1. Atomistic Simulation of Carbon Nanotube FETs Using Non-Equilibrium Green’s Function Formalism Jing Guo 1, Supriyo Datta 2, M P Anantram 3, and Mark Lundstrom 2 1 Department of ECE, University of Florida, Gainesville, FL 2 School of ECE, Purdue University, West Lafayette, IN 3 NASA Ames Research Center, Moffett Field, CA 1.Introduction 2.NEGF Formalism 3.Ballistic CNTFETs 4.Summary

2. 2 McEuen et al., IEEE Trans. Nanotech., 1, 78, 2002. Introduction: carbon nanotubes (see also: R. Saito, G. Dresselhaus, and M.S. Dresselhaus, Physical Properties of Carbon Nanotubes, Imperial College Press, London, 1998.)

3. 3 Introduction: device performance Javey, Guo, Farmer, Wang, Yenilmez, Gordon. Lundstrom, and Dai, Nano Lett., 2004 tube d ~1.7 nm ( W = 2d ) -0.1 V -0.4 V -0.7 V -1.0 V -1.3 V V G =0.2V nanotube diameter ~1.7 nm L ch ~50nm Gate 8nm HfO 2 SiO 2 p++ Si Pd CNT

4. 4 1.Introduction 2.NEGF Formalism 3.Ballistic CNTFETs 4.Summary Outline

5. 5 Nonequilibrium Green’s Function (NEGF) Gate molecule or device [H] D S f1f1 f2f2 device contacts scattering Datta, Electronic Transport in Mesoscopic Systems, Cambridge, 1995 Charge density (ballistic) Current

6. 6 1.Introduction 2.NEGF Formalism 3.Ballistic CNTFETs 4.Summary Outline

7. 7 CNTFETs: real-space basis (ballistic) D S Gate atomistic (p Z orbitals ) c t H= ΣDΣD ΣSΣS Recursive algorithm for G r : O(m 3 N) Lake et al., JAP, 81, 7845, 1997 (m, 0) CNT

8. 8 CNTFETs: real-space results band gap interference 2 nd subband Confined states Gate n+n+ n+n+ i

9. 9 CNTFETs: mode-space approach (ballistic) c t k t The qth mode -  S (1,1) and  D (N,N) analytically computed -Computational cost: O(N) real space O(m 3 N) (m,0) CNT

10. 10 CNTFETs: mode-space results n+n+ n+n+ i 2 modes real space band profile (ON) coaxial G V D =0.4V d CNT ~1nm coaxial G 2 modes real space coaxial G Gate 8nm HfO 2 SiO 2 p++ Si Pd CNT

11. 11 CNTFETs: treatment of M/CNT contacts M metallic tube band band discontinuity Kienle et al, ab initio study of contacts in progress

12. 12 CNTFETs: treatment of M/CNT contacts Gate V D =V G =0.4V Charge transfer in unit cell: Leonard et al., APL, 81, 4835, 2002 Metal S metal D tunneling

13. 13 CNTFETs: 3D Poisson solver Gate 8nm HfO 2 SiO 2 p++ Si Pd CNT Method of moments: Electrostatic kernel: for 2 types of dielectrics available in Jackson, Classical Electrodynamics, 1962 Neophytou, Guo, and Lundstrom, 3D Electrostatics of CNTFETs, IWCE10

14. 14 CNTFETs: numerical techniques given n: --- > U scf “Poisson” given U scf : --- > n transport equation Iterate until self - consistent given n: --- > U scf Poisson given U scf : --- > n NEGF Transport Iterate until self - consistent -Non-linear Poisson -Recursive algorithm for -Gaussian quadrature for doing integral -Parallel different bias points -~20min for full I-V of a 50-nm CNTFET

15. 15 CNTFETs: theory vs. experiment G  Bp =0 d CNT ~1.7nm R S =R D ~1.7K  V D = -0.3V -0.2V -0.1V experiment theory Gate 8nm HfO 2 10 nm SiO 2 p++ Si Pd CNT Javey, et al., Nano Letters, 4, 1319, 2004

16. 16 Summary A simulator for ballistic CNTFETs is developed - atomistic treatment of the CNT - 3D electrostatics - phenomenological treatment of M/CNT contacts - efficient numerical techniques Theory is calibrated to experiment