Electro -Thermal Interaction in Nanoscale Devices: Carbon Nanotubes and Phase - Change Memory
Eric Pop Intel Corp. / Stanford Univ.
http://nanoheat.stanford.edu/epop/research.html
E. Pop, Intel + Stanford 1
Joule (Self -Heating) in Electronics
R ~ T (metals) Portables: batteries Reliability + Performance R ~ T 1.5 (doped silicon) CPU Power Density ~ 100 W/cm2 Power = I 2R ~ 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 Tinterconnect Hottest spots > 300 W/cm 2
Rdielectric Ctransistor
Ttransistors Cross-section 8 metal levels + ILD Rspreading Cchip Intel 65 nm
Tchip
Rchip chip carrier Cheat sink 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
1000 Rocket AMD Nozzle
) Intel 2 Power PC Nuclear 100 Trend Reactor
10 Hot Plate Material kth (W/m/K) Power Density (W/cm Si 148 F.Labonte 1 Ge 60 1990 1994 1998 2002 2006 2010 Silicides 40 Si (10 nm) 13 2 Sun surface: 6000 W/cm SiO 2 1.4
E. Pop, Intel + Stanford 6 Thermal Resistance, Electrical Resistance
P = I 2 × 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 100000 nanotube SWNT
10000
1000 GST
Phase-change 100 Memory (PCM)
(K/mW) Silicon-on- SiO 2
TH Insulator FET
R 10
Cu Cu Via 1
Si Bulk FET 0.1 0.01 0.1 1 10 L ( µm)
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: HfO 2 top gate (Al) CNT – Thermal conductivity of single-walled carbon nanotubes (SWNTs) S (Pd) D (Pd) SiO – Great thermal conductivity k, low thermal 2 conductance (small d) 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
• Typical L ~ 2 µm, d ~ 2 nm ∆∆∆T • On insulating solid substrate Pt • Heat dissipated into substrate g – Moderate power ~ 10 µW/µm SiO 2 – Peak ∆T ~ 60 K
∆∆∆T • Thermal conductivity k ~ 3000 W/m/K k • Freely suspended nanotube Pt • Heat dissipated along tube length – Moderate power ~ 10 µW (10 µA @ 1 V)
– Peak ∆T ~ 400 K! SiO 2
E. Pop, Intel + Stanford 10 Transport in Suspended Nanotubes E. Pop et al ., Phys. Rev. Lett. 95, 155505 (2005)
16 nanotube on 2 µm L = 3 µm substrate suspended 14 over trench 12 10 On Substrate A)
µ 8 I ( 6 Suspended nanotube Pt 4 2 0 Pt gate 0 0.2 0.4 0.6 0.8 1 1.2 Si 3N4 V (V) SiO 2
• 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 nanotube on 2 µm L = 3 µm substrate suspended 14 over trench 12 10 On Substrate A)
µ 8 I ( 6 Suspended nanotube Pt 4 2 0 Pt gate 0 0.2 0.4 0.6 0.8 1 1.2 Si 3N4 V (V) SiO 2
• 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 CO 2 molecule vibrations 160 meV ) -1
transverse small k 100 meV
transverse max k=2 πππ/a ωFrequency (cm
26 meV = u(r,t) = A exp[i(k ⋅r − iωt)] 300 K
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 2 µm substrate suspended over trench
Guitar string on a table 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) 2 I (R-Rc)
T 16 OP Non-equilibrium OP: L = 3 µm 14 R TOP= T AC +α( TT AC − 0 ) OP 12 T = T AC L 10 On Substrate A)
Heat transfer via AC: µ 8
R I ( TH 2 6 Suspended AkT∇∇+( ) IRR ( −C )/ L = 0 T 0 4 2 1000 0 I2(R-R ) 0 0.2 0.4 0.6 0.8 1 1.2 900 C oxidation T V (V) 800 TOP Landauer electrical resistance 700 h L + λ (V ,T ) T = T eff 600 AC L R(V ,T ) = RC + Optical 2 TOP 4q λeff (V ,T ) 500 400 Include OP absorption: Acoustic TAC −1 Phonon(K) Temperature 300 1 1 1 λ = + + eff 0 0.2 0.4 0.6 0.8 1 1.2 λAC λ OP, ems λ OP , abs V (V)
E. Pop, Intel + Stanford 15
All Suspended Tubes Exhibit NDC E. Pop et al ., Phys. Rev. Lett. 95, 155505 (2005)
12 16 o symbols: data L = 0.8 µm 10 14 across ~ 30 tubes A)
µ 12 8 10
A) L = 2.1 µm µ 6 8
I ( model with d~2 nm 6 4 L = 3 µm
Peak Current ( 4 2 L = 11 µm 2 0 0 0 0.2 0.4 0.6 0.8 1 1.2 0 2 4 6 8 10 12 14 V (V) 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 7 L = 2 µµmm 5 6 T = 250, 300, 0 5 4 350, 400 K A)
A) 4 µ µ 3 I ( 3 I ( Data 2 2 κ = κ0T0/T κ = κ0 – 4.2( T - T0) 1 1 V > 0.3 κ = κ0 0 0 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 V (V) 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 3500 YuYu etet al. (Ref.(NL’05) 12) ThisThis work 0.8 3000 ) −1
K 0.6 2500 W/K) −1 1/T −5 2000 0.4 d (10 k (Wm ⋅ 1500 k 0.2 1000 0 300 400 500 600 700 800 100 200 300 400 500 600 700 800 T (K) 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 C H 1.2 2 4 8 CH 4 7 1 CO 6 N2 2 0.8 A)
A) O 5 µ 2 µ
