1. SINANO WORKSHOP Munich, September 14 th 2007 1 R. Clerc, Q. Rafhay, M. Ferrier, G. Pananakakis, G. Ghibaudo IMEP-LAHC, INPG, Minatec, Grenoble, France P. Palestri, L. Lucci, D. Esseni, L. Selmi DIEGM, Univ. Udine, Italy Understanding Quasi Ballistic Transport in Si and Alternative Channel Material MOSFETs in collaboration with STMicroelectronics, Crolles : F. Bœuf and T. Skotnicki

2. SINANO WORKSHOP Munich, September 14 th 2007 2 Introduction To attain adequate drive current for the highly scaled MOSFETs, quasi-ballistic operation with enhanced thermal velocity and injection at the source end appears to be needed. Eventually, nanowires, carbon nanotubes, or other high transport channel materials (e.g., germanium or III-V thin channels on silicon) may be needed. ITRS 2005 Nano MOSFET (L < 20 nm) challenges our understanding of device physics SINANO project was the opportunity of a nice collaboration between : IMEP Grenoble (Analytical Modeling) and the University of Udine (Modeling and Simulation) in the framework of the WP4 : Modelling and Simulation of nanodevices Coordinator: Enrico Sangiorgi (Univ. Bologna) AIM of this presentation : discuss the state of the art of the understanding of transport in Quasi Ballistic Nano MOSFETs

3. SINANO WORKSHOP Munich, September 14 th 2007 3 Outline BASICS CONCEPTS OF QUASI BALLISTIC TRANSPORT APPLICATION TO Si UTB MOSFETs EXTENSION TO ALTERNATIVE CHANNEL MATERIALS

4. SINANO WORKSHOP Munich, September 14 th 2007 4 BASICS CONCEPTS OF QUASI BALLISTIC TRANSPORT

5. SINANO WORKSHOP Munich, September 14 th 2007 5 Basics of Ballistic transport SourceDrain L Energy Flux of carrier (In quasi equilibrium) Virtual Source Channel Gate (In quasi equilibrium) VdVd Scattering Long channel : TRANSPORT LIMITED BY THE CHANNEL when L  0, I d  +  ? Transport in long channel devices NO : (in Drift Diffusion model) velocity can not exceed saturation velocity v sat Saturation velocity applies when L >> (scattering required)

6. SINANO WORKSHOP Munich, September 14 th 2007 6 Basics of Ballistic transport Transport in Ballistic devices Performance are no longer limited by transport along the channel, but by injection at the source end SourceDrain L Energy Flux of carrier (In quasi equilibrium) Virtual Source Channel Gate (In quasi equilibrium) VdVd TRANSPORT LIMITED BY THE SOURCE INJECTION L independant M. Lundstrom.; Z. Ren, “Essential physics of carrier transport in nanoscale MOSFETs”, IEEE Trans. Elec. Dev., Volume 49, No 1, p 133 – 141, January 2002

7. SINANO WORKSHOP Munich, September 14 th 2007 7 1 10 100100010000 Channel Length (nm) Drain Current (a.u) Drift Diffusion including V sat L independent Ballistic limit L independent Drift Diffusion 1/L Ballistic enhancement factor Mean Free Path Concept of Ballistic Enhancement Factor Ballistic limit (L independent) : Ballistic Enhancement Factor : M. Lundstrom.; Z. Ren, “Essential physics of carrier transport in nanoscale MOSFETs”, IEEE Trans. Elec. Dev., Volume 49, No 1, p 133 – 141, January 2002 In Si, BEF close to 1. Necessity to improve V inj

8. SINANO WORKSHOP Munich, September 14 th 2007 8 0.0 0.2 0.40.60.8 1 2 Injection velocity (10 5 m/s) Gate Voltage Vg (V) t si = 3 nm t si = 6 nm MC simulation Natori Injection velocity in the Natori Model Natori’s approximation : Charge at the entrance of the channel controlled by the gate i.e ideal MOSFET with negligible DIBL. Comparison with MC simulations (L ~ 4 t si ) K. Natori, “ Ballistic metal oxide semiconductor field effect transistor ” Journal of Applied Physics, vol. 76 p. 4879 - 4890 (1994).

