Electro -Thermal Interaction in Nanoscale Devices: Carbon...

E. Pop, Intel + Stanford 1

ElectroElectro--Thermal Interaction in Nanoscale Thermal Interaction in Nanoscale

Devices: Carbon Nanotubes and PhaseDevices: Carbon Nanotubes and Phase--

Change MemoryChange Memory

Eric PopEric PopIntel Corp. / Stanford Univ.Intel Corp. / Stanford Univ.

http://nanoheat.stanford.edu/epop/research.html


Joule (SelfJoule (Self--Heating) in ElectronicsHeating) in Electronics

R ~ T (metals)

R ~ T1.5 (doped silicon)

Power = I2R ~ 100 Watts

http://phys.ncku.edu.tw/~htsu/humor/fry_egg.html

Portables: batteries

Reliability + Performance

CPU Power Density ~ 100 W/cm2


Thermal Management MethodsThermal Management Methods


Thermal Management MethodsThermal Management Methods

System Level�� Active Microchannel Cooling (Cooligy)

Transistor Level�� electro-thermal device design

Circuit + Software Level� active power management(turn parts of circuit on/off)

IBM


ChipChip--Level Thermal NetworkLevel Thermal Network

Intel 65 nm

Ttransistors

Rconvection

Ctransistor

Cchip

Cheat sink

Tchip

Rchip

Theat sink

Cinterconnect

Tinterconnect

Tcoolant

heat spreader

Si chip

chip carrier

fan

fin array heat sink

heat spreader

Si chip

chip carrier

fan

fin array heat sink

Rdielectric

Rspreading

Top viewHottest spots > 300 W/cm2

Intel Itanium

Cross-section8 metal levels + ILD

Transistor < 100 nm


1

10

100

1000

1990 1994 1998 2002 2006 2010

Po

we

r D

en

sit

y (

W/c

m2)

AMD

Intel

Power PC

Trend

ChipChip--Level Thermal TrendsLevel Thermal Trends

1.4SiO2

13Si (10 nm)

40Silicides

60Ge

148Si

kth (W/m/K)Material

Device Level:

Confined Geometries, Novel Materials

F.Labonte

Hot Plate

Rocket Nozzle

Nuclear Reactor

E. Pop et al., Proc. IEEE 94, 1587 (2006)

Sun surface: 6000 W/cm2


Thermal Resistance, Electrical ResistanceThermal Resistance, Electrical Resistance

Ohm’s Law (1827)Fourier’s Law (1822)

∆ V = I × R∆T = P × RTH

P = I2 × R

R = f(∆T)


0.1

1

10

100

1000

10000

100000

0.01 0.1 1 10L (µm)

RTH (K/m

W)

Thermal Resistance at Device LevelThermal Resistance at Device Level

Cu

GST

SiO2

Si

Silicon-on-Insulator FET

Bulk FET

Cu Via

Phase-change Memory (PCM)

Single-wall nanotube SWNT

Sources: Mautry (1990), Bunyan (1992), Su (1994), Lee (1995), Jenkins (1995), Tenbroek (1996), Jin (2001), Reyboz (2004), Javey (2004), Seidel (2004), Pop (2004-6), Maune (2006).


• Carbon nanotube = rolled up graphene sheet

• Great electrical & thermal conductors

– Semiconducting � transistors

– Metallic � interconnects

– σ ≈ 100 x σCu ; k ≈ kDiamond

• (Some) open questions:

– Thermal conductivity of single-walled

carbon nanotubes (SWNTs)

– Great thermal conductivity k, low thermal

conductance (small d)

– Optimizing high-field transport

back gate

(p++ Si)

HfO2

S (Pd) D (Pd)

SiO2

top gate (Al) CNT

Carbon Nanotubes for ElectronicsCarbon Nanotubes for Electronics

d ~ 1-3 nm


BackBack--ofof--thethe--Envelope EstimatesEnvelope Estimates

• Typical L ~ 2 µm, d ~ 2 nm

• On insulating solid substrate

• Heat dissipated into substrate

– Moderate power ~ 10 µW/µm

– Peak ∆T ~ 60 K

E. Pop et al., Phys. Rev. Lett. 2005; Proc. IEDM 2005

SiO2

k∆∆∆∆T

Pt

• Thermal conductivity k ~ 3000 W/m/K

• Freely suspended nanotube

• Heat dissipated along tube length

– Moderate power ~ 10 µW (10 µA @ 1 V)

– Peak ∆T ~ 400 K!

g

∆∆∆∆T

Pt

SiO2


Transport in Suspended NanotubesTransport in Suspended NanotubesE. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)

SiO2

Si3N4

nanotube Pt

Pt gate

2 µmnanotube on

substrate suspended

over trench

• Observation: significant current degradation and negative

differential conductance at high bias in suspended tubes

• Question: Why? Answer: Tube gets HOT (how?)

