Surface Scattering Grain Boundary Scattering Background Scattering (ρo)

22 32 45 65 90

At 300 K

Intermediate Tier Wires Impact is worse for local wires and vias Increases wire delay: even in local wires

MFP of Cu ~ 40 nm at room temperature

Based on analytical models in Based on analytical models in Steinhogl Steinhogl et al., et al., J. Appl. Phys.

• J. Appl. Phys., 2005.

, 2005.

SLIDE 7

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

I nterconnect Temperature I nterconnect Temperature

Worst case temperature rise with respect to the junction temperature (85ºC)

• S. Im et al., TED, 2005

Cu Resistivity Current density Cu thermal conductivity Low-K dielectric ILD thermal conductivity Temperature rises significantly due to self-heating…..

SLIDE 8

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Current Carrying Capability of Cu Current Carrying Capability of Cu

• Electromigration

Electromigration Lifetime: strongly reduces with temperature Lifetime: strongly reduces with temperature

• Limits maximum current carrying capacity

Limits maximum current carrying capacity… …. .

Current Density (MA/cm2)

• N. Srivastava and K. Banerjee, JOM 2004.

Maximum allowed J based on self- consistent (EM+Self-heating) solutions… Significant deficit in current carrying capacity for local vias…. Increasing via size and/or number will be expensive….

SLIDE 9

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Reliability and Current Carrying Capacity of Carbon Nanotubes Reliability and Current Carrying Capacity of Carbon Nanotubes

• Current density up to 1010

A/ cm2 without heatsink (not embedded in SiO2)

• Equivalent Au-, Cu-, Al-

wires deteriorate at 107 A/ cm2

B.Wei et al. APL 79, 1172 (2001)

SWCNTs [M. Radosavljevic et al., PRB, 2001] and Graphene [K. S. Novoselov et al., Science,

2004] show similar current carrying capacity…

SLIDE 10

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I : Part I :

• Limitations of Copper Interconnects

Limitations of Copper Interconnects

• Carbon

Carbon Nanomaterials Nanomaterials: Basics : Basics

• Circuit Elements of CNT/GNR

Circuit Elements of CNT/GNR

• Fabrication and Integration of CNT/GNR

Fabrication and Integration of CNT/GNR Interconnect Interconnect

SLIDE 11

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Forms of Carbon… Forms of Carbon…

Carbon atom can form several distinct types of valence bonds….

allotropes allotropes

3D: diamond graphite 2D: graphene 1D: nanotube (CNT) nanoribbon (GNR) 0D: fullerenes

SLIDE 12

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

A bit of history…. A bit of history….

SLIDE 13

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Carbon Nanomaterials Carbon Nanomaterials

SLIDE 14

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Carbon Based I nterconnect Materials Carbon Based I nterconnect Materials

Mono-layer Graphene Nano-Ribbon Roll-up Pattern

Graphene

Stack and Pattern Multi-layer Graphene Nano-Ribbon Carbon Nanotubes

SLIDE 15

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

TEM I mages of CNTs TEM I mages of CNTs

5 shells 2 shells 7 shells 1 shell Some of Iijima’s first images of multi-walled CNTs…. SWCNT (Infineon)

SLIDE 16

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

I mages of Graphene I mages of Graphene

Most of crystal’s faces are either Zigzag or armchair edges SEM image of Graphene crystal

• A. K. Geim et al,

Naturematerial, 2007

AFM image of Graphene Nanoribbon X. Li et al, Science, 2008

SLIDE 17

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT/ GNR Crystal Structures CNT/ GNR Crystal Structures

Armchair CNT (3, 3) Zigzag CNT (5, 0) Zigzag GNR Armchair GNR

CNT/GNR have different definitions, but share similar properties…

SLIDE 18

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Chirality of CNTs Chirality of CNTs

• Indices (n, m) represent

Indices (n, m) represent the magnitude of vectors in the magnitude of vectors in the the a a1

1 and

and a a2

2 direction

direction

• CNT

CNT’ ’s s circumference is circumference is determined by magnitude determined by magnitude

• f the
• f the chiral

chiral vector vector C Ch

h

• Diameter

Diameter D D is is

• Roll

Roll-

• up direction (n, m),

up direction (n, m), determines the chirality of determines the chirality of CNTs CNTs

• Metallic:

Metallic: n n-

• m

m = 3i = 3i ( (i i is an is an integer) integer)

1 2 h

C na ma = + r r r

2 2

3

h c c

C D a n nm m π π

−

= = + +

SLIDE 19

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Metallicity of CNT/ GNR Metallicity of CNT/ GNR

2 i C k π ⋅ = ⋅

Periodic boundary condition quantizes the allowed k values If slices hit the apex of cone zero gap

Graphene bandstructure

Otherwise Band gap

i w k π ⋅ = ⋅

• metallic

N=3i-1 GNR n-m=3i n or m = 3i metallic CNT Chiral Zigzag Armchair Similarly, GNR also has boundary condition

SLIDE 20

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Metallic Condition Metallic Condition

C: the chiral vector (circumference) T: the translational vector

Cr: reciprocal vector of T Tr: reciprocal vector of T K: Dirac point of Brillouin zone

Reciprocal space

Cr: Quantized due to circumferential boundary condition

2 3

r

n m XK C + = uuur

Hence, the condition for metallicity is

(2n+m)=3i, or equivalently (n-m)=3i

SLIDE 21

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Band Structure of CNTs with Different Chirality Band Structure of CNTs with Different Chirality

• 1
• 0.5

0.5 1

• 10
• 5

5 10

K

Energy (eV)

• 1
• 0.5

0.5 1

• 10
• 5

5 10

K Energy (eV)

(n, m)= (7, 7) D= 0.95 nm (n, m)= (9, 0) D= 0.7 nm (n, m)= (13, 0) D= 1 nm Zero gap, metallic Zero gap, metallic Semiconducting

SLIDE 22

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Bandgap of CNT vs Diameter Bandgap of CNT vs Diameter

• Bandgap

Bandgap scales with scales with diameter of the diameter of the nanotube due to nanotube due to confinement confinement ~ ~ 0.8eV/D 0.8eV/D

• Additional small gaps

Additional small gaps due to curvature of due to curvature of the the CNTs CNTs

• Large diameter (>5

Large diameter (>5 nm nm) MWCNTs will ) MWCNTs will have a vanishing gap have a vanishing gap @ 300K @ 300K

Kane et al., PRL, 1997

SLIDE 23

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Band Structure and Density of States (DOS) for Small Diameter (SWCNT) Band Structure and Density of States (DOS) for Small Diameter (SWCNT)

• DOS of SWCNT is very small

DOS of SWCNT is very small

• Doping has almost no influence on its DOS

Doping has almost no influence on its DOS

• F. Kreupl, et al., AMC, 2005

SLIDE 24

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Band Structure and DOS for Large Diameter (MWCNT) Band Structure and DOS for Large Diameter (MWCNT)

• DOS of MWCNT is larger

DOS of MWCNT is larger

• Doping can shift Fermi energy and DOS easily

Doping can shift Fermi energy and DOS easily

• F. Kreupl, et al., AMC, 2005

SLIDE 25

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Conducting Channel of CNTs Conducting Channel of CNTs

• For SWCNT = 4

For SWCNT = 4

– – L Lattice degeneracy (x2) attice degeneracy (x2) – – S Spin degeneracy (x2) pin degeneracy (x2)

• F

For MWCNT (depends on diameter)

• r MWCNT (depends on diameter)
• 1
• 0.5

0.5 1

• 10
• 5

5 10

K

( ) , 3

shell

N D aD b D nm ≈ + >

• A. Naeemi, et al., IEEE EDL, 2006

a=0.0612 nm-1, b=0.425

1 exp( ) 1

shell i subbands subbands i F B

N f E E k T = = − +

∑ ∑

Almost Linear with the diameters. Almost Linear with the diameters. Can be approximated by:

tot i i shells shells

N N a D b = = ⋅ +

∑ ∑

(n, m)= (7, 7) SWCNT, D= 0.95 nm

SLIDE 26

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

We can set λ ≈ 1000 D

Electron Mean Free Path (λ) of CNTs Electron Mean Free Path (λ) of CNTs

• Dependence of diameter

Dependence of diameter

– – Metallic shells Metallic shells – – Semiconducting shells Semiconducting shells

2 2 2

3 2 9

ε ψ

πψ λ σ σ = ⋅ + D

• J. Jiang, et al., Phys. Rev. B, 2001

λ α = ⋅

F

v D T

• X. Zhou, et al., Phys. Rev. Lett., 2005
• Based on measurements,

Based on measurements, λ λ~1 ~1μ μm m for D=1nm CNT for D=1nm CNT

Hence, λ is proportional to the diameter.

