Carbon Nanotube Field-Effect Transistors: An Evaluation D.L. Pulfrey, L.C. Castro, D.L. John Department of Electrical and Computer Engineering University of British Columbia Vancouver, B.C. V6T1Z4, Canada

S.Iijima, Nature 354 (1991) 56 Single-wall and multi-wall NANOTUBES Compare: flaxen hair - 20,000 nm

J.Kong et al., Nature, 395, 878, 1998 CNT formation by catalytic CVD 5  m islands in PMMA patterned by EBL LPD of Fe/Mo/Al catalyst Lift-off PMMA CVD from methane at 1000C 2000nm No field Growth in field (1V/micron) A. Ural et al., Appl. Phys. Lett., 81, 3464, 2002

Single-Walled Carbon Nanotube 2p orbital, 1e - (  -bonds) Hybridized carbon atom  graphene monolayer  carbon nanotube

Chiral tube (5,2) Tube Structure (n,m): VECTOR NOTATION FOR NANOTUBES Adapted from Richard Martel

E-E F (eV) vs. k || (1/nm) (5,0) semiconducting(5,5) metallic E g /2

Doping Substitutional unlikely Adsorbed possible e.g., K, O Interior possible Tubes are naturally intrinsic

Phonons Acoustic phonons (twistons) mfp  300 nm Ballistic transport possible Optical phonons mfp  15 nm

Fabricated Carbon Nanotube FETs Few prototypes –[Tans98]: 1 st published device –[Wind02]: Top-gated CNFET –[Rosenblatt02]: Electrolyte-gated Nanotube

CLOSED COAXIAL NANOTUBE FET STRUCTURE chirality: (16,0) radius: 0.62 nm bandgap: 0.63 eV length: nm oxide thickness: (R G -R T ): nm

kxkx kxkx kzkz E METAL (many modes) CNT (few modes) Doubly degenerate lowest mode MODE CONSTRICTION and TRANSMISSION T

gate insulator nanotube C ins CQCQ Quantum Capacitance Limit EbEb source

Quantum Capacitance and Sub-threshold Slope High k dielectrics: zirconia - 25 water mV/decade ! - Javey et al., Nature Materials, 1, 241, 2002

AMBIPOLAR CONDUCTION Experimental data: M. Radosavljevic et al., arXiv: cond-mat/ v1 Vds= - 0.4V Vgs=

Minimize the OFF Current  G = 4.2 eV Increasing  S,D  3.9, 4.2, 4.5 eV  S,D = 3.9 eV Increasing  G  3.0, 4.37 eV ON/OFF  10 3

General non-equilibrium case E f(E) E FS 0.5 E f(E) E FD 0.5 g(E) E 1D DOS Non-equilib f(E) Q(z,E)=qf(E)g(E) Solve Poisson iteratively

CURRENT in 1-D SYSTEMS

Quantized Conductance In the low-temperature limit: Interfacial G: even when transport is ballistic in CNT 155  S for M=2

Measured Conductance A. Javey et al., Nature, 424, 654, 2003 No tunneling barriers Low R contacts (Pd) G  0.4 G max at 280K !!

Drain Saturation Current If T=1 Get BJT behaviour! V GS  EbEb EFEF Zero-height Schottky barrier

Present world record Javey et al., Nature, 424, 654, 2003 ON Current: Measured and Possible  S,D = 3.9eV  G = 4.37eV C Q limit 80% of QC limit!

Predicted Drain Current -ve 0 +ve Vgs=Vds=0.4V 70mA/  m !!

Transconductance Low V DS : modulate for G High V DS : modulate V GS for g m

Transconductance: Measured and Possible Highest measured: Rosenblatt et al. Nano. Lett., 2, 869, 2002 C Q limit  S,D = 3.9eV  G = 4.37eV 80% of QC limit!

CNFET Logic A.Javey et al., Nature Materials, 1, 241, 2002 Gain=60 1 st OR-gate 0,0

Williams, Veenhuizen, de la Torre, Eritja and Dekker Nature, 420, 761, CNTs Functionalized with DNA Recognition-based assembly

Self-assembly of DNA-templated CNFETs K.Keren et al., Technion.

CONCLUSIONS Schottky barriers play a crucial role in determining the drain current. Negative barrier devices enable: control of ambipolarity, high ON/OFF ratios, near ultimate-limit S, G, I D, g m. CNFETs can be self-assembled via biological recognition. CNs have excellent thermal and mechanical properties. CNFETs deserve serious study as molecular transistors.

Extra Slides

Nanoscale Bandgap tunability Metals and semiconductors Ballistic transport Strong covalent bonding: -- strength and stability of graphite -- reduced electromigration (high current operation) -- no surface states (less scattering, compatibility with many insulators) High thermal conductivity -- almost as high as diamond (dense circuits) Let’s make transistors! Compelling Properties of Carbon Nanotubes

From: Dresselhaus, Dresselhaus & Eklund Science of Fullerenes and Carbon Nanotubes. San Diego, Academic Press. Adapted from Richard Martel. Armchair Zig-Zag Chiral CHIRAL NANOTUBES

Carbon Nanotube Properties Graphene sheet 2D E(k //,k  ) –Quantization of transverse wavevectors k  (along tube circumference)  Nanotube 1D E(k // ) Nanotube 1D density-of-states derived from [  E(k // )/  k] -1 Get E(k // ) vs. k(k //,k  ) from Tight-Binding Approximation

Density of States k || or k z

Tight Binding David John, UBC Wolfe et al., “Physical Properties of Semiconductors”

Density of States (5,0) tube David John E(eV) vs. k || (1/nm) E(eV) vs. DOS (100/eV/nm)

Tuning the Bandgap T. Odom et al., Nature, 391, 62, 1998 E g 7 nm “zero bandgap” semiconductor

nanotube oxide gate Planar Coaxial The Ideal Structure

J.Kong et al., Nature, 395, 878, 1998 CNT formation by catalytic CVD 5  m islands in PMMA patterned by EBL LPD of Fe/Mo/Al catalyst Lift-off PMMA CVD from methane at 1000C 1000nm 300nm 2000nm

CNT formation by E-field assisted CVD A. Ural et al., Appl. Phys. Lett., 81, 3464, 2002 V applied between Mo electrodes. CVD from catalytic islands. No field 10V applied

Bottom-gated Nanotube FETs A. Javey et al., Nature, 424, 654, 2003 Note very high I D 10mA/  m Nanotube 1 st CNFET S. Tans et al., Nature, 393, 49, 1998

Phenomenological treatment of metal/nanotube contacts Evidence of work function-dependence of I-V : A. Javey et al., Nature, 424, 654, 2003 Zero hole barrier

Schrödinger-Poisson Model Need full QM treatment to compute: -- Q(z) within positive barrier regions -- Q in evanescent states (MIGS) -- S  D tunneling -- resonance, coherence

Schrödinger-Poisson Model L.C. Castro, D.L. John SDCNT Unbounded plane waves

Increasing the Drain Current Vgs=Vds=0.4V 70mA/  m !!

Array of vertically grown CNFETs W.B. Choi et al., Appl. Phys. Lett., 79, 3696, x10 11 CNTs/cm 2 !!