9. SINANO WORKSHOP Munich, September 14 th 2007 9 Injection velocity of one subband: 0.40.20 0.40.6 1 2 3 4 5 E F – E 0 (eV) Injection Velocity (  10 5 m/s) 0.40.20 0.40.6 0 0.1 0.2 0.3 kT  E F – E 0 (eV) Average kinetic energy (eV) E F – E 0 (eV) Injection Velocity (  10 5 m/s) 0.40.20 0.40.6 2 3 4 5 1 V inj 0 V inj V inj 1 One subbandTwo subbands decrease m T increase E F - E 0 decrease the number of subband The role of Density of State (DOS) in Injection Velocity Enhancement Decrease the 2D Density of States

10. SINANO WORKSHOP Munich, September 14 th 2007 10 Quantum Capacitance and Density of State (DOS) M. De Michielis, D. Esseni, F. Driussi, “Analytical Models for the Insight Into the Use of Alternative Channel Materials in Ballistic nano-MOSFETs” IEEE Trans. Elec. Dev., p. 155-122, January 2007 DOS reduction leads to Quantum Capacitance reduction (Dark Space effect enhancement) Quantum Limit (= 1 fully degenerated subband) with DG : Dark Space = 2.7 Å 0 0.2 0.4 0.60.81 0 2 4 6 8 10 Transverse Eff. Mass m t Injection velocity (10 5 m/s) EOT = 5 Å V dd = 0.8 V Quantum Limit w. Q. Capa w.o. Q. Capa v th

11. SINANO WORKSHOP Munich, September 14 th 2007 11 APPLICATION TO Si UTB MOSFETs

12. SINANO WORKSHOP Munich, September 14 th 2007 12 1.3 1.4 1.51.61.71.81.9 2 3 4 5 6 1.5 3 6 10 6 3 1.5 t si (nm) = Fully Ballistic Quasi Ballistic r =0.4 Drain Current I DG /2 (10 3 µA/µm) Injection Velocity (10 5 m/s) How to reduce DOS in Si MOSFET ? M. Ferrier, R. Clerc, L. Lucci, Q. Rafhay, G. Pananakakis, G. Ghibaudo, F. Boeuf, T. Skotnicki. « Conventional Technological Boosters for Injection Velocity in Ultra Thin Body MOSFETs » accepted in IEEE Transaction On Nanotechnology by scaling body thickness ? Not efficient using biaxial strain (+ 40 %) no significant enhancement of quantum capacitance

13. SINANO WORKSHOP Munich, September 14 th 2007 13 Is Ballistic Transport Realistic ? S. Eminente, D. Esseni, P. Palestri, C. Fiegna, L. Selmi, E. Sangiorgi “ Understanding Quasi-Ballistic Transport in Nano-MOSFETs: Part II – Technology Scaling Along the ITRS”, IEEE Transactions on Electron Devices, 52 p. 2736 - 2743 (2005). MC simulation reports that transport in Si MOSFETs can not be considered as Fully Ballistic

14. SINANO WORKSHOP Munich, September 14 th 2007 14 The role of scattering in Quasi Ballistic Devices intuited as a generalization of r LF r HF = Back Scattering Coefficient at High Field M. Lundstrom Z. Ren, IEEE TED 49 p.133 (2002) empirical Gate Source Drain F+ F- kT L kT L Introducting the concept of Back Scattering Coefficient r : theory of the High Field Backscattering coefficient has been re investigated in : R. Clerc, P. Palestri, L. Selmi, IEEE TED 53, p 1634 – 1640 (2006)

15. SINANO WORKSHOP Munich, September 14 th 2007 15 100200300400500 0 10 20 0 MC low field mobility ( cm 2 V -1 s -1 ) Extracted Dev (nm) DG 10 nm DG 4 nm Bulk Strained Bulk Validation by MC simulations r HF extracted is in fact a function of LkT ?? extracted is in fact proportional to µ IEDM 2006 « Multi Subband Monte Carlo investigation of the mean free path and of the kT layer in degenerated quasi ballistic MOSFETs » P. Palestri, R. Clerc, D. Esseni, L. Lucci, L. Selmi