• J. Y. Park et al., NanoLetter, 2004.

SLIDE 27

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Band Structure of GNRs Band Structure of GNRs

E (eV)

3ka

Metallic ac-GNR N = 44 w = 11 nm E (eV) Semiconducting ac-GNR

3ka

N = 45 0.12 eV w = 11 nm

E0 E1 E2 −E1 −E2

E (eV)

ka

zz-GNR N = 26 w = 11 nm

N = 3m −1 Metallic N = 3m, 3m +1 Semiconducting Always Metallic Small variation of N Negligible change in band structure

• C. Xu et al., TED, 2009

SLIDE 28

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Thermal Transport Thermal Transport

• Quantized thermal conductance

Quantized thermal conductance

• At room temperature

At room temperature – – Electron contribution Electron contribution (4 conduction modes, (4 conduction modes, bandgap bandgap ~ ~ eV eV) ) – – Phonon: A large number of modes ( Phonon: A large number of modes (bandgap bandgap ~ ~ meV meV) )

• H. Li et al., TED, 2009

ka/π

2 2

/3

BT

h κ π κ = ~ 4

el

κ κ

• F. Kreupl, et al., AMC, 2005
• T. Yamamoto, PRL, 2004

Phonon dominates thermal transport!

SLIDE 29

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Basic Properties of Cu, CNT and GNR Basic Properties of Cu, CNT and GNR

~1,000 ~1,000

Bolotin Bolotin, et al., , et al.,

• Phys. Rev. Let.
• Phys. Rev. Let., 2008

, 2008

25,000 25,000

Li, et al., Li, et al.,

• Phys. Rev. Let.
• Phys. Rev. Let., 2005

, 2005

>1,000 >1,000

McEuen McEuen, et al., , et al.,

• Trans. Nano
• Trans. Nano., 2002

., 2002

40 Mean free path (nm) @ room temp.

• 1.47

Shao Shao et al., et al., Appl

• Appl. Phys.

. Phys. Lett Lett. ., 2008 , 2008

• 1.37

Kwano Kwano et al., et al., Nano Nano Lett Lett. ., 2007 , 2007

<1.1

Kane, et al., Kane, et al., Europhys Europhys. . Lett Lett., ., 1998 1998

4

• Temp. Coefficient of

Resistance (10-3 /K) ~3.0 ~3.0-

• 5.0

5.0

Balandin Balandin, et al., , et al., Nano Let. Nano Let., 2008 , 2008

3.0 3.0

Kim, et al., Kim, et al.,

• Phys. Rev. Let.
• Phys. Rev. Let., 2001

, 2001

1.75 1.75-

• 5.8

5.8

Hone, et al., Hone, et al.,

• Phys. Rev. B
• Phys. Rev. B, 1999

, 1999

0.385 Thermal conductivity (×103 W/m-K) 11-63 22.2±2.2 0.22 Tensile strength (GPa) 3800 (graphite) 1356 Melting point (K) >1x10 >1x108

8

Novoselov Novoselov, et al., , et al., Science, Science, 2001 2001

>1x10 >1x109

9

Wei, et al., Wei, et al.,

• Appl. Phys. Let.,
• Appl. Phys. Let., 2001

2001

>1x10 >1x109

9

Radosavljevic Radosavljevic, et al., , et al.,

• Phys. Rev. B
• Phys. Rev. B, 2001

, 2001

107 Max current density (A/cm2) Graphene or GNR MWCNT SWCNT Cu

SLIDE 30

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I : Part I :

• Limitations of Copper Interconnects

Limitations of Copper Interconnects

• Carbon

Carbon Nanomaterials Nanomaterials: Basics : Basics

• Circuit Elements of CNT/ GNR

Circuit Elements of CNT/ GNR

• Fabrication and Integration of CNT/GNR

Fabrication and Integration of CNT/GNR Interconnect Interconnect

SLIDE 31

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT/ GNR Resistances: RQ, RC and RS CNT/ GNR Resistances: RQ, RC and RS

• R

RQ

Q :

: Intrinsic quantum contact resistance Intrinsic quantum contact resistance -

• even for very

even for very short lengths with no scattering and perfect contacts short lengths with no scattering and perfect contacts ( (lowest possible R lowest possible R— —hence need CNT hence need CNT-

• bundles or multi

bundles or multi-

• layer

layer GNRs GNRs) )

• R

RC

C :

: Imperfect parasitic contact resistance ( Imperfect parasitic contact resistance (can be can be high high… …up to 100 K up to 100 KΩ Ω) )

• R

RS

S: length dependent scattering resistance

: length dependent scattering resistance ( (for Length >> MFP = for Length >> MFP =λ λ) )

2

2 h N e =

2

2 h L N e λ =

N = number of conducting channels

SLIDE 32

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT/ GNR Conductance Model CNT/ GNR Conductance Model

2

2 ( )

n n

f q G E dE h E τ ∂ ⎛ ⎞ = − ⎜ ⎟ ∂ ⎝ ⎠

∫

Linear response Landauer formula

Gn: Conductance of the nth conduction channel f0(E): Fermi-Dirac distribution function τn(E): Transmission coefficient

2

2

n

q G M h τ = ⋅ ⋅

( )

1

1 exp

n F B n

M E E k T

−

⎡ ⎤ = + − ⎣ ⎦

∑

M: Total number of conducting channel If all channels are identical, it can be simplified as: τ: Effective transmission coefficient Can be calculated from bandstructure τ = 1, if it is ballistic, otherwise…

• H. Li et al., TED, vol. 56, no. 9. 2009

SLIDE 33

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT/ GNR Conductance Model (contd.) CNT/ GNR Conductance Model (contd.)

λD: Mean free path corresponding to non-edge scattering mechanisms

1

1 1 ( ) 1 cos cot

n D

E L w τ λ θ θ

−

⎡ ⎤ ⎛ ⎞ = + + ⎢ ⎥ ⎜ ⎟ ⎝ ⎠ ⎣ ⎦

1

( ) 1

n CNT

L E τ λ

−

⎡ ⎤ = + ⎢ ⎥ ⎣ ⎦

λCNT: Mean free path (MFP) of CNT

• C. Xu et al., TED, 2009

SLIDE 34

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

1 10 100 1000 1 10 100

Cu: W=32nm, =4.83 Cu: W=22nm, =6.01 Cu: W=14nm, =8.19

Resistivity [

• cm]

Length [ m]

Comparison of Resistivity Comparison of Resistivity

Area of MWCNT is much larger than that of SWCNT

• short length: MWCNTs have larger resistivity than SWCNTs

However, MWCNTs have longer MFP than SWCNTs

• long length: Rs is much smaller for MWCNTs, so that resistivity
• f MWCNT becomes comparable to SWCNT
• H. Li et al., TED, 2008

( )

Q S

A R R L ρ = +

SLIDE 35

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Resistance Comparison Resistance Comparison

Resistance per micron [ m] Resistance per micron [ m]

