Electro-Thermal Interaction in Nanoscale
Devices: Carbon Nanotubes and PhaseChange Memory
Eric Pop
Intel Corp. / Stanford Univ.
http://nanoheat.stanford.edu/epop/research.html
E. Pop, Intel + Stanford
1
Joule (Self-Heating) in Electronics
Portables: batteries
R ~ T (metals)
Reliability + Performance
R ~ T1.5 (doped silicon)
CPU Power Density ~ 100 W/cm2
Power = I2R ~ 100 Watts
http://phys.ncku.edu.tw/~htsu/humor/fry_egg.html
E. Pop, Intel + Stanford
2
Thermal Management Methods
E. Pop, Intel + Stanford
3
Thermal Management Methods
System Level
Active Microchannel Cooling (Cooligy)
IBM
Circuit + Software Level
active power management
(turn parts of circuit on/off)
Transistor Level
electro-thermal device design
E. Pop, Intel + Stanford
4
Chip-Level Thermal Network
Intel Itanium
Cinterconnect
Top view
Hottest spots > 300 W/cm2
Tinterconnect
Ctransistor
Rdielectric
Ttransistors
Cchip
Cross-section
8 metal levels + ILD
Rspreading
Intel 65 nm
Tchip
Cheat sink
Rchip
chip carrier
Si chip
Theat sink
heat spreader
fin array heat sink
Rconvection
fan
Tcoolant
Transistor < 100 nm
E. Pop, Intel + Stanford
5
Chip-Level Thermal Trends
E. Pop et al., Proc. IEEE 94, 1587 (2006)
Device Level:
Confined Geometries, Novel Materials
Rocket
Nozzle
Power Density (W/cm 2)
1000
100
AMD
Intel
Power PC
Trend
Nuclear
Reactor
Hot
Plate
10
1
1990
F.Labonte
1994
1998
2002
Sun surface: 6000 W/cm2
E. Pop, Intel + Stanford
2006
2010
Material
kth (W/m/K)
Si
148
Ge
60
Silicides
40
Si (10 nm)
13
SiO2
1.4
6
Thermal Resistance, Electrical Resistance
P = I2 × R
∆T = P × RTH
∆V=I×R
R = f(∆T)
Fourier’s Law (1822)
Ohm’s Law (1827)
E. Pop, Intel + Stanford
7
Thermal Resistance at Device Level
Single-wall
nanotube SWNT
100000
RTH (K/mW)
10000
1000
100
GST
Phase-change
Memory (PCM)
Silicon-onInsulator FET
10
Cu
SiO2
Cu Via
1
Si
0.1
0.01
0.1
Bulk FET
L (µm)
1
10
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).
E. Pop, Intel + Stanford
8
Carbon Nanotubes for Electronics
• Carbon nanotube = rolled up graphene sheet
• Great electrical & thermal conductors
– Semiconducting transistors
– Metallic interconnects
d ~ 1-3 nm
– σ ≈ 100 x σCu ; k ≈ kDiamond
• (Some) open questions:
HfO2
– Thermal conductivity of single-walled
carbon nanotubes (SWNTs)
top gate (Al)
S (Pd)
– Great thermal conductivity k, low thermal
conductance (small d)
CNT
D (Pd)
SiO2
back gate
(p++ Si)
– Optimizing high-field transport
E. Pop, Intel + Stanford
9
Back-of-the-Envelope Estimates
E. Pop et al., Phys. Rev. Lett. 2005; Proc. IEDM 2005
∆T
• Typical L ~ 2 µm, d ~ 2 nm
• On insulating solid substrate
Pt
• Heat dissipated into substrate
– Moderate power ~ 10 µW/µm
– Peak ∆T ~ 60 K
g
SiO2
∆T
• Thermal conductivity k ~ 3000 W/m/K
• Freely suspended nanotube
k
Pt
• Heat dissipated along tube length
– Moderate power ~ 10 µW (10 µA @ 1 V)
– Peak ∆T ~ 400 K!