0 0.2 0.4 0.6 0.8 1 1.20

2

4

6

8

10

12

14

16

I (µ

A)

V (V)

On Substrate

Suspended

L = 3 µm


Transport in Suspended NanotubesTransport in Suspended NanotubesE. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)

SiO2

Si3N4

nanotube Pt

Pt gate

2 µmnanotube on

substrate suspended

over trench

• Evidence for much longer phonon lifetimes in suspended SWNTs:

– Narrower Raman linewidths of suspended tubes (Dresselhaus in APL ’04)

– Observed 50x lifetime for suspended RBM mode (Dekker in Nature ’04)

– Why? Substrate interface provides phonon relaxation channels

– Consequence: hot optical phonons in suspended SWNTs under high bias

0 0.2 0.4 0.6 0.8 1 1.20

2

4

6

8

10

12

14

16

I (µ

A)

V (V)

On Substrate

Suspended

L = 3 µm


Quick Recap of PhononsQuick Recap of Phonons

• Phonons = quantized atomic lattice vibrations

• Transverse (u ⊥ k) vs. longitudinal modes (u || k), acoustic vs. optical• “Hot phonons” = highly occupied modes above room temperature

CO2 moleculevibrations

)](exp[),( tiit ω−⋅= rkAru

transversesmall k

transversemax k=2ππππ/a

k

Graphene Phonons [100]

200 meV

160 meV

100 meV

26 meV =

300 K

Frequency ω(cm-1)


Phonons and Guitar StringsPhonons and Guitar Strings

• Phonons = quantized lattice vibrations

• Transverse (u ⊥ k) vs. longitudinal modes (u || k), acoustic vs. optical• “Hot phonons” = highly occupied modes above room temperature

2 µmnanotube on

substrate suspended

over trench

Guitar string on a table Free guitar string


1

, ,

1 1 1eff

AC OP ems OP abs

λλ λ λ

−

= + +

Include OP absorption:

Transport Model Including Hot PhononsTransport Model Including Hot Phonons

0 0.2 0.4 0.6 0.8 1 1.20

2

4

6

8

10

12

14

16

I (µ

A)

V (V)

On Substrate

Suspended

L = 3 µm

++=

),(

),(

4),(

2 TV

TVL

q

hRTVR

eff

eff

C λ

λ

0( )OP AC ACT T T Tα= + −

Non-equilibrium OP:

T0

TAC = T

L

TOP

RTH

ROP

I2(R-Rc)

0 0.2 0.4 0.6 0.8 1 1.2

300

400

500

600

700

800

900

1000

V (V)

Ph

on

on

Te

mp

era

ture

(K

)

oxidation T

Optical TOP

Acoustic TAC

I2(R-RC)

TOP

TAC = TL

2( ) ( ) / 0CA k T I R R L∇ ∇ + − =

Heat transfer via AC:

Landauer electrical resistance

E. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)


0 2 4 6 8 10 12 140

2

4

6

8

10

12

14

16

Suspended Tube Length L (µm)

Pe

ak

Cu

rre

nt

(µA

)

model with d~2 nm

o symbols: data

across ~ 30 tubes

• First experimental observation of Negative Differential Conductance (NDC)

– ALL suspended tubes show NDC; longest at fields as low as 200 V/cm

– Previous work predicts velocity saturation at E-fields > 5 kV/cm (isothermal)

• Peak current: Imax ~ 1/L, which scales as the thermal conductance

– Compare to Imax > 20 µA for same L tubes on substrate

0 0.2 0.4 0.6 0.8 1 1.20

2

4

6

8

10

12

I (µ

A)

V (V)

L = 0.8 µm

L = 2.1 µm

L = 3 µm

L = 11 µm

E. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)

All Suspended Tubes Exhibit NDCAll Suspended Tubes Exhibit NDC


0 0.5 1 1.5 20

1

2

3

4

5

6

7

V (V)

I (µ

A)

L = 2 µm

Effect of Effect of κκthth at High Temperature, Biasat High Temperature, Bias

Data

L = 2 µm

• Current at high bias: I ~ λop ~ 1/Nop ~ 1/T ~ κth• Thermal conductivity κth ~ 1/T at high T (Umklapp phonon scattering)

• I-V curve at high bias indirectly measures κth(T) at high T !