• Ideal case SWCNT and DWCNT have similar resistance

Ideal case SWCNT and DWCNT have similar resistance

• For GNR, intercalation doping and high

For GNR, intercalation doping and high specularity specularity are needed are needed

• H. Li et al., TED, vol. 56, no. 9. 2009
• C. Xu et al., TED, vol. 56, no. 8, 2009

Dielectric Mono-layer GNRs w

Mono-layer GNRs

Dielectric Multi-layer GNRs w

Neutral multi-layer GNRs Intercalation doped multi-layer GNRs Dielectric Multi-layer GNRs w Intercalation Layers Graphene Layers

Stage 1 Stage 3 Graphene Layers Intercalation Layers (AsF5) Stage 2

0.815 nm 0.335 nm

SLIDE 36

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT/ GNR Capacitance: CQ and CE CNT/ GNR Capacitance: CQ and CE

{ }

( ) ( ) [ ( )]

F F

Q e dE D E f E E f E E e V = − − − +

∫

δ δ

2

2

F Q

Q C V e hv δ δ = =

2 ( )

e D E V δ =

ES F

E E E Δ = Δ + Δ

2

2 Q C δ =

2 2

2 2

E Q

Q Q C C δ δ + =

1 1 1

E Q

C C C = +

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = d y C CNT

E

4 ln 2πε

Electrostatic Capacitance, CE For single CNT: For other structures, it will depend on the geometry and may need numerical calculation. Adding electron raises up the EF

97 / aF m μ ≈ ~ / aF m μ

SLIDE 37

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Bundle Structure for Estimating CE CNT Bundle Structure for Estimating CE

GND2 GND1 gnd left gnd right CNT Bundle t w s=w w h=t h=t s=w Inner CNTs are effectively screened from the surrounding interconnect geometry

aF/um

• N. Srivastava et al., TNT, 2009

SLIDE 38

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Bundle Electrostatic Capacitance CNT Bundle Electrostatic Capacitance

22 nm 44 nm 14 nm 28 nm 18 nm 36 nm

• N. Srivastava et al., TNT, 2009

SLIDE 39

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

E k E k eδV

CNT/ GNR I nductance: LK and LM CNT/ GNR I nductance: LK and LM

d y

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = d y LCNT

M

4 ln 2π μ

Magnetic inductance, LM

Current I Small density of states cause large total kinetic energy:

16 /

K

L nH m ≈ μ

Scaling by conducting channel number N SWCNT has 4 channels, hence:

~ / pH m μ

4 /

KSWCNT

L nH m μ ≈

For single CNT: LK is 3 orders larger than LM !

2 2

1 2 2

F

h I e v = × ×

E Δ

SLIDE 40

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Existence of Lk Existence of Lk

• High

High-

• Frequency (20GHz)

Frequency (20GHz) S S-

• parameter

parameter measurements for both measurements for both individual SWCNT and individual SWCNT and SWCNT bundle (L=2 SWCNT bundle (L=2μ μm m) )

• Shows L

Shows LK

K of SWCNT is of

• f SWCNT is of
• rder of
• rder of nH

nH/ /μ μm, m, which which agrees with theoretical agrees with theoretical analysis analysis

• The inductance of CNT

The inductance of CNT bundle scales with the bundle scales with the number of number of CNTs CNTs

Plombon et al., Appl. Phys. Let., 2007

In order to analyze inductive effects in CNT interconnects, we need accurate inductance (including kinetic and magnetic) model for CNT bundles…

SLIDE 41

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I : Part I :

• Limitations of Copper Interconnects

Limitations of Copper Interconnects

• Carbon Nanotubes: Basics

Carbon Nanotubes: Basics

• Circuit Elements of CNT/GNR

Circuit Elements of CNT/GNR

• Fabrication and I ntegration of CNT/ GNR

Fabrication and I ntegration of CNT/ GNR I nterconnects I nterconnects

SLIDE 42

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT I nterconnect Fabrication CNT I nterconnect Fabrication

[Nihei et. al., (Fujitsu) IITC, 2007] [Sato et. al., (Fujitsu) IITC, 2006] [Kreupl et. al., (Infineon) IEDM, 2004] [Choi et. al., (Samsung) Nano Conf., 2006] [Awano et al., (Fujitsu) 2006]

SLIDE 43

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT I nterconnect (via) Fabrication CNT I nterconnect (via) Fabrication

Catalytic CVD Growth

nature does it for you….all you need is 3 ingredients

1. Catalyst nanocluster: Fe, Ni or Co + a reducing gas 2. Carbon containing compound (gas): CH4, C2H2, CH3CH2OH…. 3. Energy (Temperature): 400-1400 0C

Substrate –catalyst interaction is also very important….

Courtesy: F. Kreupl, Infineon

SLIDE 44

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Fabrication Techniques & Challenges-I Fabrication Techniques & Challenges-I

• Long throat catalytic deposition (via PVD) in high

aspect ratio trenches

nanotube

Via definition by resist Via etch Long throat catalyst deposition lift-off Nanotube growth

Challenges: i) sidewall deposition causes sidewall CNT growth---via filled but no electrical contact to the bottom! ii) catalyst thickness and nucleation depends strongly on surface condition after etch, results are irreproducible….

Duesberg et al., Nanoletters, 2003

SLIDE 45

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

[Graham et. al., Diamond and Related Materials, 2004, Liebau et al., AIP P., Kirchberg, 2004]

• Buried catalyst layer

Buried catalyst layer

• Etching of via stops on top of 1

Etching of via stops on top of 1-

• 3 nm thick catalyst layer

3 nm thick catalyst layer

Fabrication Techniques & Challenges-I I Fabrication Techniques & Challenges-I I

Challenges: i) etch stop on thin catalyst layer is critical ii) Wafer/chip scale homogeneity not yet demonstrated

Via definition by resist Via etch stop

• n catalyst

Resist strip Nanotube growth

SLIDE 46

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

• S. Sato et al., IITC, 2006
• M. Nihei et. al., IITC, 2007

Diameter-Controlled Nanoparticles Diameter-Controlled Nanoparticles

Size distribution, Diameter: ~ 4 nm, δ: ~25% CMP: to cut-off the cap and make contact with inner shells…

SLIDE 47

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

• Overcomes the need for etching high aspect ratio

Overcomes the need for etching high aspect ratio vias vias needed needed in future technologies in future technologies

• Can reliably grow MWCNT bundles

Can reliably grow MWCNT bundles

Metal Deposition Catalyst Patterning Top Metal Layer Deposition PECVD CMP TEOS CVD

Li et. al., APL, 2003

Alternative Process: Bottom up Alternative Process: Bottom up

Challenges: i) quality of CNTs is low and so is electrical conductivity ii) tilt for small diameter tubes is also considerable---subsequent litho step is difficult

SLIDE 48

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Process I mprovements Process I mprovements

• Densification

Densification

• Increase fraction of metallic

Increase fraction of metallic NTs NTs

• Z. Liu et. al., IITC, 2007]

(a) Before and (b) after densification.

Applying an electrical field makes metallic CNT and semiconducting CNTs to have different movements. Hence, increase the fraction of metallic… However, this method is difficult to combine with CNT interconnect fabrication… and even when they increase the fraction of metallic, the density of CNT is quite low…

Krupke et. al., Science, 2003; Peng, J. Appl. Phys. 2006

Increases the density of CNT bundle by 5~25 times.

SLIDE 49

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Low Temperature CNT Growth Low Temperature CNT Growth

450oC 400oC 365oC

• A. Kawabata et. al., IITC, 2008

Growth temperature down to 365 0C

• the lowest reported for interconnect application.

However, the lower the growth temperature, the worse it gets for CNT quality…

SLIDE 50

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Wafer CNT Wafer

• Y. Hayamizuet. al., Nature Nanotech., 2008

SLIDE 51

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

I ntegration with Low-K Dielectric I ntegration with Low-K Dielectric

CNT Single Kelvin via CNT Single Kelvin via grown at 400 grown at 400 0

0C

C CNT via is robust under current high CNT via is robust under current high-

• density

density stress over long time stress over long time… ….. ..

