© 2010 Eric Pop, UIUCECE 598EP: Hot Chips 1 Recap (so far) Ohm’s & Fourier’s LawsOhm’s & Fourier’s Laws Mobility & Thermal ConductivityMobility & Thermal Conductivity Heat CapacityHeat Capacity Wiedemann-Franz RelationshipWiedemann-Franz Relationship Size Effects and Breakdown of Classical LawsSize Effects and Breakdown of Classical Laws

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips 2 Low-Dimensional & Boundary Effects Energy Transport in Thin Films, Nanowires, NanotubesEnergy Transport in Thin Films, Nanowires, Nanotubes Landauer TransportLandauer Transport − Quantum of Electrical and Thermal Conductance Electrical and Thermal ContactsElectrical and Thermal Contacts Materials ThermometryMaterials Thermometry Guest Lecture: Prof. David Cahill (MSE)Guest Lecture: Prof. David Cahill (MSE)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips  ~ 200 nm Si D Ox Size and Non-Equilibrium Effects −optical-acoustic −small heat source −impurity scattering −boundary scattering −boundary resistance Macroscale (D >>  ) Nanoscale (D <  ) “Sub-Continuum” Energy Transport Ox Me t si

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Thermal Simulation Hierarchy 4 defect lattice wave phonon D D ~  Waves & Atoms Continuum Fourier’s Law, FE Phonon Transport BTE & Monte Carlo Waves & Atoms MD & QMD D ~ MFP ~ 200 nm at 300 K in Si Wavelength

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Thermal and Electrical Simulation 5 Atomistic Phonons Diffusion BTE or Monte Carlo BTE with Wave models much work Wachutka (1994) Shur (1990) Apanovich (1995) Sverdrup, Ju, Goodson (2000) Lai, Majumdar (1995) Drift Diffusion BTE Moments Monte Carlo & BTE Monte Carlo with Quantum Models Stratton (1962) Bloetekjaer (1970) Baccarani (1985) Rudan (1986) Jacoboni (1983) Fischetti (1988) Electrons Full Quantum Lundstrom Datta (1995) Winstead (2003) Isothermal ~1 nm~5 nm ~100 nm~5 nm MFP phononselectrons

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Nanowire Formation: “Bottom-Up” Vapor-Liquid-Solid (VLS) growth Need gas reactant as Si source (e.g. silane, SiH 4 ) Generated through –Chemical vapor deposition (CVD) –Laser ablation or MBE (solid target) 6 Lu & Lieber, J. Phys. D (2006)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips “Top-down” = through conventional lithography “Guided” growth = through porous templates (anodic Al 2 O 3 ) –Vapor or electrochemical deposition 7 Suspended nanowire (Tilke ‘03) “Top-Down” and Templated Nanowires

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Semimetal-Semiconductor Transition Bi (bismuth) has semimetal-semiconductor transition at wire D ~ 50 nm due to quantum confinement effects 8 Source: M. Dresselhaus (MIT)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips When to Worry About Confinement 9 d 2-D Electrons 2-D Phonons d

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Nanowire Applications Transistors Interconnects Thermoelectrics Heterostructures Single-electron devices 10

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Nanowire Thermal Conductivity 11 Li, Appl. Phys. Lett. 83, 3187 (2003) Nanowire diameter

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Interconnects = Top-Down Nanowires 12 SEM of AMD’s “Hammer” microprocessor in 130 nm CMOS with 9 copper layers Intel 65 nm Cross-section 8 metal levels + ILD Transistor M1 pitch

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Cu Resistivity Increase <100 nm Lines Size Matters Why? Remember Matthiessen’s Rule 13

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Cu Interconnect Delays Increase Too Source: ITRS 14

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Industry Acknowledged Challenges 15 Source: ITRS

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Cu Resistivity and Line Width 16 Steinhögl et al., Phys. Rev. B66 (2002)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Modeling Cu Line Resistivity 17 Steinhögl et al., Phys. Rev. B66 (2002)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Model Applications 18 Steinhögl et al., Phys. Rev. B66 (2002) Plombon et al., Appl. Phys. Lett 89 (2006)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Resistivity Temperature Dependence 19

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Other Material Resistivity and MFP Greater MFP (λ) means greater impact of “size effects” Will Aluminum get a second chance?! 20

