Toward Carbon Based Electronics Philip Kim Department of Physics Columbia University

Outline: Carbon Based Electronics Material Platform: Low dimensional graphitic systems 1-D: Carbon Nanotubes (since 1991) 2-D: Graphene (since 2004) Device Concepts Conventional: (extended) CMOS, SET Non-Conventional: Quantum Interference, Spintronics, valleytronics

SP2 Carbon: 0-Dimension to 3-Dimension Atomic orbital sp2 s p 0D 1D 2D 3D Fullerenes (C60) Carbon Nanotubes Graphene Graphite

Graphene : Dirac Particles in 2-dimension Band structure of graphene (Wallace 1947) kx' ky' E kx ky Energy hole electron Zero effective mass particles moving with a constant speed vF

Single Wall Carbon Nanotube ky kx Allowed states Metallic nanotube E k1D Semiconducting nanotube Eg ~ 0.8 ev / d (nm)

Extremely Long Mean Free Path in Nanotubes Multi-terminal Device with Pd contact L (mm) R (kW) T = 250 K R (kW) L (mm) Length (mm) Resistance (kW) T = 250 K r = 8 kW/mm R ~ L le ~ 1 mm R ~ RQ * Scaling behavior of resistance: R(L) Room temperature mean free path > 0.5 mm M. Purewall, B. Hong, A. Ravi, B. Chnadra, J. Hone and P. Kim, PRL (2007)

Nanotube FET Band gap: 0.5 – 1 eV On-off ratio: ~ 106 Vsd (V) -0.4 -0.8 -1.2 Isd (mA) Ph. Avouris et al, Nature Nanotechnology 2, 605 (2007) Schottky barrier switching Band gap: 0.5 – 1 eV On-off ratio: ~ 106 Mobility: ~ 100,000 cm2/Vsec @RT Ballistic @RT ~ 300-500 nm Fermi velocity: 106 m/sec Max current density > 109 A/cm2

Advantages of CNTFET Thin body (1-2 nm) -> suppressed short channel effect channel length ~ 10 nm has been demonstrated Javey et al. PRL (2004). No-dangling bond at surface -> high k-dielectric compatible Cg ~ CQ can be attainable; small RC, low energy Appenzeller et al., PRL (2002) Novel architecture -> Band-to-band tunneling FET: subthreshold slop ~ 40 meV/dB @RT

Nanotube Electronics: Challenges Pros: High mobility High on-off ratio High critical current density Small channel length Small gate capacitance Large Fermi velocity Con: Controlled growth graphene Rodgers, UIUC Aligned growth of Nanotubes Artistic dream (DELFT) IBM, Avouris group Nanotube Ring Oscillators

Discovery of Graphene Large scale growth efforts: CVD, MBE, chemical synthesis

Growth of Graphene Papers Jun 07 Dec 06 Mar 07 Sep 06 Jun 06 Mar 06 Dec 05 Sep 05 Jun 05 Mar 05 Dec 04 Sep 04 Sep 07 Jun 07 Dec 06 Mar 07 Sep 06 Jun 06 Mar 06 Dec 05 Sep 05 Jun 05 Mar 05 Dec 04 Sep 04 Sep 07 factor 4.5 / year Discovery of QHE in graphen Scotch tape method

Graphene Mobility GaAs HEMT Scattering Mechanism? Ripples Modulate Doped GaAs: Pfeiffer et al. GaAs HEMT n (1012 cm-2) Mobility (cm2/V sec) TC17 TC12 TC145 TC130 Mechanically exfoliated graphene Scattering Mechanism? Ripples Substrate (charge trap) Absorption Structural defects Tan et al. PLR (2007)

Enhanced Room Temperature Mobility of Graphene Graphene mobility: > 100,000 cm2/Vsec @ room temperature unsuspended best before annealing after annealing Density ( 1012 cm-2) Mobility (cm2/V sec) T (K) R (W) |n|=2X1011 cm-2 Resistance at High Density 0.24 W/K 0.13 W/K Strong density dependence! High mobility materials have been under intensive research as an alternative to Silicon for higher performance mobility: Si (1,400 cm2/Vsec), InSb (77,000 cm2/Vsec)

Graphene FET characteristics Low temperature direct atomic layer deposition (ALD) of HfO2 as high-κ gate dielectric Top-gate electrode is defined with a final lithography step. I-V measurements at two different back gate voltages show a distinct “kink” for different top-gate voltages Transconductance can be as high as gm = 328μS (150μS/μm) Poor on-off ratio: ~ 5-10 due to zero gap in bulk Meric, Han, Young, Kim, and Shepard (2008)

Graphene FET: High Saturation Velocity Meric, Han, Young, Kim, and Shepard (2008) Vtop = 0 V Vtop = -1.5 V Vtop = -2 V Vtop = -3 V VtopDirac = 2 V @ Vg = -40 V EF (eV) vsat (108 cm/s) Saturation velocity GaAs: 0.7x107 cm/s vFermi = 1x108 cm/s For comparison: Silicon: 1x107 cm/s Operation current density > 1 mA/mm

Graphene Device Fabrication Developing Graphene Nanostructure Fabrication Process graphene Contacts: PMMA EBL Evaporation Graphene patterning: HSQ EBL Development Graphene etching: Oxygen plasma Local gates: ALD HfO2 EBL Evaporation Graphene device structure with local gate control Oezyilmaz, Jarrilo-Herrero and Kim APL (2007)

