1. Scaling of the performance of carbon nanotube transistors 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 S. Heinze 1, M. Radosavljević 2, J. Tersoff 3, and Ph. Avouris 3

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

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

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

5. Evidence for Schottky barriers: Influence of the contacts for CNFETs NT VgVg V s = 0 VdVd 10 -13 10 -12 10 -11 10 -10 10 -9 10 -8 10 -7 10 -6 Current [A] -2.00.01.0 Gate Voltage [V] V d =-0.9V to -0.5V 0.2V steps VdVd V s = 0 L=300nm t ox =5nm 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.

6. d NT =1.4nm  E g ~0.6eV Typical SBs for NTs ~ 0.3eV Conventional vs. Schottky barrier FET Schottky Barrier Transistor ambipolar Characteristic Conventional Transistor p-type Characteristic

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

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

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

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

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

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

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

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

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

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

17. Gas adsorption: Change in metal workfunction Metal workfunction increased by 0.2eV Calculated Gas Adsorption Characteristics NT Metal Gate

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

19. Device geometry Turn-on vs oxide thickness for bottom gate SB-CNFETs  V scale ~ sqrt(t ox )

20. Analytic model for thin sheet contact Potential near the Edge:

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

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

23. Scaling of drain voltage for ultra-thin oxide CNFETs? -1.2 -0.9 -0.6 -0.3 0.0 0.3 Energy (eV) 4003002001000 Position along Nanotube (nm) Source Drain t ox =30nm t ox =2nm V drain =+0.8V, V gate =+0.4V Minimal Current (OFF-current) rises with lower oxide thickness independent barriers – one controlled by V g, the other by V d –V g identical (and minimal) hole/electron current at V g = V d –V g  V d = 2V g 120 80 40 0 Height (nm) 4003002001000 Length (nm) Source Drain=0.5V Top Electrode Bottom Gate=1V 0.9 Nanotube 0.4 0.3 0.2 0.1 Ultra-thin oxide: turn-on voltage ~ Vd

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

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

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

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

28. Conclusions 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(t ox ) Scaling of drain voltage at ultra-thin oxides necessary New device physics: light emission device New device designs may be favorable CN Transistors competetive with Si MOSFETs, however: