1. IEEE Central NC EDS/MTT/SSC Society Friday, Nov. 5th, 2010 The Nanoscale MOSFET: Physics and Limits Mark Lundstrom 1 Electrical and Computer Engineering and Network for Computational Nanotechnology Birck Nanotechnology Center Purdue University, West Lafayette, Indiana USA

2. 2 21 st Century: microelectronics  nanoelectronics transistors per cpu chip Lundstrom

3. 3 nanoscale MOSFETs 2010 source drain SiO 2 silicon channel ~ 32 nm gate oxide EOT ~ 1.1 nm gate electrode SGD

4. 4 MOSFET IV characteristic (Courtesy, Shuji Ikeda, ATDF, Dec. 2007) S D G circuit symbol gate-voltage controlled current source gate-voltage controlled resistor

5. 5 MOSFET IV: low V DS V G >V T VDVD 0 gate-voltage controlled resistor

6. 6 MOSFET IV: “pinch-off” at high V DS VGVG VDVD 0

7. 7 MOSFET IV: high V DS VGVG VDVD 0 2 gate-voltage controlled current source

8. 8 velocity saturation electric field V/cm ---> velocity cm/s ---> 10 7 10 4 10 5

9. 9 MOSFET IV: velocity saturation VGVG VDVD 0 (Courtesy, Shuji Ikeda, ATDF, Dec. 2007)

10. 10 carrier transport nanoscale MOSFETs Lundstrom Velocity (cm/s)  D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992.

11. 11 ~1995 - 2000 Lundstrom Moore’s Law? Molecular electronics http://www.eng.yale.edu/reedlab/

12. 12 objectives 1)Present a simple, physical picture of the nanoscale MOSFET (to complement, not supplement simulations). 2)Discuss ballistic limits, velocity saturation, and quantum limits in nanotransistors. 3)Compare to experimental results for Si and III-V FETs 4)Discuss scattering in nano-MOSFETs Lundstrom

13. 13 outline Lundstrom 1)Introduction 2) The nano-MOSFET 3)The ballistic MOSFET 4) Scattering in nano-MOSFETs 5) Summary

14. 14 how transistors work 2007 N-MOSFET electron energy vs. position ( Courtesy, Shuji Ikeda, ATDF, Dec. 2007) electron energy vs. position E.O. Johnson, “The IGFET: A Bipolar Transistor in Disguise,” RCA Review, 1973

15. MOSFETs are barrier controlled devices 3) Additional increases in V DS drop near the drain and have a small effect on I D A. Khakifirooz, O. M. Nayfeh, D. A. Antoniadis, IEEE TED, 56, pp. 1674-1680, 2009. 2) region under strong\ control of gate 1) “Well-tempered MOSFET” M. Lundstrom, IEEE EDL, 18, 361, 1997. 15

16. 16 current flows when the Fermi-levels are different gate Lundstrom

17. 17 “top of the barrier model” energy position contact 1 contact 2 “device” LDOS Lundstrom

18. 18 outline Lundstrom 1)Introduction 2) The nano-MOSFET 3)The ballistic MOSFET 4) Scattering in nano-MOSFETs 5) Summary

19. 19 ballistic MOSFET: linear region Lundstrom near-equilibrium

20. 20 linear region with MB statistics Lundstrom (MOS electrostatics) ✔ Boltzmann statistics:

21. 21 ballistic MOSFET: linear region Lundstrom near-equilibrium

22. 22 relation to conventional expression Lundstrom ballistic MOSFET conventional MOSFET

23. 23 ballistic MOSFET: on-current Lundstrom

24. 24 saturated region with MB statistics Lundstrom Boltzmann statistics: ✔

25. 25 under low V DS Lundstrom

26. 26 under high V DS Lundstrom

27. 27 velocity vs. V DS Lundstrom

28. 28 velocity vs. V DS Velocity saturates in a ballistic MOSFET but at the top of the barrier, where E-field = 0. Lundstrom

29. 29 velocity saturation in a ballistic MOSFET (Courtesy, Shuji Ikeda, ATDF, Dec. 2007) 2007 N-MOSFET velocity saturation Lundstrom

30. 30 aside: relation to conventional expression Lundstrom ballistic MOSFET conventional MOSFET

31. 31 the ballistic IV (Boltzmann statistics) K. Natori, JAP, 76, 4879, 1994. ballistic channel resistance ballistic on-current Lundstrom

32. 32 comparison with experiment: Silicon A. Majumdar, Z. B. Ren, S. J. Koester, and W. Haensch, "Undoped-Body Extremely Thin SOI MOSFETs With Back Gates," IEEE Transactions on Electron Devices, 56, pp. 2270-2276, 2009. Device characterization and simulation: Himadri Pal and Yang Liu, Purdue, 2010. Si MOSFETs deliver > one-half of the ballistic on-current. (Similar for the past 15 years.) MOSFETs operate closer to the ballistic limit under high V DS.

33. 33 comparison with experiment: InGaAs HEMTs Jesus del Alamo group (MIT) Lundstrom

34. 34 outline Lundstrom 1)Introduction 2) The nano-MOSFET 3)The ballistic MOSFET 4) Scattering in nano-MOSFETs 5) Summary

35. 35 transmission and carrier scattering X X X λ 0 is the mean-free-path for backscattering Lundstrom

36. 36 the quasi-ballistic MOSFET Lundstrom

37. 37 on current and transmission Lundstrom

38. 38 the quasi-ballistic MOSFET Lundstrom

39. 39 scattering under high V DS Lundstrom

40. 40 connection to traditional model (low V DS ) Lundstrom

41. 41 connection to traditional model (high V DS ) how do we interpret this result? Lundstrom

42. 42 the MOSFET as a BJT ‘bottleneck’ “collector”“base” Lundstrom

43. 43 outline Lundstrom 1)Introduction 2) The nano-MOSFET 3)The ballistic MOSFET 4) Scattering in nano-MOSFETs 5) Summary

44. 44 physics of nanoscale MOSFETs 1) Transistor-like I-V characteristics are a result of electrostatics. 2) The channel resistance has a lower limit - no matter how high the mobility is. 3) The on-current is controlled by the ballistic injection velocity - not the high-field, bulk saturation velocity. 4) Channel velocity saturates near the source, not at the drain end. Lundstrom

45. 45 limits to barrier control: quantum tunneling from M. Luisier, ETH Zurich / Purdue 4) 3) 2) 1)

46. 46 21 st Century electronics? Lundstrom Moore’s Law?

47. 47 21 st Century electronics Lundstrom 1) Information processing dominated by “Si CMOS” 2) SOC’s complemented by “CMOS+” technologies 3) and….. macroelectronics, power electronics, PV, solid-state lighting, thermoelectrics, …

48. 48 for more information Lundstrom 1) “Physics of Nanoscale MOSFETs,” a series of eight lectures on the subject presented at the 2008 NCN@Purdue Summer School by Mark Lundstrom, 2008. http://nanohub.org/resources/5306 2)“Electronic Transport in Semiconductors,” Lectures 1-7, by Mark Lundstrom, 2009. http://nanohub.org/resources/7281

49. 49 questions Lundstrom 1)Introduction 2) The nano-MOSFET 3)The ballistic MOSFET 4) Scattering in nano-MOSFETs 5) Summary