• A. Kawabata et. al., IITC, 2008

SLIDE 52

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT I nterconnect I ntegration I ssues CNT I nterconnect I ntegration I ssues

• Process Advantages vis

Process Advantages vis-

• à

à-

• vis Copper

vis Copper

– – Diffusivity into Si/dielectric is not a problem Diffusivity into Si/dielectric is not a problem---

• --no need for barrier

no need for barrier – – Bottom Bottom-

• up growth processes can eliminate the need for etching high

up growth processes can eliminate the need for etching high aspect ratio aspect ratio vias vias – – No No “ “dishing dishing” ” type effect type effect… …. .

• Key Issues:

Key Issues: – – Difficult to grow dense high Difficult to grow dense high-

• metallic fraction

metallic fraction SWCNT SWCNT bundles bundles – – Most interconnect processes so far employ Most interconnect processes so far employ MWCNTs MWCNTs which have which have been easier to grow been easier to grow--

• -recently it has become possible to

recently it has become possible to grow grow bundles of SWCNTs bundles of SWCNTs also by adding water or oxygen to increase also by adding water or oxygen to increase activity (to 84%) of the growth catalyst activity (to 84%) of the growth catalyst [Futaba et al.,

[Futaba et al., J. Phys. Chem. B

• J. Phys. Chem. B, 2006]

, 2006]

– – High temperatures High temperatures involved in CNT growth involved in CNT growth— —recently grown at 365 recently grown at 365

0C (Fujitsu), but need better quality.

C (Fujitsu), but need better quality. – – Metal Metal-

• CNT

CNT contact resistance contact resistance – – Control over growth mode Control over growth mode (substrate (substrate-

• catalyst interaction)

catalyst interaction)

• H. Li et al., TED, vol. 56, no. 9. 2009

SLIDE 53

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Graphene Fabrication Methods and I mplication for I nterconnect Application Graphene Fabrication Methods and I mplication for I nterconnect Application

• 1. Chemical vapor deposition
• - Not single crystal; low electrical conductivity
• 2. Thermal decomposition of single crystal SiC
• - Requires high processing temperature
• 3. Mechanical exfoliated from graphite, and deposited
• nto an insulating substrate
• - Uncontrollable for massive fabrication
• 4. Segregation, transferring and removing substrate
• - Seems OK, will be explained in the next slide
• G. Aichmayr, IEEE Symp. VLSI Tech. 2007
• C. Berger, Science, 2006
• J. C. Meyer, Nature, 2007
• Q. Yu, APL, 2008

SLIDE 54

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

GNR I nterconnect Fabrication… GNR I nterconnect Fabrication…

Nickel Substrate Nickel Substrate Segregate Transfer to desired substrate Nickel Substrate Silicone film Nickel Substrate Desired substrate

Implication from Q. Yu, APL, 2008

Nickel Substrate Silicone film Desired substrate Silicone film Remove Nickel Desired substrate Silicone film Graphene Graphene Graphene Graphene Graphene Pattern GNR wire Desired Substrate Silicone film Pattern & make via contacts Desired Substrate Silicone film GNR Graphene

• C. Xu et al., TED, 2009

SLIDE 55

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Hybrid Graphene/ CNT I nterconnects Hybrid Graphene/ CNT I nterconnects

http://www.fujitsu.com/global/news/pr/archives/month/2008/20080303-01.html

• Vertical via is based on

Vertical via is based on CNTs CNTs and horizontal wire is based and horizontal wire is based CNTs CNTs

SLIDE 56

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Part I : References (1) Part I : References (1)

Limitations of Cu Limitations of Cu

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• f Copper Wires With Lateral Dimensions of 100 nm and Smaller”

”. .

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Xu, N. , N. Srivastav Srivastav, K. , K. Banerjee Banerjee, , “ “Carbon Carbon Nanomaterials Nanomaterials for Next Generation Interconnects and Passives: for Next Generation Interconnects and Passives: Physics, Status and Prospects Physics, Status and Prospects” ”. .

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Xu, H. Li, and K. , H. Li, and K. Banerjee Banerjee, , “ “Modeling, Analysis and Design of Graphene Modeling, Analysis and Design of Graphene Nano Nano-

• Ribbon Interconnects

Ribbon Interconnects” ”

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Srivastav, H. Li, F. , H. Li, F. Kreupl Kreupl, and K. , and K. Banerjee Banerjee, , “ “On the Applicability of Single On the Applicability of Single-

• Walled Carbon Nanotubes as VLSI

Walled Carbon Nanotubes as VLSI Interconnects Interconnects” ”

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Imperial College Press, 1998. London, U. K.

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SLIDE 57

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Part I : References (2) Part I : References (2)

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Anantram and F. and F. L Lé éonard

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Liew, C. H. Wong, X. Q. He, and M. J. Tan, , C. H. Wong, X. Q. He, and M. J. Tan, “ “Thermal stability of single and multi Thermal stability of single and multi-

• walled carbon nanotubes

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Novoselov, A. K. , A. K. Geim Geim, S.V. , S.V. Morozov Morozov, D. Jiang, Y. Zhang, , D. Jiang, Y. Zhang, S.V.Dubonos S.V.Dubonos, , I.V.Grigorieva I.V.Grigorieva, and , and A.A.Firsov A.A.Firsov, , “ “Electric Electric field effect in atomically thin carbon films field effect in atomically thin carbon films” ” CNT/ GNR I nterconnect Fabrication CNT/ GNR I nterconnect Fabrication

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• up Approach for Carbon Nanotube

up Approach for Carbon Nanotube Interconnects Interconnects“ “. .

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Shioya, M. , M. Sakaue Sakaue, T. Iwai, M. , T. Iwai, M. Ohfuti Ohfuti, and Y. , and Y. Awano Awano, , “ “Low Low-

• resistance

resistance multi multi-

• walled carbon nanotube

walled carbon nanotube vias vias with parallel channel conduction of inner shells, with parallel channel conduction of inner shells,” ”

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232.

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Shioya, T. Iwai, M. , T. Iwai, M. Mishma Mishma, M. , M. Ohfuti Ohfuti and Y. and Y. Awano Awano, , “ “Novel Novel approach to fabricating carbon nanotube via interconnects using approach to fabricating carbon nanotube via interconnects using size size-

• controlled catalyst

controlled catalyst nanoparticles nanoparticles” ”. .

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206

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SLIDE 58

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Part I : References (3) Part I : References (3)

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• M. Ohfuti

Ohfuti, H. , H. Kawarada Kawarada, T. Sakai, M. Nihei, and Y. , T. Sakai, M. Nihei, and Y. Awano Awano, , “ “Robustness of CNT via interconnect fabricated by Robustness of CNT via interconnect fabricated by low temperature process over a high low temperature process over a high-

• density current

density current” ”. .

