Map of China

Mulitphysics Solution for Nanoelectronics

Wen-Yan Yin

Center for Optical and EM Research(COER)

Zhejiang University, Hangzhou, China

E-mail: wyyin@zju.edu.cn and wyyin@sjtu.edu.cn

http://coer.zju.edu.cn and http://cmrft.sjtu.edu.cn

3

Silicon-based Transmission Lines

4

0 5 10 15 20 25 30

0

2

4

6

8

10

12

14

16

458K

418K

378K

318K

298KAtt

en

uati

on

co

nsta

nt(

dB

/cm

)

Freqeuncy(GHz)

G

G

SW

Le

Finite electrical conductivity and semiconducting substrate!

Electrothermal Effects

5

(1) Temperature effects on electrical conductivities of most

metal materials?

(2) Temperature effects on thermal conductivities of most

semiconducting materials?

Problems

6

1 10 100

0

2

4

6

Model

Symbols: Q3D

Re

sista

nce

(

)

Frequency (GHz)

W(m) t(m) max error

15 1 7.4%

30 110%

40 1 9.6%

10 2 7.5%

152 0.4%

30 24.4%

40 2 3.4%

50 2 1.1%

60 2 2.3%

K. Kang, L. Nan, S. C. Rustagi, W. Y. Yin, et al, “A wideband scalable and SPICE-compatible model for on-chip interconnects up to 110

GHz,” IEEE Trans. Microwave Theory Tech., 56(4), 942-951, 2008.

Silicon-based Millimeter Wave TLs

7

7dB

Silicon-based Millimeter Wave TLs

8

.

After 2014: Jmax > 1.06 x 107 A/cm2

ITRS

9

.

Y. Awano, et al., PIEEE, 98(12), 2015-2031, 2010.

Final Solutions are not Known

10

Size Effect in Cu Interconnect

Cu resistivity will be increased rapidly!

Electric performance and reliability will

be decreased due to self-heating effect ! Steinhogl et al., JAP, 2005

11

Reliability Electric

Performance

Cu Resistivity Current Density

Time Delay SHE& EM

CNT ？

Decrease in Transmission Line Size

CNT and GRAPHENE Solutions?

GRAPHENE？

12

Carbon Nanotube Transmission Lines (CNTL):

Beyond Maxwell’s Equations

13

CNT

Courtesy: F. Kreupl, Infineon

GR SWCNT MWCNT

14

CNT Classification

Arm-Chair CNT(M) Zig-Zag CNT ( M & S)

About 1/3 of all SWCNTs are metallic and 2/3 are semiconducting

MWCNT

(each wall can be S or M, most walls are M)

Metallic SWCNT Properties

• Length: um-mm

• Diameter: 0.4-100nm

• Strength : 45 Tpa! (Steel ~ 2Tpa)

• Thermal stability: operating temperature up to 700 º C.

CNT Cu

Maximum current carrying density(A/cm*cm)

>1X109

Radosavljevic, et al., Phys. Rev. B, 2001

<1X107

Thermal conductivity (W/mK) 5800 Hone, et al., Phys. Rev. B,

1999

385

Mean free path（diameter=1nm） >1000 McEuen, et al., IEEE Trans.

Nano., 2002

40

CNT Vias

T. Wang, et al., IEEE Electronic Devices Lett., 33(3), 420-422, Mar.2012

17

Carbon Nanotubes for Active Nano Devices

Semiconducting SWCNT Properties

19

CNTFETs

GFETs

2012.5：350GHz (IBM)

21 K. Ryu, and H.S.P. Wong, et al., Nano Lett., 9(1), 189-197, 2009.

CNT Fabrication

22

Han Wang, et al, “Graphene electronics for RF Applications,” IEEE Microwave Magazine, June 2012.

Graphene Fabrication

23

Electromagnetic Capability-Oriented Study on

CNTLs

Multiphysics Issues:

Beyond Maxwell’s Equations: Quantum Effects

Both Frequency- and Temperature-Dependent

Distributed Parameters of a SWCNT

mn HL K /1 6

ln2

CNT

M

yL

d

)/2ln(

2

dhC E

Quantum Capacitance

~ 96 /Q

QC aF m

V

d

y

Kinetic Inductance

22k CNT

F

hL

v e

SWCNT Bundle

Quantum Resistance

d

CNT

Dout

heig

ht, N

H-

width, Nw

1

out

W

out

width DN Inter

D d

1( 3 2)( )

out

H

out

heigth DN Inter

D d

Din

(1 )CNT

CNT C Q

mfp

R R R 6.45QR K

CR

Contact Resistance

( )Q

C Q CNT

mfp

RR R

;l d CNTR R

( )C Q QCNT

b CNT

CNT CNT CNT mfp

R R RRR

n n n

4

k CNT

k b

CNT

LL

n

.k b M b

t CNT t d CNT

CNT

L LL L

Q b Q CNTC C n

;lb db CNTR R

Equivalent circuit model of a SWCNT bundle

DWCNT

int( )

' ' '

C Qi Qi

i b CNT

CNT CNT CNT mfpi

R R RRR

n n n

;il b id b CNTR R

( )

' ' '

C Qe Qeext

e b CNT

CNT CNT CNT mfpe

R R RRR

n n n

.el b ed b CNTR R

2 1

2;

ln( / )CMC

D D

' ;ES b ESext CNTC C n

' ;CM b CM CNTC C n

' .Q b Q CNTC C n

DWCNT Bundle

Equivalent circuit model of a DWCNT bundle

S. N. Pu, Wen-Yan Yin, J. F. Mao, et al. , "Crosstalk prediction of single and double-walled carbon nanotube(SWCNT/DWCNT) bundle

interconnects," IEEE Trans. Electron Devices, 56(4), 560-568, 2009

DWCNT Bundle TL

Multi-SWCNT/DWCNT Bundle TL

Equivalent circuit model of a tri-SWCNT bundle interconnect.