I( Ar Vac 0.6 I ( 4 ∆ 1 atm Ar Highest thermal 3 0.4 He conductivity 1 atm N2 2 1 atm C H 2 4 0.2 1 Model Vacuum 0 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 1 2 3 4 5 6 V (V) # 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 Dry icePt gate encased 15 2 A)
µ 10 I (
5 T = 300 K Suspended in vacuumPt gate 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Si N V (V) 3 4 SiO 2
• 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 D. Mann et al ., Nature Nano (2007) 5 source m) 4 • HOT metallic tubes emit light µ ~ σT – Comes from center – Highly polarized 0 trench – Emitted photons @ higher energy Distance ( Distance than applied bias -5 drain 0 1 2 Wavelength (nm) γ (a.u.) 900 750 600 3 S Polarization Vds = 1.4 V suspended 1 2 D (a.u.) γ (a.u.) γ 1 Vds = 7 V on substrate S 0 0 1.4 1.6 1.8 2.0 2.2 0 90 Energy (eV) 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
SiO 2
E. Pop, Intel + Stanford 22 Nanotube Temperature Gauge
Pt
g
SiO 2
E. Pop, Intel + Stanford 23
Nanotube Temperature Gauge
• Doesn’t exist • But… oxidation (burning) temperature is known
o O TBD ~ 600 C 2
On substrate Suspended Pt
g
SiO 2
E. Pop, Intel + Stanford 24 Breakdown of SWNTs in Air (Oxygen)
25 Model Data 20
15 (V) BD
V 10 Weight (%) Weight 5
0 0 1 2 3 4 5 T ( oC) L (µm) K. Hata, Science 306, 1362 (2004) E. Pop, Proc. IEDM (2005) I. Chiang, JPCB 105, 8297 (2001) A. Javey, PRL 92, 106804 (2004)
• Thermogravimetric (TGA) data shows SWNTs exposed to air break o down by oxidation at 500 < TBD < 700 C (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 Model Data 20 A∇(k∇T ) + p'−g(T −T0 ) = 0 15 (V) BD
At breakdown: p'= I BDVBD / L V 10
5 VBD = gL(TBD −T0 )/ I BD 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 R Pt 20 Rcontact tube d T = 100, 200, 293 K 15 A) g ~ 0.17 Wm -1K-1 µ 10 I (
Data L L 5 contact tube Isothermal model SiO 2 T−dependent model 0 0 0.5 1 1.5 2 V (V)
• Same model as that used for suspended SWNTs • Include Joule heating, couple with heat conduction equation
• Self-consistent solution A∇(k∇T ) + p'−g(T −T0 ) = 0 • 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
900 Understanding transport 700 in a 3 µµµm metallic SWNT
T (K) 500 up to breakdown: T ~ 600 oC = 873 K 300 max −1.5−1−0.5 0 0.5 1 1.5 Vmax ~ 15 V X (µm)
• 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
55 nm 25 L=2 µm 6 0 Short tubes
20 L=5 µm 85 nm 4 0 A) A) 15 µ µ 150 nm ( I ( DS
10 L=15 µm I 300 nm 2 0 700 nm 5 Isothermal With self−heating Javey, PRL’04 0 0 0 1 2 3 4 5 0.0 0.5 1.0 1 .5 V (V) V DS (V )
• 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 µµµm) tubes current enhancement (> 20 µµµA) very likely aided by Joule heating shifting towards the contacts
E. Pop, Intel + Stanford 29
From Nanotubes to Phase -Change Memory
Single-wall 100000 nanotube SWNT High thermal resistance: 10000 • SWNT due to small 1000 GST thermal conductance (very
Phase-change small d ~ 2 nm) 100 Memory (PCM) • PCM due to low thermal (K/mW)
TH conductivity materials (SiO 2,
R 10 Ge 2Sb 2Te 5) 1
0.1 0.01 0.1 1 10 L ( µm)
E. Pop, Intel + Stanford 30 What Is Phase -Change Memory?
Flash PCM Bit (1/0) is stored as resistance change with Bit (1/0) is ~2000 material phase electrons stored on Floating Gate SiO 2 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
RESET PCM Pulse Melting Temperature Polycrystalline ~ 600 oC
GST Amorphous Glass Temperature ~ 150 oC Bottom electrode Temperature SET heater (e.g. TiN) Pulse
Time
• Based on Ge 2Sb 2Te 5 reversible phase change: R amorph / R xtal > 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 non- volatile memory market.” Source: http://www.eweek.com/article2/0,1895,2021841,00.asp
E. Pop, Intel + Stanford 34 PCM Material Challenges
GST
SiO 2 GST Separate GST and top/bottom electrode
Ti(Al)N
SiO 2
• 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] a) 0 2 10 -8 4 10 -8 6 10 -8 8 10 -8 1 10 -7 1.2 10 -7 1.4 TIR = 5.0e-8 m2K/W
1.2 d = 50 nm 1
0.8 TIR = 2.5e-8 m2K/W
0.6 700 oC Programming Voltage [V]
0.4 c) 0 0.2 0.4 0.6 0.8 1 1.2 k [W*m^-1*K^-1] TIR = 0 25 oC
• GST thermal conductivity 0.2–1.0 W/m/K (SiO 2 ~ 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- V H - L A w A V+ I + AC heating SiO 2 ~20nm
Si Substrate ~500µµµm Ti(Al)N 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 SiO 2 • 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