Scaling of the performance of carbon nanotube transistors

Scaling of the performance of carbon nanotube transistors S. Heinze 1, M. Radosavljević2, J. Tersoff 3, and Ph. Avouris 3 1 Institute of Applied Physics, University of Hamburg, Germany 2 Novel Device Group, Intel Corporation, Hillsboro, OR 3 IBM Research Division, TJ Watson Research Center, Yorktown Heights, NY • Why carbon nanotube transistors? • Evidence for Schottky barriers • Carbon nanotube Schottky barrier transistors • Gas adsorption versus doping • Scaling of transistor performance • New device designs & capabilities • Conclusions

Carbon nanotube field-effect transistors comparable with Si MOS-FETs Nanotube FETs with top gates: • turn-on gate voltage is about 1 V • favorable device characteristics S. J. Wind et al. , Appl. Phys. Lett. 80, 3817 (2002).

Evidence for Schottky barriers: scanned gate microscopy at contacts map transport current as a function of moving, charged AFM tip (a) (b) Vtip = -2 V current increase when gating the source junction barrier thinning. M. Freitag et al. , Appl. Phys. Lett. 79, 3326 (2001).

Evidence for Schottky barriers: ambipolar conduction in SWNTs Bottom gate CNFETs with Ti contacts annealed; conversion from p-type to ambipolar conductance R. Martel et al. , PRL 87, 256805 (2001).

Evidence for Schottky barriers: Influence of the contacts for CNFETs Current [A] 10 10 -6 -500 L=300 nm -7 -8 tox=5 nm -9 -10 -11 -12 -13 Vd=-0. 9 V to -0. 5 V 0. 2 V steps -2. 0 -1. 0 0. 0 1. 0 -300 -200 0 0. 0 -0. 5 -1. 0 -1. 5 Drain Voltage [V] Vd Vs = 0 Vg Vg=-1. 5 V to 0 V 0. 5 V steps -100 Gate Voltage [V] NT -400 Current [n. A] 10 Vs = 0 Vd Switching S & D changes: – Slope by factor of 2 – ON-state by factor of 5 not due to bulk, it is a contact effect M. Radosavljević et al.

Conventional vs. Schottky barrier FET Conventional Transistor p-type Characteristic Schottky Barrier Transistor d. NT=1. 4 nm Eg~0. 6 e. V ambipolar Typical SBs Characteristic for NTs ~ 0. 3 e. V

Transmission through Schottky barrier WKB approximation + single NT band: Landauer-Büttiker formula for current:

Self-consistent SB-transistor model for needle-like contact • Cylindrical gate at RGate • Metal electrode of NT diameter • Analytic electrostatic kernel G • Test of approximations for Gate NT Electrostatic potential: Charge on the nanotube: Solution by self-consistency cycle Metal

Needle-like contact: conductance vs. gate voltage Ideal sharp Metal-NT Contact turn-on voltage ~ Eg/2 Gate Metal NT

Carbon nanotube transistors with planar gates Conductance Electrostatic. Modulation Potential Calculated NT-potential • Solve a 2 D boundary value problem Vext(x) • Local approximation for potential from NT charge

Influence of the contact geometry Gate Metal NT Scaled Characteristics PRL 89, 106801 (2002)

Gas adsorption vs. doping: Experimental observations Doping with Potassium Gas Adsorption (O 2) Increase of Potassium Increase of O 2 V. Derycke et al. , APL 80, 2773 (2002).

Uniform doping: Experiment vs. SB model Doping with Potassium Increase of Potassium Gate Metal NT Needle-Contact Model

Uniform doping of nanotube Calculated Doping Characteristics n-doped at 5 10 -4 e/atom Gate Metal NT

Uniform doping of nanotube Calculated Doping Characteristics n-doped at 1 10 -3 e/atom Gate Metal NT

Gas adsorption: Experiment vs. SB model Gas Adsorption (O 2) Increase of O 2 Gate Metal NT Needle-Contact Model

Gas adsorption: Change in metal workfunction Calculated Gas Adsorption Characteristics Metal workfunction increased by 0. 2 e. V Gate Metal NT

How does the performance of Schottky barrier CNFETs scale? ultra-thin oxide CNFETs: Scaling law with oxide thickness? Why is thermal limit of 60 m. V/decade not reached? J. Appenzeller et al. , PRL 89, 126801 (2002).

Turn-on vs oxide thickness for bottom gate SB-CNFETs Device geometry Vscale ~ sqrt(tox)

Analytic model for thin sheet contact Potential near the Edge:

Analytic model applied to bottom gate SB-CNFETs Single, empirical factor for bottom gate devices

Scaling of turn-on performance of CNFETs with oxide thickness Analytic Model Largest improvements by optimization of the contact geometry PRB 68, 235418 (2003)

Scaling of drain voltage for ultra-thin oxide CNFETs? Top Electrode Minimal Current (OFF-current) rises with lower oxide thickness 0. 1 0. 2 0. 3 80 0. 3 40 Source 0. 4 Nanotube Energy (e. V) 0. 9 0 0. 0 Drain=0. 5 V tox=30 nm tox=2 nm Bottom Gate=1 V 0 100 -0. 3 200 Source Height (nm) 120 300 400 Length (nm) -0. 6 Drain • independent barriers –-0. 9 Vdrain=+0. 8 V, Vgate=+0. 4 V one controlled by Vg, the other by Vd–Vg -1. 2 • identical (and minimal) hole/electron Ultra-thin oxide: turn-on 0 100 voltage 200 ~ Vd 300 400 current at Vg = Vd–Vg Vd = 2 V g Position along Nanotube (nm)

Effect of drain voltage for ultra-thin oxide CNFET Bottom-gate: tox=2 nm exponential increase of OFF current with Vd

Scaling of drain voltage: model vs. experiment tox=2 nm APL 83, 2435 (2003)

OFF state problem for transistor light emission device Infrared light emission from a SWNT: J. Misewich et al. , Science 300, 783 (2003).

Asymmetric device design to solve OFF state problem Symmetric CNFET (tox=2 nm) unfavorable OFF state Asymmetric CNFET low OFF current & p- and n-type device for Vd<0 and Vd>0 APL 83, 5038 (2003)

Conclusions CN Transistors competetive with Si MOSFETs, however: • Transistor action in CNFETs due to Schottky barriers ambipolar transfer characteristic (I vs Vg) • Nanoscale features of contacts are essential • Gas adsorption modifies band line-up at the contact • Scaling in turn-on regime with sqrt(tox) • Scaling of drain voltage at ultra-thin oxides necessary • New device physics: light emission device • New device designs may be favorable