16. SINANO WORKSHOP Munich, September 14 th 2007 16 Strain Silicon : double advantage in QB devices 0 0.5 1 1.5 2 2.5 BulkDG 12 Injection Velocity 10 7 cm/s Analytical Model Multi Subband Monte Carlo Simulations 0 0.1 0.2 0.3 0.4 0.5 Bulk DG 12 Back Scattering r Ph. Acoustic Ph. Optical Surf. Roughness T si Fluctuation D. Ponton et.al. Proc. Essderc 2006 p. 166

17. SINANO WORKSHOP Munich, September 14 th 2007 17 0 500 1000 1500 2000 2500 3000 3500 110100100010000 Bulk Undoped UTB Strained Undoped UTB I on Current (µA/µm) Channel Length (nm) DD v sat =10 5 m/s BULK µ = 130 cm 2 V -1 s -1 V inj = 1.2  10 5 m/s N inv = 1.45  10 13 cm -2 Undoped UTB µ = 200 cm 2 V -1 s -1 V inj = 1.2  10 5 m/s N inv = 1.45  10 13 cm -2 Strained Undoped UTB µ = 370 cm 2 V -1 s -1 V inj = 1.3  10 5 m/s N inv = 1.45  10 13 cm -2 2 possible strategies to improve Ion : improving V inj (subband engineering) by DOS reduction improving, which mean improving  = effective field mobility like in pure Drift Diffusion model ! Conclusion : Device Optimisation in the Quasi Ballistic Regime Still no clear experimental evidence

18. SINANO WORKSHOP Munich, September 14 th 2007 18 EXTENSION TO ALTERNATIVE CHANNEL MATERIALS

19. SINANO WORKSHOP Munich, September 14 th 2007 19 Improving Quasi Ballistic Performance by changing Channel Material improving, which mean improving  improving V inj, by DOS reduction Bulk Mobility at room temperature Eff. Masses Si ml = 0.98 mt = 0.19 µ = 1500 cm 2 V -1 s -1 Ge ml = 1.64 mt = 0.082 µ = 3900 cm 2 V -1 s -1 GaAs m = 0.067 µ = 8500 cm 2 V -1 s -1 Electrons However, it is not so easy !

20. SINANO WORKSHOP Munich, September 14 th 2007 20 t GaAs =5nm, oriented 110 The role of quantum confinement in the occupancy of subbands with light isotropic mass ULIS 2007 « Further Investigations of the Impact of Channel Orientation on Ballistic Current of nDGFETs with Alternative Channel Materials » Q. Rafhay, R. Clerc, M. Bescond, M. Ferrier, G. Ghibaudo ISSUE 1 :

21. SINANO WORKSHOP Munich, September 14 th 2007 21 ISSUE 2 : Substrate orientation and channel direction have to be re-optimized ULIS 2007 « Further Investigations of the Impact of Channel Orientation on Ballistic Current of nDGFETs with Alternative Channel Materials » Q. Rafhay, R. Clerc, M. Bescond, M. Ferrier, G. Ghibaudo Literature : T. Low et al, IEDM 2003 : Ge best on (110)/[110] A. Pethe et al, IEDM 2005 : Carriers in III-V moves from Γ to L (110)/[110] optimum direction of the ballistic drain current for Ge – GaAs – InAs and InSb DGFETs

22. SINANO WORKSHOP Munich, September 14 th 2007 22 ISSUE 3 : A good MATERIAL mobility does not necessary imply a good DEVICE mobility Example : MC Inversion layer electron mobility simulation of Ge 100 MATERIALDEVICE SSDM 2007 « Mobility and Backscattering in Germanium n-type Inversion Layers » Q. Rafhay, P. Palestri, D. Esseni, R. Clerc, L. Selmi 0.20.40.60.81.01.21.4 400 800 1200 1600 Effective Mobility (cm².V.s ) Effective Field (MV/cm) Si  2.6 Ge Si

