From nanoscale technology scenarios to compact device models for ambipolar devices

1. From nanoscale technology scenarios to compact device models for ambipolar devices Sébastien Frégonèse, Cristell Maneux, Thomas Zimmer CNRS, Université Bordeaux, UMR 5218, Laboratoire IMS, Bordeaux

2. Outline • Introduction • Development of a dual-gate compact model • Material parameter • Drain current modeling • Charge modeling • Equivalent circuit and self-consistent potential calculation • Comparison of compact model with measurement of the literature • Circuit simulation • Conclusion

3. Introduction • New materials: • Nanowire • Carbon nanotube (single wall : 1993) • Graphene and graphene nanoribbon (2004) (Nobel Prize 2010) New transistors

4. Introduction New transistor development using emerging material Y.-M. Lin, J. Appenzeller, J. Knoch, and Ph. Avouris, “High performance carbon nanotube field-effect transistor with tunable polarities,” IEEE Trans. On Nanotech., vol. 4, N° 5, pp. 481–489, September 2005 Open new design paradigm

5. Introduction Possibility to develop new reconfigurable logic cells I. O’Connor, J. Liu, F. Gaffiot, F. Prégaldiny, C. Lallement, C. Maneux, J. Goguet, S. Frégonèse, T. Zimmer, L. Anghel, TT Dang, R. Leveugle, “CNTFET Modeling and Reconfigurable Logic-Circuit Design”, IEEE Trans. On Circuits And Systems I, Vol. 54, No. 11, November 2007 pp 2365-2379 • Needs an accurate compact model to : • validate the approach • evaluate the performances • develop new structures

6. Introduction Ti D FG Al2 O3 S D BG D CNT Al SiO2 Si (P++) DG-CNTFET Schottky barrier Carrier Charge Source access Drain access Inner part Thermionic transport Tunneling (SB) Vsi Conduction Band source VCNTi Vdi VCNTS VCNTD Valence Band drain Electrostatic control with back-gate Electrostatic control with front-gate

7. Material parameter Zone Folding model of a (10,0) nanotube Numerical calculation • Analytical model for Density of states • subband value • effective mass • non-parabolicity parameter Band structure Density of states J. C. Charlier et al. , Rev. Mod. Phys., Vol. 79, No. 2, April–June 2007 Input data for charge model and drain current model

8. Drain current modeling Thermionic contribution BTBT Current spectrum in a MOS-like CNTFET using NEGF simulation * • Thermionic contribution : T(E) = 1 above conduction band • = 0 otherwise • BTBT contribution : T(E) = for E =[CB access, VB channel] • 0 otherwise * NEGF simulator is originally created in Purdue University

9. Charge modeling Vsi source Vdi drain Carriers from the drain are reflected on the source SB VCNTi VCNTD Same method is applied for electrons and holes and in each region VCNTS integration limits for carrier coming from source Analytical approximate solution proposed in IEEE Trans Elec. Devices integration limits for carrier coming from drain

10. Equivalent circuit Charge in Source and Drain access from Drain Charge in inner part from Drain Charge in inner part from Source Charge in Source and Drain access from Source Thermionic, SB, BTBT current Self consistent potential calculation in each region

11. Validation of the model: comparison with the IBM device Y.-M. Lin, J. Appenzeller, J. Knoch, and Ph. Avouris, vol. 4, N° 5, pp. 481–489, September 2005

12. Validation of the model: comparison with the Stanford device Prior front gate fabrication A. Javey, et al., Nano Letters, vol. 4, Mar. 2004, p. 447-450

13. Evaluation of parasitic element with TCAD Finite element simulation D BG FG Parasitic parameter extraction to metal 1 S

14. Circuit application: voltage controlled ring oscillator 5 stages ring oscillator Parameters used in the simulation are the one obtained from the IBM technology except VFB which is reduced to have a better symmetry of the CMOS like inverter

15. Conclusion • A compact model dedicated to dual gate device • Drain current modeling • Charge modeling • Equivalent circuit • Validation with measurement from 2 different technologies • Stanford University • IBM • Circuit simulation • Parasitic element • Voltage controlled oscillator • Outlook • Main limitation for technology developpement: control of nanotube chirality and density • Technological breakthrough needed

16. Outlooks Alternative solutions for dual gate devices “Dual-gate silicon nanowire transistors with nickel silicide contacts” J. Appenzeller et al. 1IBM, 2Institute for Thin Film and Interfaces,Julich “Dual-gate Graphene FETs With fT of 50 GHz”, LIN et al., IEEE EDL, VOL. 31, NO. 1, JANUARY 2010 • Model can be easily extended to graphene nanoribbon and very small nanowire (1D and ballistic)

17. Acknowledgement • Work was supported by the French National Research Agency ANR through ARPEGE “NANOGRAIN” project. • The authors would also like to thank all partners of this project for the fruitful discussions.

18. Conclusion and outlooks Peak of inflated expectation Visibility Through of disillusionment Plateau of productivity Slope of enlightenment Technology trigger Time 1991-1993 Discover of CNTs ~2008-2010 CNTFET Technological breakthrough needed (control of nanotube chirality and density)

19. Performance of an optimized structure • SB height is optimized to get ambipolar symmetric behavior • Optimize ION current for both N an P behavior • Back-gate insulator is optimized to improve the tradeoff between parasitic and SB thickness control (ION current) 50nm 50nm 20nm 12 tubes /50 nm (Optimum theoretical limit with this configuration) 6 tubes /50 nm 1 tube /50 nm

20. Calculation of the Schottky barrier 0.123meV on Valence band side Z. Chen, J. Appenzeller, J. Knoch, Y. Lin, and P. Avouris, “The Role of Metal-Nanotube Contact in the Performance of Carbon Nanotube Field-Effect Transistors”, Nano Letters, 2005, Vol. 5, No. 7, 1497-1502

21. Modeling: Tunneling through Schottky barrier WKB calculation Effective Schottky barrier model • Tunneling through barrier is usually performed using WKB approximation • WKB is too complex to obtain analytical expression of current • => Effective Schottky barrier approach* *Knoch, J.; Appenzeller, J., physica status solidi (a), vol. 205, issue 4, pp. 679-694 (2008). Fitting parameter

22. Thermionic / Schottky Current modeling Transition between Thermionic /Schottky behavior: Landauer equation Electron contribution:

23. BTBT Current modeling Analytical model: Current spectrum in a MOS-like CNTFET using NEGF simulation * Analytical solution is straightforward * NEGF simulator is originally created in Purdue University