Graphene Nanostructures Quantum Dot AB Ring Graphene with local barrier Goldhaber-Gordon (Stanford) Geim (Manchester) Morpurgo (DELFT) Graphene nanoribbons & nanoconstrictions Graphene PN junctions Graphene Side Gates Ensslin (ETH) Marcus (Harvard) Kim (Columbia)

Graphene Nanoribbons: Confined Dirac Particles 1 mm Gold electrode Graphene 10 nm < W < 100 nm W W Dirac Particle Confinement x y Egap~ hvF Dk ~ hvF/W W Zigzag ribbons Graphene nanoribbon theory partial list

Scaling of Energy Gaps in Graphene Nanoribbons W (nm) Eg (meV) 30 60 90 1 10 100 P1 P2 P3 P4 D1 D2 Eg = E0 /(W-W0) Han, Oezyilmaz, Zhang and Kim PRL (2007)

Top Gated Graphene Nano Constriction SEM image of device source drain top gate graphene 1 mm Hf-oxide 30 nm wide x 100 nm long drain source graphene SiO2 Back gate -8 -4 4 8 75 50 25 -25 -50 -75 VLG (V) VBG (V) 10-7 10-5 10-3 10-1 G (e2/h) -8 -4 4 8 10-6 10-5 10-4 10-3 10-2 10-1 VLG (V) G (e2/h) OFF

Graphene Nanoribbons Edge Effect Crystallographic Directional Dependence 30 60 90 20 40 Eg (meV) q (degree) Son, et al, PRL. 97, 216803 (2006) 2mm Rough Graphene Edge Structures

Localization of Edge Disordered Graphene Nanoribbons Querlioz et al., Appl. Phys. Lett. 92, 042108 (2008) See also: Gunlycke et al, Appl. Phys. Lett. 90 (14), 142104 (2007). Areshkin et al, Nano Lett. 7 (1), 204 (2007) Lherbier et al, PRL 100 036803 (2008) Transport ‘gap’

Variable Range Hopping in Graphene Nanoribbons Conductance (mS) Vg (V) W = 37 nm 0.1 1 10 100 60 40 20 4K 15K 100K 200K 300K E d: dimensionality T EF x ln(R) T-1/3 70 nm 48 nm 37 nm 22 nm 15 nm 31 nm 2D VRH ln(R) T-1/2 70 nm 48 nm 37 nm 22 nm 15 nm 31 nm 1D VRH T-1 ln(R) 3 2 1 -1 -2 0.2 0.1 0.0 Arrhenius plot 70 nm 48 nm 37 nm 22 nm 15 nm 31 nm

Graphene Electronics: Challenges Pros: High mobility High on-off ratio High critical current density Small channel length Small gate capacitance Large Fermi velocity Con: Controlled growth tunability of band gaps Edge control Rodgers, UIUC Aligned growth of Nanotubes This can be turned into advantage: doping site, functionality, and etc… Artistic dream (DELFT)

Graphene Electronics: Conventional & Non-conventional Conventional Devices Band gap engineered Graphene nanoribbons Graphene quantum dot (Manchester group) FET Nonconventional Devices Son et al. Nature (07) Graphene Spintronics Trauzettel et al. Nature Phys. (07) Graphene psedospintronics Cheianov et al. Science (07) Graphene Veselago lense

Carbon Nanotube Superlattice Purewal, Takekosh, Jarillo-Herrero, Kim (2008) Conductance (mS) 1 Pd (under HfO2) Pd (over HfO2) SWCNT (under HfO2) HfO2 on SiO2/Si+ 20 nm 60 nm 1 mm Kouwenhoven PRL (1992)

Realistic smooth potential distribution Graphene NPN junctions Ballistic Quantum Transport in Graphene Heterojunction Realistic smooth potential distribution Requirements for Experimental Observation: Small d -> better collimination Graphene NPN junctions Long Mean free path -> Ballistic conduction n p x potential Cheianov and Fal’ko (2006) Zhang and Fogler (2008) Tunneling through smooth pn junction Top gate width: 50 nm < Lm graphene electrode 1 mm SEM image of device Klein Tunneling Transmission coef Novoselov et al (2006) Ballistic transport in the barrier Total Internal Reflection

Transport Ballistic Graphene Heterojunction Young and Kim (2008) VTG (V) -10 -2 -4 -6 -8 10 8 6 4 2 Conductance (mS) 12 graphene electrode 1 mm Mean free path ~ 200 nm ppp pnp npn nnn 18 V -18 V VBG = 90 V Junction length < 100 nm VBG = -90 V PN junction resistance Zhang and Fogler (2008) See also Shavchenko et al and Goldhaber-Gordon’s recent preprint q´ q L n1,, k1, T R R* n2,, k2 Conductance Oscillation: Fabry-Perot k1 /k2= sinq’ / sinq Df= 2L /cosq’

Quantum Oscillations in Ballistic Graphene Heterojunction Oscillation persist high temperature! Resistance Oscillations ntop (1012 cm2) nback (1012 cm2) 5 -5 1 -1 dR/dntop ( h/e2 10-15 cm-2)

Conclusions Carbon nanotube FET is mature technology demonstrating substantial improvement over Si CMOS Controlled growth and scaling up of CNTFET remains as a challenge Graphene provides scaling up solution of carbon electronics with high mobility Controlled growth of graphene and edge contol remains as a challenge Novel quantum device concepts have been demonstrated on graphene and nanontubes