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“Graphene segregated on Ni surfaces and Graphene segregated on Ni surfaces and transferred to insulators transferred to insulators” ”

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Cai, J. An, S. Kim, J. Nah, D. Yang, R. , J. An, S. Kim, J. Nah, D. Yang, R. Piner Piner, A. , A. Velamakanni Velamakanni, I. Jung, E. , I. Jung, E. Tutuc Tutuc, S. K. , S. K. Banerjee Banerjee, L. , L. Colombo, R. S. Colombo, R. S. Ruoff Ruoff, , “ “Large Large-

• Area Synthesis of High

Area Synthesis of High-

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Quality and Uniform Graphene Films on Copper Foils” ”

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• dimensional

dimensional microelectromechanical microelectromechanical devices from devices from processable processable carbon nanotube wafers, carbon nanotube wafers,” ”

SLIDE 59

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Part I I Part I I

SLIDE 60

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I : Part I :

• Limitations of Copper Interconnects

Limitations of Copper Interconnects

• Carbon

Carbon Nanomaterials Nanomaterials: Basics : Basics

• Circuit Elements of CNT/GNR

Circuit Elements of CNT/GNR

• Fabrication and Integration of CNT/GNR Interconnects

Fabrication and Integration of CNT/GNR Interconnects Part I I : Part I I :

• Performance Evaluation of CNT/ GNR

Performance Evaluation of CNT/ GNR I nterconnects I nterconnects

• Electro

Electro-

• thermal Analysis of CNT

thermal Analysis of CNT Vias Vias

• High

High-

• Frequency Analysis of CNT Interconnects

Frequency Analysis of CNT Interconnects

• Passives and Other Applications

Passives and Other Applications

SLIDE 61

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Equivalent Circuit Equivalent Circuit

• H. Li et al., TED, vol. 56, no. 9,

2009

• H. Li et al., TED, 2008

SWCNT and GNR MWCNT (including DWCNT)

SLIDE 62

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Delay Comparison: Local I nterconnects Delay Comparison: Local I nterconnects

• Ideal SWCNT and DWCNT are similar

Ideal SWCNT and DWCNT are similar

• MWCNT has better performance due to smaller capacitance

MWCNT has better performance due to smaller capacitance

• For GNR, intercalation doping and high

For GNR, intercalation doping and high specularity specularity are needed are needed

– – Some Mono Some Mono-

• layer could have low delay due to much smaller capacitance

layer could have low delay due to much smaller capacitance

Delay Ratio w.r.t Cu Delay Ratio w.r.t Cu

W=14 nm H = 28 nm

• H. Li et al., TED, vol. 56, no. 9, 2009

SLIDE 63

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Delay Comparison: I ntermediate and Global Delay Comparison: I ntermediate and Global

100 1000 0.4 0.6 0.8 1.0 1.2 1.4

Length of Interconnect [ m]

Intermediate Global 14 nm technology node

• Almost all

Almost all CNTs CNTs could outperform Cu could outperform Cu

• For GNR, intercalation doping and high

For GNR, intercalation doping and high specularity specularity are needed are needed

• H. Li et al., TED, vol. 56, no. 9, 2009

SLIDE 64

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I I : Part I I :

• Performance Evaluation of CNT/GNR Interconnects

Performance Evaluation of CNT/GNR Interconnects

• Electro

Electro-

• thermal Analysis of CNT

thermal Analysis of CNT Vias Vias

• High

High-

• Frequency Analysis of CNT Interconnects

Frequency Analysis of CNT Interconnects

• Passives and Other Applications

Passives and Other Applications

SLIDE 65

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Interface effect Short length Bundle density

Expectation vs. Reality of CNT Vias Expectation vs. Reality of CNT Vias

Provide guidelines to fabrication community

Expectation

Ideally, ballistic transport High thermal conductivity

• Isolated SWCNT

>2000 W/mk (L=2.76μm)

• C. Yu et al., Nano Letter, 2005
• Isolated MWCNT

>3000 W/mk (L=2.5 μm, D=14 nm)

• P. Kim et al., PRL, 2001

Reality

Reliability is a more important concern in CNT via Need accurate electro-thermal analysis

SLIDE 66

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Electrically Ballistic CNT Vias Electrically Ballistic CNT Vias

For SWCNT: λ >300nm even in worst case (D = 0.4nm @110oC). For MWCNT: λ will be longer than SWCNT due to large diameter. From ITRS, height of vias will always be smaller than λ. It’s safe to assume that CNT vias are electrically ballistic conductors Local Global

• Resistance of ballistic CNT

Resistance of ballistic CNT

λ = < ,

Q

R R length N N: Number of conducting channels

• H. Li et al., IEDM, 2007

SLIDE 67

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Via: Resistance CNT Via: Resistance

MWCNT via SWCNT via RMWCNT Via > RSWCNT Via > RCu Via (<100Ω) ( ~10Ω)

• H. Li et al., IEDM, 2007

CNT via can always be assumed to be electrically ballistic... With perfect contact, only smallest SWCNTs have comparable resistance to Cu With non-zero Rmc, SWCNT resistance will be even larger than Cu

5 10 15 20 300 350 400 450 500 200 400 600 800 Diameter [nm] Via Resistance [Ω]

SLIDE 68

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

I mpact of Via Resistance on I nterconnect Delay I mpact of Via Resistance on I nterconnect Delay

Local interconnect (M1) Global interconnect (buffered) Local via resistance has slight impact on interconnect performance (electrical latency)

10 20 30 40 50 1 2 3 4 5

RCNT/R

Cu

32 nm 22 nm 14 nm

Local Global Global via resistance could have larger impact on performance If CNT resistance can be within an order of magnitude of Cu via resistance, the delay penalty is small….

• H. Li et al., IEDM, 2007

SLIDE 69

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Thermal Transport in CNT Vias: I s I t Ballistic? Thermal Transport in CNT Vias: I s I t Ballistic?

• Phonon mean free path (

Phonon mean free path (L Lo

• )

)

,

( ) ( ) ( , ) 2

n

th n n n n n v

dq f G q v q q T

>

∂ = ∂

∑ ∫

hω τ ω π

L=2.76 μm, D=1 nm (SWCNT), T= 100-300 K, ballistic Lo >2.76 μm L=2.5 μm, D=14 nm (MWCNT), T= 10-300 K, estimated Lo ~500 nm

• C. Yu et al., Nano Letter, 2005
• J. Wang and J. Wang, APL, 2006
• N. Mingo et al., PRL, 2005
• P. Kim, et al., PRL, 2001

CNT vias (<300 nm) can be regarded as thermal ballistic

• Ballistic thermal conductance model of CNT

Ballistic thermal conductance model of CNT

ω(q): phonon dispersion, f(ω,T) is Bose-Einstein distribution function

SLIDE 70

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Thermal Conductivity of CNT Thermal Conductivity of CNT

KCNT increases with temperature Smaller diameter SWCNT has higher KCNT For long length, KCNT >> KCu For short length (via case), KCNT ~ KCu

Thermal conductivity (KCNT) as a function of D, T and L

• H. Li et al., IEDM, 2007

SLIDE 71

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Electro-thermal Simulations Electro-thermal Simulations

Cu: Tmax occurs at M2 SWCNT (D = 0.47nm): Perfect contact Tmax occurs at M2, ~ Tmax of Cu MWCNT (D =5 nm): Perfect contact Tmax >> Tmax of Cu

• Contact is the bottleneck
• Large Joule heating due to large

electrical contact resistance

• H. Li et al., IEDM, 2007

SLIDE 72

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

I mpact of I ncreasing Via Height I mpact of I ncreasing Via Height

Tmax of Cu via increases with height Tmax of SWCNT via almost remains constant Even with imperfect contact, SWCNT could be better than Cu for tall vias MWCNT via is worse than Cu even at 300nm height Advantage of ballistic CNT: KCNT Via and RCNT Via remains the same for tall vias Dense and small diameter SWCNT vias with good electrical and thermal contact are needed…..and would be better as tall vias

• Max. Temperature [K]
• H. Li et al., IEDM, 2007

SLIDE 73

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I I : Part I I :

• Performance Evaluation of CNT/GNR Interconnects

Performance Evaluation of CNT/GNR Interconnects

• Electro

Electro-

• thermal Analysis of CNT

thermal Analysis of CNT Vias Vias

• High

High-

• Frequency Analysis of CNT I nterconnects

Frequency Analysis of CNT I nterconnects

• Passives and Other Applications

Passives and Other Applications

SLIDE 74

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

High-Frequency Effects in Cu High-Frequency Effects in Cu

• Resistance increases due

Resistance increases due to skin & proximity to skin & proximity effects effects

Krauter et al., DAC, 1998

Skin effect Proximity effect

• Current distribution is no

Current distribution is no longer uniform longer uniform Z = R + j ω L

What will happen in CNT interconnects?