23. SINANO WORKSHOP Munich, September 14 th 2007 23    GAP Λ Δ Λ Δ Tentative Explanation : Q. Confinement enhances Phonon Limited poor  mobility

24. SINANO WORKSHOP Munich, September 14 th 2007 24 Thermoionic Current including SCE & DIBL Source to Drain Tunneling (SDT) Band to Band Tunneling (SDT) CB VB E FS E FD ISSUE 4 : Alternative Material may enhance leakages A serious hindrance […] is the lack of an adequate quantitative model for interband tunneling in indirect materials like Si and Ge. Most of the available expressions contain adjustable parameters for the electron– phonon coupling constant […]. Their quantitative accuracy is open to question […] S. Luryi et al. SSE 51 p212 (2007)

25. SINANO WORKSHOP Munich, September 14 th 2007 25 An simple model to illustrate the role of Source To Drain Tunneling in Alternative Channel Materials We consider : - Si like Material operating in the quantum limit - 2 valleys with ml = 1 and mt varies from 0.01 to 1 mtmt mtmt I on is computed according the Natori Model in the quantum limit (accounting for quantum capacitance) Potential Energy in weak inversion is computed according the Liu model Source to Drain Tunneling is computed using WKB transparency (more accurate simulations including all subbands will be presented elsewhere)

26. SINANO WORKSHOP Munich, September 14 th 2007 26 10.50 11.5 10 18 10 17 10 16 10 15 10 14 10 13 10 12 10 11 10 9 8 7 6 5 4 3 0.01 0.1 1 10 100 10 3 4 5 ideal slope Gate Voltage (V) L = 6 nm EOT = 5 Å V dd = 0.8 V V T  0.2 V Drain current (µA/µm) 00.20.40.60.81 Normalized Distance (y/L) Potential Energy (a.u) Leakages modeling versus Eff. Masses mtmt VgVg L = 6 nm tsi = 2 nm, EOT = 6 Å

27. SINANO WORKSHOP Munich, September 14 th 2007 27 Si already offers a not so bad trade off after all !! I on - I off Trade Off versus Eff. Masses I off kept constant at 0.11 µA/µm (tuning V FB ) w. Q. Capa w.o. Q. Capa Transverse Eff. Mass m t L = 9 nm EOT = 5 Å V dd = 0.8 V 22 nm node Ion current (a.u.) 00.20.40.60.81 0 0.20.40.60.81 w.o. Q. Capa w. Q. Capa Si Transverse Eff. Mass m t L = 6 nm EOT = 5 Å V dd = 0.8 V 16 nm node Ion current (a.u) Si

28. SINANO WORKSHOP Munich, September 14 th 2007 28 Conclusions Quasi Ballistic Transport may lead to an improvement of On state current in nano MOSFETs (L  mfp ) Strategies for performance enhancements : improving long channel low field mobility improving injection velocity by DOS reduction using Strain Si for instance Alternative Channel materials have to face several challenges : Quantum Capacitance Reduction of device mobility due to quantum confinement Leakages and especially Source to Drain Tunneling Simulators have to improve to properly model leakage (BTBT, SDT) Experimental validations are needed, especially on short channel device with Ultra Thin Body Again Strain Si might offer the best trade off !!

29. SINANO WORKSHOP Munich, September 14 th 2007 29 BACK UP SLIDES

30. SINANO WORKSHOP Munich, September 14 th 2007 30 0.20.40.60.8 11.2 Gate Voltage (V) Drain Current (a.u) w.o Q. Capa w Q. Capa m t = 0.2 EOT = 6 Å 00.2 0.40.60.81 Transverse Eff. Mass m t Drain Current (a.u) w Q. Capa w.o Q. Capa EOT = 6 Å I on current in the quantum limit approximation

31. SINANO WORKSHOP Munich, September 14 th 2007 31

32. SINANO WORKSHOP Munich, September 14 th 2007 32