• Back out to T ~ 300 K � κ0 ~ 3600 W/m/K

κ = κ0

κ = κ0 – 4.2(T - T0)

κ = κ0T0/T

0 0.2 0.4 0.6 0.8 1 1.2 1.40

1

2

3

4

5

6

V (V)

I (µ

A)

T0 = 250, 300,

350, 400 K

V > 0.3


Extracting SWNT Thermal ConductivityExtracting SWNT Thermal Conductivity

• Numerical extraction of k from the high bias (V > 0.3 V) tail

• Subtle second-order effect of three-phonon scattering introduces 1/T2

temperature dependence (N. Mingo, NL Jun’05)

• Comparison to data from 100-300 K of UT Austin group (C. Yu, NL Sep’05)

• Result: first “complete” picture of SWNT thermal conductivity from 100 – 800 K

E. Pop et al., Nano Letters 6, 96 (2006)

300 400 500 600 700 800

1000

1500

2000

2500

3000

3500

T (K)

k (

Wm

−1K

−1)

1/T

100 200 300 400 500 600 700 8000

0.2

0.4

0.6

0.8

1

T (K)

k⋅d

(10

−5 W

/K)

Yu et al. (Ref. 12)

This workYu et al. (NL’05)This work


Gas Environment Dependence of NDCGas Environment Dependence of NDC

0 0.2 0.4 0.6 0.8 1 1.2 1.40

1

2

3

4

5

6

7

8

9

V (V)

I (µ

A)

Vac

1 atm Ar

1 atm N21 atm C2H4Model

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

1.2

1.4

# of Atoms

∆I(

µA

) N2

Ar

He

CH4

C2H4

CO2

O2

Vacuum

D. Mann et al., J. Phys. Chem. B 110, 1502 (2006)

• Current enhancement (∆I) in ambient gases does not scale with thermal conductivity of gas

• It scales with the number of atoms in the physisorbed gas molecules

• Physisorbed gases act like “weak substrates” for suspended SWNTs,

providing more vibrational modes for OP decay

Highest thermalconductivity


Effects of Extreme EnvironmentEffects of Extreme Environment

0 0.2 0.4 0.6 0.8 1 1.2 1.40

5

10

15

20

V (V)

I (µ

A)

Pt gateCO

2

icePt gate

Dry ice encased

SiO2

Pt gate

Si3N4 SiO2

Pt gate

Si3N4

Suspended in

vacuum

• If the surrounding molecules are dense enough, they act as a

substrate, dissipating heat and relaxing optical phonons

• Environment can be engineered to modify properties of devices

D. Mann et al., J. Phys. Chem. B 110, 1502 (2006)

T = 50 K

T = 300 K


Light Emission from Suspended SWNTsLight Emission from Suspended SWNTs

• HOT metallic tubes emit light

– Comes from center

– Highly polarized

– Emitted photons @ higher energy

than applied bias

D. Mann et al., Nature Nano (2007)

Energy (eV)2.2

suspended

1

0

2

1.4 1.6 1.8

3

2.0

on substrate S

S

D

γ(a.u.)

Vds = 1.4 V

Vds = 7 V

900 750 600Wavelength (nm)

-5

5

0

1 2

source

drain

Distance (µm)

γ (a.u.)0

trench

angle0 90

γ(a.u.)

1

0

~ σT4

Polarization


Return to SWNTs On SubstratesReturn to SWNTs On Substrates

• SWNT on insulating solid substrate

• Heat dissipated into substrate rather than along tube length

• What is the heat loss coefficient g?

• [A: need some gauge of the tube temperature]

g

∆∆∆∆T

Pt

E. Pop et al., Proc IEDM 2005; Proc IEEE 2006

SiO2


Nanotube Temperature GaugeNanotube Temperature Gauge

g

Pt

SiO2


Nanotube Temperature GaugeNanotube Temperature Gauge

g

Pt

• Doesn’t exist

• But… oxidation (burning) temperature is known

O2

SiO2

TBD ~ 600 oC

Suspended On substrate


Breakdown of SWNTs in Air (Oxygen)Breakdown of SWNTs in Air (Oxygen)

• Thermogravimetric (TGA) data shows SWNTs exposed to air break

down by oxidation at 500 < TBD < 700 oC (800–1000 K)

• Joule breakdown voltage data shows VBD scales with L in air

• Supports cooling mechanism along the length, into the substrate

K. Hata, Science 306, 1362 (2004)I. Chiang, JPCB 105, 8297 (2001)

E. Pop, Proc. IEDM (2005)A. Javey, PRL 92, 106804 (2004)

T (oC)

Weight (%)

0 1 2 3 4 50

5

10

15

20

25

L (µm)