1 δ πμσ = f

Skin depth:

SLIDE 75

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

2 4

ln ln ln ln 0.1( ), / 2.51, 0.31, 3.81, 1.61 2

• ut

in

• ut
• ut

GMD D a b c d D D a b c d D AMD ξ ζ γ γ γ γ π = − = − − + = = = = = ≈

Magnetic I nductance of I ndividual CNT Magnetic I nductance of I ndividual CNT

2 2 2 2

ln 1 1 2 μ π ⎡ ⎤ ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ = ⋅ ⋅ + + − + + ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦

m

L L S S L L S L S L

Using Geometric Mean Distance (GMD) to calculate inductance. GMD is valid if we assume current in each CNT to be uniform.

• Self

Self-

• inductance

inductance

• Mutual inductance

Mutual inductance

S

2 ln 1 2

self CNT

L AMD L L GMD L μ π ⎡ ⎤ = ⋅ − + ⎢ ⎥ ⎣ ⎦

Arithmetic Mean Distance

• H. Li et al., TED, vol. 56, no. 10, 2009

SLIDE 76

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

I mpedance of CNT Bundle I mpedance of CNT Bundle

• Impedance matrix

Impedance matrix

[ ]

1 21 1 21 2 2 1 2 n CNT m m n m CNT m matrix n n n m m CNT

Z j L j L j L Z j L Z j L j L Z ω ω ω ω ω ω ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ L L M M O M L

Each self-impedance (Zi

CNT) includes R, Lself, and LK

Effective value of total inductance and total resistance

• f CNT bundle can be calculated

, (1 / ), 6.5 , 1/ 1/ , (1 / ) / , 1000

i CNT Q Q i CNT shell shell Q shell shell

SWCNT R R L R K MWCNT R R R R L N D λ λ λ = + = Ω = = + =

∑

= + + ( )

i Self kinetic i CNT CNTi CNTi CNT

Z j L L R ω

[ ] [ ][ ]

bundle tot to matri t x

V Z I Effective Z R j L ω = + = ⇒

• H. Li et al., TED, vol. 56, no. 10, 2009

SLIDE 77

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Understanding of Current Redistribution Understanding of Current Redistribution

Impedance of each filament Impedance of each filament

• 3D metal: no L

3D metal: no LK

K

– low frequency, R (Zself) dominates, Z1~Z2 – high frequency, jωL becomes important

1 2 Mutual Mutual

Z > Z

1 2

• CNT: has large L

CNT: has large LK

K

1 2

Self mutual

Z = Z + Z

Self Mutual

Z >> Z

Z1 ~ Z2 Negligible skin effect

Self self K

Z = R + j L + j L ω ω

Z1> Z2 nonuniform current skin effect

LK > > LMutual ，

SLIDE 78

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

High-Frequency I mpedance of CNT High-Frequency I mpedance of CNT

• SWCNT: resistance/inductance saturate at high frequencies
• MWCNT: resistance/inductance negligible shift
• Reduced skin effect in CNT interconnect!

1 10 100 1000 5 10 15 20 25 30

Equivalent d.c. Conductivity Model Length = 500 μm Width=2μm, Height=1μm Cu wire SWCNT D=1nm, Fm=1 MWCNT D=20nm MWCNT D=40nm

Resistance [Ω] Frequency [GHz]

1 10 100 1000 0.60 0.62 0.64 0.66 0.68

Equivalent d.c. Conductivity Model Length = 500 μm Width=2μm, Height=1μm

Inductance [nH] Frequency [GHz]

MWCNT D=40nm MWCNT D=20nm SWCNT D=1nm Fm=1 Cu wire

• H. Li et al., TED, vol. 56, no. 10, 2009

SLIDE 79

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

High-Frequency Behavior of CNT Bundle—From Maxwell’s Equations High-Frequency Behavior of CNT Bundle—From Maxwell’s Equations

2 E

j E ωμσ ∇ = u r u r

2 2

2 [( ) 1] ( ) 1 δ ωτ ωτ ωτ ωμσ ⎡ ⎤ = ⋅ + ⋅ + − ⎣ ⎦

Skin Depth [ m]

• H. Li et al., TED, vol. 56, no. 10, 2009
• CNT: skin depth saturates after

certain frequencies

• Saturation depends on the

momentum relaxation time

• MWCNT has largest skin depth

and lowest saturation frequency ωτ~1 ωτ<<1

SLIDE 80

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Outline Outline

Part I I : Part I I :

• Performance Evaluation of CNT/GNR Interconnects

Performance Evaluation of CNT/GNR Interconnects

• Electro

Electro-

• thermal Analysis of CNT

thermal Analysis of CNT Vias Vias

• High

High-

• Frequency Analysis of CNT Interconnects

Frequency Analysis of CNT Interconnects

• Passives and Other Applications

Passives and Other Applications

– – CNT Based Inductors and Capacitors CNT Based Inductors and Capacitors – – CNT Off CNT Off-

• chip Applications

chip Applications – – CNT NEMS CNT NEMS – – CNT ESD applications CNT ESD applications – – System System-

• level Applications

level Applications

SLIDE 81

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Based I nductor CNT Based I nductor

• Metal contact at each corner

Metal contact at each corner

• Take advantage of high

Take advantage of high-

• frequency properties of CNT

frequency properties of CNT bundle bundle

Metal Contact CNT Bundle

S W

Dout

• Ls & Rs: Using previous method

– Ls: including kinetic and magnetic inductance – Rs: includes RQ, RS, and Rmc

• Since the CNT bundle cross-sectino is

very large (μm order), CQ is very large and can be neglected

• C

CS

S, C

, Cox

• x and

and C Csub

sub is using distributed

is using distributed capacitance model capacitance model

• L

Leddy

eddy and R

and Reddy

eddy are captured by complex

are captured by complex image theory image theory

I I

• H. Li et al., TED, vol. 56, no. 10, 2009

SLIDE 82

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

( )

tot upbound m k mag kinetic

L Q L L Q Q R R ω ω = = + = +

I mpact of Kinetic I nductance on Q-factor I mpact of Kinetic I nductance on Q-factor

1 1 1

k k Q Q

L L R R L λ ω ω λ ⋅ = < ⋅ ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠

_

/ 1 ω ω λ × = = ⎛ ⎞ + ⎜ ⎟ ⎝ ⎠

K Bundle k kinetic Bundle Q

L L L N Q L R R N

λ=1μm, Lk=4nH/μm, RQ=6.5KΩ Qkinetic< 0.062 at 100 GHz

Kinetic inductance itself has very little impact on Q…

Traditional Q factor Q factor due to LK

• Consider upper

Consider upper-

• bound of Q factor

bound of Q factor ω ωL Ltot

tot/R

/R

– – Has two component in CNT Has two component in CNT

Q factor due to LK

10 10

1

10

2

10

3

10

4

0.01 0.02 0.03 0.04 0.05 0.06 0.07 10GHz 50GHz 100GHz

• H. Li et al., TED, vol. 56, no. 10, 2009

SLIDE 83

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Role of Kinetic I nductance Role of Kinetic I nductance

• Although, L

Although, LK

K itself has marginal impact on Q factor

itself has marginal impact on Q factor… …

– – L LK

K increases the total inductance

increases the total inductance – – More importantly, L More importantly, LK

K reduces skin & proximity effects

reduces skin & proximity effects at high frequency in CNT interconnects at high frequency in CNT interconnects – – Prevents decrease of total inductance with frequency Prevents decrease of total inductance with frequency – – Prevents increase of resistance with frequency Prevents increase of resistance with frequency

• Very promising for high

Very promising for high-

• frequency interconnect

frequency interconnect application application

– – Inductor design: potential low loss, high Inductor design: potential low loss, high-

• Q

Q… …

SLIDE 84

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Q Factor Comparison Q Factor Comparison

• CNT can give better performance than Cu

CNT can give better performance than Cu – – MWCNT can obtain 2.4 times higher Q factor than that of Cu MWCNT can obtain 2.4 times higher Q factor than that of Cu – – Even for higher resistivity case (D=10 nm), still have higher Q Even for higher resistivity case (D=10 nm), still have higher Q – – I ndicating reduced skin effect has significant impact I ndicating reduced skin effect has significant impact

Resistivity [

• cm]

Dout=200 μm, N=4, W=10 μm, H=2 μm, S=1 μm

0.1 1 10 10 20 30 40 50 60 70

(a)

Frequency [GHz]

142%

ρsub= 10 Ω-cm

Cu SWCNT Fm=1/3 SWCNT Fm=1 MWCNT D=10nm MWCNT D=20nm MWCNT D=40nm

Quality Factor

• H. Li et al., TED, vol. 56, no. 10, 2009

SLIDE 85

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Q Factor Comparison (Ultra High-Frequency) Q Factor Comparison (Ultra High-Frequency)

• Advantage of CNT is enhanced for ultra

Advantage of CNT is enhanced for ultra-

• high

high-

• frequency

frequency applications applications

• Maximum Q factor enhancement is 3.3 times!