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Same Effect for Thermal Conductivity! Material with longer (bulk, phonon-limited) MFP λ  suffers a stronger % decrease in conductivity in thin films or nanowires (when d ≤ λ) Nanowire (NW) data by Li (2003), model Pop (2004) 21 Recall: bulk Si k th ~ 150 W/m/K bulk Ge k th ~ 60 W/m/K Approximate bulk MFP’s: λ Si ~ 100 nm λ Ge ~ 60 nm (at room temperature)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Back-of-Envelope Estimates 22 C (MJm -3 K -1 ) λ b ( nm ) v L (m/s) v T (m/s) k b (Wm -1 K -1 ) Si 1.66~ Ge 1.73~ (at room temperature)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips More Sophisticated Analytic Models 23 δ = d/λ < 1S = (1 – δ 2 ) 1/2 Flik and Tien, J. Heat Transfer (1990)Goodson, Annu. Rev. Mater. Sci. (1999)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips A Few Other Scenarios 24 Goodson, Annu. Rev. Mater. Sci. (1999) anisotropy

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Onto Nanotubes… Nanowires: –“Shrunk-down” 3D cylinders of a larger solid (large surface area to volume ratio) –Diameter d typically < {electron, phonon} bulk MFP Λ: surface roughness and grain boundary scattering important –Quantum confinement does not play a role unless d < {electron, phonon} wavelength λ ~ 1-5 nm (rarely!) Nanotubes: –“Rolled-up” sheets of a 2D atomic plane –There is “no” volume, everything is a surface* –Diameter 1-3 nm (single-wall) comparable to wavelength λ so nanotubes do have 1D characteristics 25 * people usually define “thickness” b ~ 0.34 nm b

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Single-Wall Carbon Nanotubes 26 Carbon nanotube = rolled up graphene sheet Great electrical properties – Semiconducting  Transistors – Metallic  Interconnects – Electrical Conductivity σ ≈ 100 x σ Cu – Thermal Conductivity k ≈ k diamond ≈ 5 x k Cu HfO 2 S (Pd)D (Pd) SiO 2 top gate (Al) CNT d ~ 1-3 nm Nanotube challenges: – Reproducible growth – Control of electrical and thermal properties – Going “from one to a billion”

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips CVD Growth at ~900 o C 27

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Fe Nanoparticle-Assisted Nanotube Growth Particle size corresponds to nanotube diameter Catalytic particles (“active end”) remain stuck to substrate The other end is dome-closed Base growth 28

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Water-Assisted CVD and Breakdown People can also grow “macroscopic” nanotube- based structures Nanotubes break down at ~600 o C in O 2, 1000 o C in N 2 29 Hata et al., Science (2004) in N 2 in O 2

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Graphite Electronic Structure 30 b ~ 3.4 Å a CC ~ 1.42 Å |a 1 | = |a 2 | = √3a CC

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Nanotube Electronic Structure 31 E G > 0 E G = 0 E G > 0 E G = 0 Collins and Avouris, Scientific American (2000)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Band Gap Variation with Diameter 32 Red: metallic Black: semiconducting E 11,M E 22,M E 22,S E 11,S = E G ≈ 0.8/d Charlier, Rev. Mod. Phys. (2007) “Kataura plot”

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips Nanotube Current Density ~ 10 9 A/cm 2 Nanotubes are nearly ballistic conductors up to room temperature Electron mean free path ~ nm 33 S (Pd)D (Pd) SiO 2 CNT G (Si) Javey et al., Phys. Rev. Lett. (2004) L = 60 nm V DS = 1 mV

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips 34 Transport in Suspended Nanotubes E. Pop et al., Phys. Rev. Lett. 95, (2005) SiO 2 Si 3 N 4 nanotube Pt Pt gate 2 μm nanotube 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?)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips 35 Include OP absorption: Transport Model Including Hot Phonons Non-equilibrium OP: T0T0 T AC = T L T OP R TH R OP I 2 (R-R c ) oxidation T Optical T OP Acoustic T AC I 2 (R-R C ) T OP T AC = T L Heat transfer via AC: Landauer electrical resistance E. Pop et al., Phys. Rev. Lett. 95, (2005)

© 2010 Eric Pop, UIUCECE 598EP: Hot Chips 36 Extracting SWNT Thermal Conductivity Ask the “inverse” question: Can I extract thermal properties from electrical data? Numerical extraction of k from the high bias (V > 0.3 V) tail of I-V data Compare to data from 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) Yu et al. (NL’05) This work ~T ~1/T