VB

D (

V)

Model

Data


Breakdown of SWNTs: AnalysisBreakdown of SWNTs: Analysis

• For on-substrate tubes, empirically note that:

– VBD vs. L in air scales linearly, as about 5 V/µm

– Breakdown currents for L > 1 µm always around IBD ≈ 20 µA

• Analytic solution of heat conduction equation

– Heat loss per unit length: g ≈ 0.17 ± 0.03 WK-1m-1

• No assumption was made about electrical transport model

0)(')( 0 =−−+∇∇ TTgpTkA

( ) BDBDBD ITTgLV /0−=

At breakdown: LVIp BDBD /'=

0 1 2 3 4 50

5

10

15

20

25

L (µm)

VB

D (

V)

Model

Data

E. Pop et al., Proc. IEDM (2005)


ElectroElectro--Thermal Model for mThermal Model for m--SWNTsSWNTs

• Same model as that used for suspended SWNTs

• Include Joule heating, couple with heat conduction equation

• Self-consistent solution

• No assumptions of hot phonons needed

0 0.5 1 1.5 20

5

10

15

20

I (µ

A)

V (V)

Data

Isothermal model

T−dependent model

T = 100, 200, 293 K

SiO2

PtRtubeRcontact d

Ltube

g ~ 0.17 Wm-1K-1

Lcontact

L = 3 µm

0)(')( 0 =−−+∇∇ TTgpTkA

E. Pop et al., Proc. IEDM (2005)


Modeling Long SWNTs up to BreakdownModeling Long SWNTs up to Breakdown

• Thermal “healing length” along SWNT ~ 0.25 µm

• Current saturation ~ 20 µA in long tubes (> 1 µm) due to self-heating

• Self-heating not significant when p’ < 5 µW/µm (design goal?)

Understanding transport

in a 3 µµµµm metallic SWNT

up to breakdown:Tmax ~ 600

oC = 873 KVmax ~ 15 V

Model

Data

E. Pop et al., submitted to JAP, pre-print cond-mat/0609075

−1.5−1−0.5 0 0.5 1 1.5300

500

700

900

X (µm)

T (

K)


Some Notes on Some Notes on ShorterShorter SWNTsSWNTs

• Thermal “healing length” along SWNT ~ 0.2 µm

• Current saturation ~ 20 µA in long tubes (> 1 µm) due to self-heating

• Self-heating not significant when p’ < 5 µW/µm (design goal?)

• In short (< 1 µµµµm) tubes current enhancement (> 20 µµµµA) very likely

aided by Joule heating shifting towards the contacts

60

40

20

0

I DS (µA)

1 .51 .00 .50 .0VDS (V )

0 1 2 3 4 50

5

10

15

20

25I (µ

A)

V (V)

Isothermal

With self−heating

L=2 µm

L=5 µm

L=15 µm

55 nm

85 nm

150 nm

300 nm

700 nm

Javey, PRL’04

Short tubes


From Nanotubes to PhaseFrom Nanotubes to Phase--Change MemoryChange Memory

0.1

1

10

100

1000

10000

100000

0.01 0.1 1 10L (µm)

RTH (K/m

W) GST

Phase-change Memory (PCM)

High thermal resistance:

• SWNT due to small

thermal conductance (very

small d ~ 2 nm)

• PCM due to low thermal

conductivity materials (SiO2,

Ge2Sb2Te5)

Single-wall nanotube SWNT


What Is PhaseWhat Is Phase--Change Memory?Change Memory?

• PCM: Like Flash memory (non-volatile)

• PCM: Unlike Flash memory (resistance change, not charge storage)

• Faster than Flash (100 ns vs. 0.1–1 ms), smaller than Flash (which is

limited by ~1000 electrons stored/bit)

• For: iPod nano, mobile phones, PDAs, solid-state hard drives…

Si

GST

Flash PCM

Bit (1/0) is ~2000

electrons stored on

Floating Gate

Bottom electrode

heater (e.g. TiN)

Bit (1/0) is stored as

resistance change with

material phase

SiO2


How PhaseHow Phase--Change Memory WorksChange Memory Works

• Based on Ge2Sb2Te5 reversible phase change: Ramorph / Rxtal > 100

• Short (10 ns), high pulse (0.5 mA) melts, amorphizes GST

• Longer (100 ns), lower pulse (0.1 mA) crystallizes GST

• Small cell area (sits on top of heater), challenge is reliability and

lowering programming current (BUT, helped by scaling!)