E. Pop, Intel + Stanford
SiO2
10
Transport in Suspended Nanotubes
E. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)
16
2 µm
14
suspended
over trench
nanotube
L = 3 µm
12
I (µA)
nanotube on
substrate
10
On Substrate
8
Suspended
6
Pt
4
2
0
0
Pt gate
Si3N4
0.2
0.4
0.6
V (V)
0.8
1
1.2
SiO2
• Observation: significant current degradation and negative
differential conductance at high bias in suspended tubes
• Question: Why? Answer: Tube gets HOT (how?)
E. Pop, Intel + Stanford
11
Transport in Suspended Nanotubes
E. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)
16
2 µm
14
suspended
over trench
nanotube
L = 3 µm
12
I (µA)
nanotube on
substrate
10
On Substrate
8
Suspended
6
Pt
4
2
Pt gate
Si3N4
0
0
0.2
0.4
0.6
V (V)
0.8
1
1.2
SiO2
• 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
E. Pop, Intel + Stanford
12
Quick Recap of Phonons
Graphene Phonons [100]
200 meV
CO2 molecule
vibrations
transverse
small k
transverse
max k=2π
π/a
Frequency ω (cm-1)
160 meV
100 meV
26 meV =
300 K
u(r, t ) = A exp[i (k ⋅ r − iωt )]
k
• Phonons = quantized atomic lattice vibrations
• Transverse (u ⊥ k) vs. longitudinal modes (u || k), acoustic vs. optical
• “Hot phonons” = highly occupied modes above room temperature
E. Pop, Intel + Stanford
13
Phonons and Guitar Strings
nanotube on
substrate
Guitar string on a table
2 µm
suspended
over trench
Free guitar string
• Phonons = quantized lattice vibrations
• Transverse (u ⊥ k) vs. longitudinal modes (u || k), acoustic vs. optical
• “Hot phonons” = highly occupied modes above room temperature
E. Pop, Intel + Stanford
14
Transport Model Including Hot Phonons
E. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)
I2(R-Rc)
TOP
ROP
Non-equilibrium OP:
16
TOP = TAC + α (TAC − T0 )
14
12
10
I (µA)
TAC = TL
Heat transfer via AC:
RTH
L = 3 µm
A∇ ( k ∇T ) + I 2 ( R − RC ) / L = 0
On Substrate
8
Suspended
6
4
T0
2
Phonon Temperature (K)
1000
0
0
I2(R-RC)
900
800
0.2
0.4
oxidation T
TOP
0.8
1
1.2
Landauer electrical resistance
700
TAC = TL
600
0.6
V (V)
R (V , T ) = RC +
Optical TOP
500
h  L + λeff (V , T ) 


4 q 2  λeff (V , T ) 
Include OP absorption:
400
Acoustic TAC
300
0
0.2
0.4
0.6
V (V)
0.8
1
λeff
1.2
 1
1
1
=
+
+
λ
λ
λ
OP , ems
OP , abs
 AC



−1
E. Pop, Intel + Stanford
15
All Suspended Tubes Exhibit NDC
E. Pop et al., Phys. Rev. Lett. 95, 155505 (2005)
12
16
Peak Current (µA)
L = 0.8 µm
10
I (µA)
8
L = 2.1 µm
6
4
L = 3 µm
L = 11 µm
2
0
0
0.2
0.4
0.6
V (V)
0.8
o symbols: data
across ~ 30 tubes
14
12
10
8
model with d~2 nm
6
4
2
1
1.2
0
0
2
4
6
8
10
12
14
Suspended Tube Length L (µm)
• 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
E. Pop, Intel + Stanford
16
Effect of κth at High Temperature, Bias
6
L = 2 µm
6
5
5
4
I (µA)
I (µA)
7
4
3
Data
κ = κ0T0/T
κ = κ0 – 4.2(T - T0)
κ = κ0
2
1
0
0
0.5
1
1.5
T0 = 250, 300,
350, 400 K
3
2
2
1
V > 0.3
0
0
0.2 0.4 0.6 0.8
V (V)
1
1.2 1.4
V (V)
• 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
E. Pop, Intel + Stanford
17
Extracting SWNT Thermal Conductivity
E. Pop et al., Nano Letters 6, 96 (2006)
1
Yu et
et al.
12)
Yu
al. (Ref.
(NL’05)
This work
work
This
0.8
W/K)
3000
1/T
2000
0.6
−5
2500
k⋅d (10
−1 −1
k (Wm K )
3500
1500
0.4
0.2
1000
300
400
500
600
700
800
0
100
200
300
400
T (K)
500
600
700
800
T (K)
• 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, Intel + Stanford
18
Gas Environment Dependence of NDC
D. Mann et al., J. Phys. Chem. B 110, 1502 (2006)
1.4
9
6
∆I(µA)
I (µA)
CH4
1
7
5
Vac
1 atm Ar
1 atm N2
1 atm C2H4
Model
4
3
2
1
0
0
C2H4
1.2
8
0.2 0.4 0.6 0.8
CO2
N2
0.8
O2
Ar
0.6
Highest thermal
conductivity
He
0.4
0.2
Vacuum
1
1.2 1.4
V (V)
0
0
1
2
3
4
5
6
# of Atoms
• 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
E. Pop, Intel + Stanford
19
Effects of Extreme Environment
D. Mann et al., J. Phys. Chem. B 110, 1502 (2006)
20
T = 50 K
CO ice encased
ice
Dry
Pt gate
I (µA)
15
2
10
T = 300 K
5
0
0
Suspended in
Pt gate
vacuum
0.2 0.4 0.6 0.8
V (V)
1
1.2 1.4
Si3N4
SiO2
• 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
E. Pop, Intel + Stanford
20
Light Emission from Suspended SWNTs
γ (a.u.)
Wavelength (nm)
900
750
600
3
S
Vds = 1.4 V
suspended
2
D
1 Vds = 7 V
on substrate
0
1.4
1.6 1.8 2.0
Energy (eV)
~ σT4
0
trench
– Comes from center
– Highly polarized
– Emitted photons @ higher energy
than applied bias
source
5
-5
drain
0
1
2
γ (a.u.)
Polarization
1
γ (a.u.)
• HOT metallic tubes emit light
Distance (µm)
D. Mann et al., Nature Nano (2007)
S
0
2.2
0
90
angle
E. Pop, Intel + Stanford
21
Return to SWNTs On Substrates
E. Pop et al., Proc IEDM 2005; Proc IEEE 2006
• 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]
∆T
Pt
g
SiO2
E. Pop, Intel + Stanford
22
Nanotube Temperature Gauge
Pt
g
SiO2
E. Pop, Intel + Stanford
23
Nanotube Temperature Gauge
• Doesn’t exist
• But… oxidation (burning) temperature is known
O2
TBD ~ 600 oC
Suspended
On substrate
Pt
g
SiO2
E. Pop, Intel + Stanford
24
Breakdown of SWNTs in Air (Oxygen)
25
Model
Data
VBD (V)
Weight (%)
20
15
10
5
0
T
0
1
2
3
4
5
L (µm)
(oC)
K. Hata, Science 306, 1362 (2004)
I. Chiang, JPCB 105, 8297 (2001)
E. Pop, Proc. IEDM (2005)
A. Javey, PRL 92, 106804 (2004)
• 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
E. Pop, Intel + Stanford
25
Breakdown of SWNTs: Analysis
E. Pop et al., Proc. IEDM (2005)
25
A∇(k∇T ) + p '− g (T − T0 ) = 0
p' = I BDVBD / L
VBD = gL(TBD − T0 ) / I BD
VBD (V)
At breakdown:
Model
Data
20
15
10
5
0
0
1
2
3
4
5
L (µm)
• 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
E. Pop, Intel + Stanford
26
Electro-Thermal Model for m-SWNTs
E. Pop et al., Proc. IEDM (2005)
L = 3 µm
Rtube
Rcontact
Pt
20
d
T = 100, 200, 293 K
g ~ 0.17 Wm-1K-1
Lcontact
Ltube
I (µA)
15
10
Data
Isothermal model
5
SiO2
T−dependent model
0
0
0.5
1
V (V)
1.5
2
• Same model as that used for suspended SWNTs
• Include Joule heating, couple with heat conduction equation
A∇( k∇T ) + p '− g (T − T0 ) = 0
• Self-consistent solution
• No assumptions of hot phonons needed
E. Pop, Intel + Stanford
27
Modeling Long SWNTs up to Breakdown
E. Pop et al., submitted to JAP, pre-print cond-mat/0609075
Data
Model
T (K)
900
700
500
300
−1.5−1−0.5 0 0.5 1 1.5
X (µm)
Understanding transport
in a 3 µm metallic SWNT
up to breakdown:
Tmax ~ 600 oC = 873 K
Vmax ~ 15 V
• 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?)