Maximum Q factor enhancement is 3.3 times!

1 10 100 20 40 60 80 100

231% 60GHz

ρsub= 10 Ω-cm

MWCNT D=10nm MWCNT D=20nm MWCNT D=40nm Cu SWCNT Fm=1/3 SWCNT Fm=1

Quality Factor

Frequency [GHz]

• H. Li et al., TED, vol. 56, no. 9, 2009

SLIDE 86

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Based Capacitor CNT Based Capacitor

Expectation of CNT capacitor: Expectation of CNT capacitor:

• High density due to small form factor of

High density due to small form factor of CNTs CNTs

• High aspect ratio, especially for DRAM applications

High aspect ratio, especially for DRAM applications

• Lower electrode resistance

Lower electrode resistance

• Higher Q factor

Higher Q factor

• Higher switching speed

Higher switching speed Important concern: Important concern:

• Lower leakage current

Lower leakage current

SLIDE 87

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Fabricated MWCNT Based Capacitor Fabricated MWCNT Based Capacitor

• J. E. Jang, et.al., ESSDERC, 2005

Diameter: 70nm Height of MWCNT: 3.5um Insulator thickness: 65nm

6.5fF/μm2 1e-8 A/cm2

(ITRS 2014)

Can not match the ITRS requirement at 2014, need more efforts…

10 μm

SLIDE 88

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Based Capacitors CNT Based Capacitors

28.99 30.25 Square (Sparse, d = 20 nm) 38.39 39.48 Square (Dense, d = 0.34 nm) 30.65 31.76 Circular Total effective capacitance density (including CQ, fF/μm2) Electrostatic capacitance density (fF/μm2)

Height = 1 μm Take advantage of bottom up approach to achieve high aspect ratio…

20 nm 20 nm

(a) Circular

210 nm 480 nm

Much larger than ITRS requirement for 2014: 7 fF/μm2

• H. Li et al., TED, vol. 56, no. 9, 2009

SLIDE 89

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Off-chip Applications CNT Off-chip Applications

Some Concerns and Requirements Some Concerns and Requirements

• Form factor:

Form factor:

– – Number of I/O pads Number of I/O pads – – Area of pads Area of pads – – Smaller form factor is required Smaller form factor is required

• Low parasitics:

Low parasitics:

– – Lower inductance Lower inductance – – Lower noise Lower noise

• Good thermal properties

Good thermal properties

– – Heat dissipation Heat dissipation

• High predictability

High predictability

– – Easier to model and design Easier to model and design

• High reliability

High reliability

– – Electromigration Electromigration – – Thermal/Mechanical Thermal/Mechanical

SLIDE 90

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Example 1: Flip-chip Bumps Example 1: Flip-chip Bumps

• T. Iwai et al., IEDM., 2005 (Fujitsu)

12μm

MWCNT, D~10 nm

SLIDE 91

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Example 2: TI M for Packaging Example 2: TI M for Packaging

• K. Zhang et al., ICEPT., 2006 (HKUST)

MWCNT, D= 20-30 nm Length ~ 50 μm

SLIDE 92

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Example 3: Chip Cooling Example 3: Chip Cooling

• K. Kordas et al., APL, 2007 (RPI )

MWCNT, Length~1.2 mm, D= 10-90 nm CNT Heat Spreader, 1*1 mm

N2 gas flow

SLIDE 93

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Transfer Tech. CNT Transfer Tech.

• High temperature CVD

High temperature CVD growth (@ 775 growth (@ 775 o

• C

C) )

• Open

Open-

• ended

ended CNTs CNTs

• Low temperature

Low temperature bonding (@ 270 bonding (@ 270 o

• C

C) )

• Substrate is Cu

Substrate is Cu

• L. Zhu et al., Nano Lett., 2006;
• L. Zhu et al., MRSSP, 2007

Open-ended CNTs Closed-ended CNTs CNTs break along the axis rather than at the CNT-solder interface

SLIDE 94

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT Vias in 3D-I C Applications CNT Vias in 3D-I C Applications

CNT through CNT through-

• wafer via

wafer via

• High aspect ratio (>10)

High aspect ratio (>10)

• Long length (>100

Long length (>100 μ μm m) ) Process steps: Process steps:

① ①

Through holes in the top wafer Through holes in the top wafer

② ②

Bonding layer is deposited onto Bonding layer is deposited onto top wafer top wafer

③ ③

Catalyst film is deposited onto the Catalyst film is deposited onto the bottom layer bottom layer

④ ④

Two wafers are bonded together Two wafers are bonded together

⑤ ⑤

Grow CNT via thermal CVD Grow CNT via thermal CVD

• T. Xu et al., APL., 2007

SLIDE 95

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT NEMS…. CNT NEMS….

• CNT NEMS can operate in

CNT NEMS can operate in GHz GHz range due to very small mass range due to very small mass

CNT-based Relay

Lee, et al. Appl. Phys. 2003

• H. Dadgour et al., IEDM, 2008

SLIDE 96

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

ESD Metal Current Density ESD Metal Current Density

• Failure current decreases with scaling

Failure current decreases with scaling

• High current carrying capability material will be preferred

High current carrying capability material will be preferred

• C. Duvvury, IEDM., 2008

SLIDE 97

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Using CNT to Enhance Charge Dissipation Using CNT to Enhance Charge Dissipation

• The rate of charge dissipation is governed by

The rate of charge dissipation is governed by τ τ= =ρε ρε

– – ρ ρ, resistivity of material , resistivity of material – – ε ε, permittivity of material , permittivity of material

• Applications in Polymer filling

Applications in Polymer filling

– – By filling MWCNT, it will By filling MWCNT, it will

• ρ

ρ is small since MWCNT has good conductance is small since MWCNT has good conductance

• ε

ε is small since the filling fraction could be small due to its h is small since the filling fraction could be small due to its high aspect ratio igh aspect ratio

– – Desirable for fast charge dissipation Desirable for fast charge dissipation

• One of the largest bulk application of

One of the largest bulk application of CNTs CNTs today today

– – Company: Company: Hyperison Hyperison Catalysis International Catalysis International

Hyperion Catalysis (www.fibrils.com)

SLIDE 98

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

ESD Protection Using MWCNTs in Polymer ESD Protection Using MWCNTs in Polymer

Hyperion Catalysis (www.fibrils.com)

SLIDE 99

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

CNT I nterconnects: System-Level Applications ? CNT I nterconnects: System-Level Applications ?

CNT I nterconnect Enhanced: CNT I nterconnect Enhanced:

• Memory (Cache) design

Memory (Cache) design

• FPGA design

FPGA design

• Network

Network-

• on
• n-
• chip design

chip design

• Multi

Multi-

• core processor design

core processor design

Note: it is important to use the correct physical and compact models for CNT/GNR, depending

• n the application….