GST

PCM

Amorphous

PolycrystallineRESET

Pulse

Time

SET

Pulse

Glass Temperature

~ 150 oC

Melting Temperature

~ 600 oC

Tem

pera

ture

Bottom electrode

heater (e.g. TiN)


Samsung 512 Mb PCM PrototypeSamsung 512 Mb PCM Prototype

“Samsung completed the first working prototype of what is expected to be the main memory

device to replace high density Flash in the next decade – a Phase-change Random Access

Memory (PRAM). The company unveiled the 512 Mb device at its sixth annual press conference

in Seoul today.” Source:

http://samsung.com/PressCenter/PressRelease/PressRelease.asp?seq=20060911_0000286481

Sep 11, 2006

Put in perspective:NAND Flash chips of8+ Gb in production


Intel/ST PhaseIntel/ST Phase--Change Memory WaferChange Memory Wafer

“Intel CTO of Flash Memory Ed Doller holds the first wafer of 128 Mbit phase change memory

(PCM) chips, which has just been overnighted to him from semiconductor maker

STMicroelectronics in Agrate, Italy. Intel believes that PCM will be the next phase in the non-

volatile memory market.” Source: http://www.eweek.com/article2/0,1895,2021841,00.asp

Sep 28, 2006


PCM Material ChallengesPCM Material Challenges

• Thermal and electrical conductivities 25 – 625 oC

• Thermal resistance of interfaces between materials (high surface to

volume ratio)

• Phase change physics – thermal and temporal evolution

• (Practical goal: memory cell with lower programming current)

GST

GST

Ti(Al)N

SiO2

SiO2

Separate GSTand top/bottom electrode


GST Thermal Conductivity and InterfaceGST Thermal Conductivity and Interface

• GST thermal conductivity 0.2–1.0 W/m/K (SiO2 ~ 1.3 W/m/K)

• Thermal interface resistance (TIR) ≈ equivalent to 10-20 nm GST

• TIR alters temperature profile and may be key to device operation

J. Reifenberg et al., ITHERM 2006

c)

a)

d = 50 nm

TIR = 0

TIR = 2.5e-8 m2K/W

TIR = 5.0e-8 m2K/W

700 oC

25 oC

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2

0 2 10-8

4 10-8

6 10-8

8 10-8

1 10-7

1.2 10-7

Pro

gra

mm

ing

Vo

ltag

e [

V]

k [W*m^-1*K^-1]

Boundary Resistance [m^2*K*W^-1]


AC and DC Thermal MeasurementsAC and DC Thermal Measurements

• AC harmonic heating of thin GST films (3-ω method)

– 35-70-140 nm thin GST films, capped by SiO2

• DC electrical thermometry of electrode metals

– Transport physics (electrical, thermal) in amorphous materials

L

Si Substrate ~500µµµµm

A A

SiO2 ~20nm

I-

V-

V+I+

w

HL

Si Substrate ~500µµµµm

A A

SiO2 ~20nm

I-

V-

V+I+

w

HL

A A

I-

V-

V+I+

w

H

Au

GST (35-140 nm)

SiO2 (20 nm)

Si Substrate

SiO2 (20 nm)

AC heating

DC heating

Ti(Al)N


ConclusionsConclusions

Summary:

• Self-heating due to small dimensions or thermal insulation

• HOT metallic single-wall carbon nanotubes at high bias:

– Hot phonons and thermal conductivity of SWNTs

– Light emission and breakdown (burning) of SWNTs in air

• Role of interface thermal resistance and material properties (amorphous vs. crystalline) in phase-change memory

Publications (see http://nanoheat.stanford.edu/epop/research.html)

• E. Pop, D. Mann, J. Cao, Q. Wang, K. Goodson, H. Dai, Phys. Rev. Lett. 95, 155505 (2005)

• E. Pop, D. Mann, J. Reifenberg, K. Goodson, H. Dai, Proc. IEDM, Washington DC (2005)

• J. Reifenberg, E. Pop, A. Gibby, S. Wong and K. Goodson, ITHERM 106 (2006)

• D. Mann, E. Pop, Q. Wang, K. Goodson, H. Dai, J. Phys. Chem. B 110, 1502 (2006)

• E. Pop, D. Mann, Q. Wang, K. Goodson, H. Dai, Nano Letters 6, 96 (2006)

• D. Mann et al., to appear in Nature Nano (2007)


AcknowledgmentsAcknowledgments

• Profs. Ken Goodson, Hongjie Dai, Philip Wong

• Drs. David Mann, Qian Wang

• John Reifenberg, SangBum Kim, Matt Panzer, Yuan Zhang

• Intel: Drs. Y. Zhang, B. Johnson, D. Kencke, I. Karpov, G. Spadini


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