E. Pop, Intel + Stanford
28
Some Notes on Shorter SWNTs
25
20
L=5 µm
85 nm
40
15
10
L=15 µm
5
Isothermal
0
1
2
3
150 nm
300 nm
700 nm
20
With self−heating
0
55 nm
Short tubes
I DS (µA)
I (µA)
60
L=2 µm
4
0
0 .0
5
V (V)
Javey, PRL’04
0 .5
1 .0
V D S (V )
1 .5
• 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 µm) tubes current enhancement (> 20 µA) very likely
aided by Joule heating shifting towards the contacts
E. Pop, Intel + Stanford
29
From Nanotubes to Phase-Change Memory
Single-wall
nanotube
100000
SWNT
High thermal resistance:
RTH (K/mW)
10000
1000
100
• SWNT due to small
thermal conductance (very
small d ~ 2 nm)
GST
Phase-change
Memory (PCM)
• PCM due to low thermal
conductivity materials (SiO2,
Ge2Sb2Te5)
10
1
0.1
0.01
E. Pop, Intel + Stanford
0.1
L (µm)
1
10
30
What Is Phase-Change Memory?
Flash
PCM
Bit (1/0) is ~2000
electrons stored on
Floating Gate
SiO2
Bit (1/0) is stored as
resistance change with
material phase
GST
Bottom electrode
heater (e.g. TiN)
Si
• 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…
E. Pop, Intel + Stanford
31
How Phase-Change Memory Works
Temperature
RESET
Pulse
PCM
Melting Temperature
~ 600 oC
GST
Glass Temperature
~ 150 oC
SET
Pulse
Polycrystalline
Amorphous
Bottom electrode
heater (e.g. TiN)
Time
• 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!)
E. Pop, Intel + Stanford
32
Samsung 512 Mb PCM Prototype
Sep 11, 2006
Put in perspective:
NAND Flash chips of
8+ Gb in production
“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
E. Pop, Intel + Stanford
33
Intel/ST Phase-Change Memory Wafer
Sep 28, 2006
“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 nonvolatile memory market.” Source: http://www.eweek.com/article2/0,1895,2021841,00.asp
E. Pop, Intel + Stanford
34
PCM Material Challenges
GST
SiO2
GST
Separate GST
and top/bottom electrode
Ti(Al)N
SiO2
• 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)
E. Pop, Intel + Stanford
35
GST Thermal Conductivity and Interface
J. Reifenberg et al., ITHERM 2006
Boundary Resistance [m^2*K*W^-1]
Programming Voltage [V]
1.4
0
-8
2 10
-8
4 10
-8
6 10
-8
8 10
-7
a)
-7
1 10 1.2 10
TIR = 5.0e-8 m2K/W
1.2
d = 50 nm
1
0.8
TIR = 2.5e-8 m2K/W
0.6
700 oC
0.4
0
0.2
0.4
0.6
0.8
k [W*m^-1*K^-1]
1
c)
1.2
TIR = 0
25 oC
• 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
E. Pop, Intel + Stanford
36
AC and DC Thermal Measurements
I-
A
V-
H
L
w
A
V+
I+
AC heating
SiO2 ~20nm
Ti(Al)N
µm
Si Substrate ~500
Au
SiO2 (20 nm)
GST (35-140 nm)
DC heating
SiO2 (20 nm)
Si Substrate
• 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
E. Pop, Intel + Stanford
37
Conclusions
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)
E. Pop, Intel + Stanford
38
Acknowledgments
•
•
•
•
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
E. Pop, Intel + Stanford
39
E. Pop, Intel + Stanford
40