Tri-SWCNT Bundle TL

Equivalent circuit model of a tri-DWCNT bundle interconnect.

Tri-DWCNT Bundle TL

MWCNT TL

h

Dmax

Ground Plane

MW

CNT

d=0.34nm

Dmin

RFC/2 RFC/2 Rmc/2Rmc/2

CQ

CE

LKRS

ShellDistributed

LM

d=0.34 nm

SWCNT D

heig

ht

width

1W

width DN Inter

D d

1( 3 2)( )

H

heigth DN Inter

D d

(c)

Ground

H

W

S

tox

Ground

CLoad

Cout

Rt

Interconnect

L

(a)

(b)

tox

tox S = W

Rmc/2

p

RQ1/2

RSp

CE

RQ2/2

RQp/2

RQ1/2

RQ2/2

RQp/2

RS2

RS1

CQ1

CQ2

CS1LK1

LK2

LKp

CQp

1, outermost shell

2 Rmc/2

GTp-1

Distributed Elements

CSp-1

LMp

LM2

LM1

innermost shell

GT1

M1p

M12

Cout

Rt

Driver Load

CLoad

•H. Li, W. Y. Yin, J. F. Mao, and K. Banerjee, “Circuit modeling and performance analysis of multi-walled carbn nanotube(MWCNT)

•interconnects,” IEEE Trans. Electron Devices, 55(6), 1328-1337, 2008.

MWCNT Bundle TL

1 10 100 1000

1

10

100

Cu: W=32nm, =4.83

Cu: W=22nm, =6.01

SWCNT(D=1nm), All Metallic

SWCNT(D=1nm), 1/3 Metallic

(Random Chirality)

Cu: W=14nm, =8.19

MWCNT,D=32nm

MWCNT,D=22nm

MWCNT,D=14nm

Re

sis

tiv

ity

[

-cm

]

Length [m]Comparison of resistivity among MWCNTs with various diameters, Cu wires with different

dimensions, and SWNCT bundles with different chiralities. Dimension of Cu wires are adopted from

ITRS. SWCNT bundles are assumed to be densely packed.

Resistivity Comparison

35

(1) How to get the breakdown voltage of a SWCNT?

(2) How to get the peak power handling capability of a

SWCNT?

Problems

SWCNT ARRAY

'

0

1

2

( , , )( ) ( ) [ ( , ) ( , , )] ( )

( 0)

( )

dT V L t d dT c T A T L T V L t p g T T

dt dx dx

T x T

T x L T

' 2

2

( , ( ), ) 1( , ( ), ) ( , , )

( , ( ), )4 eff

dR V T x L hp V T x L I V T L

dx V T x Lq

/ 2

2

/ 2

, , 14 , ,

L

C

effL

h dxR V T L R

q V T x L

1

1 1 1

, ,( , ( ) , )eff AC OP ems OP absV T x L

,300

300AC AC

T

1

, , ,1/ 1/fld abs

OP ems OP ems OP ems

elastic electron scattering

of acoustic phonon inelastic electron scattering caused

by optical phonon emission

inelastic electron scattering caused

by optical phonon absorption

7 10 2 2 1( , ) [3.7 10 9.7 10 9.3(1 0.5/ ) ]T L T T L T

1-D Heat Conducting Equation

Specific heat of a SWCNT as a function of temperature

Specific Heat

Longitudinal temperature distribution along single SWCNT in a SWCNT array biased by different

voltages, respectively, where the total contact resistance is assumed to be 100Kohm.

Temperature Distribution

The highest central temperature of the

SWCNTs in the array as a function of

length biased by different voltage,

respectively.

Breakdown voltage of the SWNCT local

interconnect as a function of its length for

different ambient temperatures at the input and

output of the array, respectively.

Breakdown Voltage

Power handling capacity of the SWNCT local interconnect as a function of its length for

different ambient temperatures at the input and output of the array, respectively.

W. C. Chen, W. Y. Yin, et al., “Electrothermal characterization of single-walled carbon nanotube (SWCNT) interconnect arrays,” IEEE Trans. Nanotechnology, 8(6), 718-728, 2009.

Power Handling Capability

Lk/4R(V,T(x),L) RQ/2RQ/2

4CQ

CES

Lk/4R(V,T(x),L) RQ/2RQ/2

Rc/2

Cc

Cc

Rc/2

Lupmed Ditributed LupmedDitributed

SWCNT 2Input Output

4CQ

CES

SWCNT 1

4CQ

CES

SWCNT N

Electro-thermal equivalent circuit model of a metallic SWCNT N-array.

Electro-thermal Equivalent Circuit Model

Crosstalk noise on the victim line in various biasing conditions with SWCNT length of 5 um.

Self-heating Effect