SLIDE 100

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Summary Summary

1 10 100 1000 10

Length = 500 μm Width=2μm, Height=1μm

20 2 4 6 8

Cu wire SWCNT D=1nm, Fm=1 MWCNT D=20nm MWCNT D=40nm

Resistance [Ω] Frequency [GHz]

Lower Lower latency latency for long for long wires wires Negligible skin effects Promising for passive devices Promising for passive devices Off-Chip and Through-Silicon Vias

100 1000 0.4 0.6 0.8 1.0 1.2 1.4

SWCNT ( Fm=1) SWCNT ( Fm=1/3) DWCNT (D=1.5nm) MWCNT (D=14nm) d-GNR (p =0.41) d-GNR (p=1)

Length of Interconnect [ m]

Metal Contact CNT Bundle

S W

Dout

SLIDE 101

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Part I I : References (1) Part I I : References (1)

CNT Modeling CNT Modeling

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IEEE Trans. Electron Device, vol. 56, no. 10, Oct. 2009.

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• H. Li, and K. Banerjee

Banerjee, , “ “High High-

• frequency analysis of carbon nanotube interconnects and implicat

frequency analysis of carbon nanotube interconnects and implications for on ions for on-

• chip

chip inductor design, inductor design,” ”

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IEEE Trans. Electron Devices, vol. 56, no. 9, Sep. 2009

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• H. Li, C. Xu

Xu, N. , N. Srivastav Srivastav, K. , K. Banerjee Banerjee, , “ “Carbon Carbon Nanomaterials Nanomaterials for Next Generation Interconnects and Passives: for Next Generation Interconnects and Passives: Physics, Status and Prospects Physics, Status and Prospects” ”

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IEEE Trans. Electron Devices, vol. 56, no. 8, pp. 1567-

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1578 Aug 2009. C.

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Xu, H. Li, and K. , H. Li, and K. Banerjee Banerjee, , “ “Modeling, Analysis and Design of Graphene Modeling, Analysis and Design of Graphene Nano Nano-

• Ribbon Interconnects

Ribbon Interconnects” ”

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IEEE Trans. Nanotechnology, vol. 8, no. 4, pp. 542-

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559, July, 2009. N.

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Srivastav, H. Li, F. , H. Li, F. Kreupl Kreupl, and K. , and K. Banerjee Banerjee, , “ “On the Applicability of Single On the Applicability of Single-

• Walled Carbon Nanotubes as VLSI

Walled Carbon Nanotubes as VLSI Interconnects Interconnects” ”

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IEEE Trans. Electron Device, pp. 1328-

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1337, June, 2008.

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“Circuit modeling and performance analysis of multi Circuit modeling and performance analysis of multi-

• walled carbon

walled carbon nanotube interconnects nanotube interconnects” ”

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210. H Li, N. Srivastava, J. F. Mao, W. Y. Yin, and K. Banerjee, H Li, N. Srivastava, J. F. Mao, W. Y. Yin, and K. Banerjee, “ “Carbon nanotube Carbon nanotube vias vias: a reality check : a reality check” ”

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885.

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• K. Banerjee and N. Srivastava, “

“Are carbon nanotubes the future of VLSI Interconnections Are carbon nanotubes the future of VLSI Interconnections” ”

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260.

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• N. Srivastava, R. V. Joshi and K. Banerjee, “

“Carbon nanotube interconnects: implications for performance, pow Carbon nanotube interconnects: implications for performance, power er dissipation and thermal management dissipation and thermal management” ”

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390.

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“Performance analysis of carbon nanotube interconnects for VLSI a Performance analysis of carbon nanotube interconnects for VLSI application pplication” ”

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IEEE Trans. Nanotechnology, vol. 1, no. 3, pp. 129-

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144, 2002.

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“Luttinger liquid theory as a model of the gigahertz electrical p Luttinger liquid theory as a model of the gigahertz electrical properties of carbon roperties of carbon nanotubes nanotubes” ”

SLIDE 102

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Part I I : References (2) Part I I : References (2)

CNT Applications CNT Applications

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IEEE Trans. Electron Devices, vol. 56, no. 9, Sep. 2009

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• H. Li, C. Xu

Xu, N. , N. Srivastav Srivastav, K. , K. Banerjee Banerjee, , “ “Carbon Carbon Nanomaterials Nanomaterials for Next Generation Interconnects and Passives: for Next Generation Interconnects and Passives: Physics, Status and Prospects Physics, Status and Prospects” ”. .

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260.

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• T. Iwai et al., Thermal and Source Bumps utilizing CNTs

CNTs for Flip for Flip-

• chip High Power Amplifiers

chip High Power Amplifiers

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• Proc. of ESSDERC, Grenoble, France, 2005
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• J. E. Jang, S. N. Cha, Y. Choi

Choi, D. , D.-

• J. Kang, D. G.
• J. Kang, D. G. Hasko

Hasko, and G. A. J. , and G. A. J. Amaratunga Amaratunga, , “ “Nanoscale Nanoscale capacitors based on capacitors based on metal metal-

• insulator

insulator-

• carbon

carbon naontbue naontbue-

• metal structures

metal structures” ”. .

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Nano Letters, vol. 6, no. 2, pp. 243 Letters, vol. 6, no. 2, pp. 243-

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247, 2006

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• L. Zhu, Y. Sun, D. W. Hess, and C. P. Wong, “

“Well Well-

• aligned open

aligned open-

• ended carbon nanotube architectures: an approach

ended carbon nanotube architectures: an approach for device assembly for device assembly” ”. .

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• Mater. Res. Soc. Symp
• Symp. Proc., 0990

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B10-

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01, 2007

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• L. Zhu, D. W. Hess, and C. P. Wong, “

“Assembly of fine Assembly of fine-

• pitch carbon nanotube bundles for electrical interconnect

pitch carbon nanotube bundles for electrical interconnect applications applications” ”. .

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• Tehc. 2006

. 2006

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• K. Zhang and M. M. F. Yuen, “

“Heat spreader with aligned Heat spreader with aligned CNTs CNTs designed for thermal management of HB designed for thermal management of HB-

• LED

LED packaging and microelectronic packaging packaging and microelectronic packaging” ”. .

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IEEE Trans. Comp. & Pack. Tech., pp. 92-

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100, March 2007

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• T. Tong, Y. Zhao, L. Delzeit

Delzeit, A. , A. Kashani Kashani, M. , M. Meyyappan Meyyappan, and A. , and A. Majumdar Majumdar, , “ “Dense vertically aligned Dense vertically aligned multiwalled multiwalled carbon nanotube arrays as thermal interface materials carbon nanotube arrays as thermal interface materials” ”. .

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Applied Physics Letters, vol. 90, 123105, 2007 R.

• R. Vajtai

Vajtai, K. , K. Kordas Kordas, G. , G. Toth Toth, P. , P. Moilanen Moilanen, M. , M. Kumpumaki Kumpumaki, J. , J. Vahakangas Vahakangas, and A. , and A. Uusimaki Uusimaki, and P. M. , and P. M. Ajayan Ajayan, , “ “Chip Chip cooling with integrated carbon nanotube cooling with integrated carbon nanotube microfin microfin architectures architectures” ”. .

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Applied Physics Letters, vol. 91, 042108, 2007 T.

• T. Xu

Xu, Z. Wang, J. Miao, X. Chen, C. M. Tan, , Z. Wang, J. Miao, X. Chen, C. M. Tan, “ “Aligned carbon nanotubes for through Aligned carbon nanotubes for through-

• wafer interconnects

wafer interconnects” ”. .

SLIDE 103

Kaustav Banerjee, UC Santa Barbara Design Automation Summer School, July 25-26 2009, San Francisco, CA Kaustav Banerjee Design Automation Sum m er School Lecture, July 26 2009, San Francisco, CA

Sponsors and Collaborators Sponsors and Collaborators