IEEE Semiconductor Interface Specialists Conference Tutorial, Nov. 30th, 2011 Understanding the Nanoscale MOSFET Mark Lundstrom Electrical and Computer Engineering and Network for Computational Nanotechnology Birck Nanotechnology Center Purdue University, West Lafayette, Indiana USA 1 nanoscale MOSFETs S G D source drain silicon 2 SiO2 gate electrode gate oxide EOT ~ 1.1 nm Lundstrom: SISC 2011 channel ~ 32 nm Moore’s Law: 2011 3 http://en.wikipedia.org/wiki/Moore's_law Lundstrom: SISC 2011 Moore’s Law: 2011 transistors per cpu chip 4 Lundstrom: SISC 2011 Moore’s Law: 2010 1980s ~2000 ? 5 Lundstrom: SISC 2011 2010 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. 5) Consider ultimate limits. 6 Lundstrom: SISC 2011 outline 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10 nm Summary This work is licensed under a Creative Commons AttributionNonCommercial-ShareAlike 3.0 United States License. http://creativecommons.org/licenses/by-nc-sa/3.0/us/ Lundstrom: SISC 2011 7 MOSFET IV characteristic gate-voltage controlled current source circuit symbol on-current D I DS VGS VDS G VGS S gate-voltage controlled resistor (Courtesy, Shuji Ikeda, ATDF, Dec. 2007) 8 Lundstrom: SISC 2011 MOSFET IV: low VDS L 0 VG>VT VD VGS () ( Qi x ≈ −Cox VGS − VT ) I D = W Qi ( x )υ x (x) ID = W Cox (VGS − VT )µeffE x V E x = DS L gate-voltage controlled resistor W ID = µeff Cox (VGS − VT )VDS L 9 Lundstrom: SISC 2011 MOSFET IV: “pinch-off” at high VDS 0 VG Qi ( x ) = −Cox (VGS − VT − V (x)) VD V ( x ) = (VGS − VT ) Qi ( x ) ≈ 0 10 Lundstrom: SISC 2011 MOSFET IV: high VDS 0 VG gate-voltage controlled current source VD V ( x ) = (VGS − VT ) Qi ( x ) = −Cox (VGS − VT − V (x)) VGS ID = W Qi ( x )υ x (x) = W Qi (0)υ x (0) I D = W Cox (VGS − VT ) µeffE x (0) W 2 ID = µeff Cox (VGS − VT ) 2L V − VT E x (0) ≈ GS L 11 Lundstrom: SISC 2011 velocity saturation velocity cm/s ---> VDS 1.0 V ≈ ≈ 3 × 10 5 V/cm L 30 nm 107 υ = υ sat υ = µE 105 104 electric field V/cm ---> 12 Lundstrom: SISC 2011 MOSFET IV: velocity saturation 0 VG VD E x >> 10 4 (Courtesy, Shuji Ikeda, ATDF, Dec. 2007) I D = W Qi ( x )υ x (x) ID = W Cox (VGS − VT )υ sat I D = W Cox υ sat (VGS − VT ) 13 Lundstrom: SISC 2011 carrier transport nanoscale MOSFETs Velocity (cm/s) quasi-ballistic EC ( µm ) υ SAT ( µm ) D. Frank, S. Laux, and M. Fischetti, Int. Electron Dev. Mtg., Dec., 1992. 14 Lundstrom: SISC 2011 how transistors work VDS = 1.0 V 2007 N-MOSFET VGS EC electron energy vs. position electron energy vs. position VDS = 0.05 V VGS (Courtesy, Shuji Ikeda, ATDF, Dec. 2007) EC E.O. Johnson, “The IGFET: A Bipolar Transistor in Disguise,” RCA Review, 1973 15 Lundstrom: SISC 2011 outline 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10 nm Summary Lundstrom: SISC 2011 16 MOS electrostatics: low drain voltage VG E low gate voltage EC EC = EC ( 0 ) − qψ s EF high gate voltage Qi (ψ S ) C/cm 2 n0 = N C e( EF − EC ) kB TL /cm 3 Lundstrom: SISC 2011 x 17 inversion charge vs. gate voltage CG = Cox || CS ≤ Cox Qi Qi ≈ −CG (VGS − VT ) ε ox Cox = F cm 2 t ox VT threshold voltage VG Lundstrom: SISC 2011 18 MOS electrostatics: high drain voltage top-of-the-barrier should be strongly controlled by the gate voltage Qinv ( 0 ) ≈ −CG (VGS − VT ) EC E TOP EF1 EF1 - qVD E C (x) x Lundstrom: SISC 2011 19 2D MOS electrostatics CΣ = CGB + CSB + C DB + C D VG EC ψ S (0) = CGB CSB VS CGB C VG + DB VD CΣ CΣ C DB ψS VD CD EC ( x ) 0 x Lundstrom: SISC 2011 20 geometric scaling length (double gate example) Λ Require L > Λ TOX = 1nm Off-state: VG = 0V, VD = 1V, Ioff = 0.1µA/µm (by H. Pal, Purdue) Lundstrom: SISC 2011 21 nonplanar MOSFETs “Transistors go Vertical,” IEEE Spectrum, Nov. 2007. See also: “Integrated Nanoelectronics of the Future,” Robert Chau, Brian Doyle, Suman Datta, Jack Kavalieros, and Kevin Zhang, Nature Materials, Vol. 6, 2007 Lundstrom: SISC 2011 22 MOSFETs are barrier controlled devices 2) region under strong\ 1) “Well-tempered MOSFET” Qi ( 0 ) ≈ −CG (VG − VT ) control of gate E EC ( x ) 3) Additional increases in VDS drop near the drain and have a small effect on ID x M. Lundstrom, IEEE EDL, 18, 361, 1997. A. Khakifirooz, O. M. Nayfeh, D. A. Antoniadis, IEEE TED, 56, pp. 1674-1680, 2009. 23 outline 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional Approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10 nm Summary Lundstrom: SISC 2011 24 Landauer approach B. J. van Wees, et al. Phys. Rev. Lett. 60, 848–851,1988. W --> 2q 2 G= T ( EF ) M ( EF ) h Lundstrom: SISC 2011 25 molecular electronics The Birth of Molecular Electronics, Scientific American, September 2001. Lundstrom: SISC 2011 26 current flows when the Fermi-levels are different gate EF1 f1 ( E ) = 1 1 + e( E − EF1 ) kB TL I= 27 EF 2 D(E) τ1 τ2 f2 ( E ) = 2q T ( E ) M ( E ) ( f1 − f2 ) dE ∫ h Lundstrom: SISC 2011 1 1 + e( E − EF 2 ) kB TL “top of the barrier model” energy U = EC − qψ S EF1 LDOS EC ( x ) “device” EF 2 ε1 ( x ) contact 1 contact 2 position 28 Lundstrom: SISC 2011 ballistic MOSFET: linear region I DS VGS = VDD VDS near-equilibrium f1 ≈ f2 I DS = GCH VDS 29 Lundstrom: SISC 2011 linear region with MB statistics GCH 2q 2 = h ∞ ⎛ ∂f0 ⎞ ∫E T ( E ) M 2 D ( E ) ⎜⎝ − ∂E ⎟⎠ dE C ( Boltzmann statistics: f0 = e EF −E ) kBTL − ∂f0 ∂E = f0 kBTL GCH υT = WnS 2k BTL q nS ≈ Cox (VGS − VT ) (MOS electrostatics) GCH = WCox 30 υT VGS − VT ) ( 2k BT q ✔ ( ) M 2D E = gV W ( 2m* E − EC π ( ) T E =1 ( ) ( E− E f0 E = 1 1+ e( F k BTL ) nS = N 2 D e( EF − EC ) kB TL ⎛ m * ⎞ ( EF − EC ) kB TL = gV ⎜ 2 ⎟ e ⎝ π ⎠ υT = 2kBTL π m* = υ x+ Lundstrom: SISC 2011 ) ) ballistic MOSFET: linear region ID VGS = VDD I DS = GCH VDS VDS near-equilibrium I DS = GCH VDS 31 f1 ≈ f2 υT I D = WCox VGS − VT )VDS ( 2k BT q Lundstrom: SISC 2011 relation to conventional expression ballistic MOSFET I DS conventional MOSFET υT = WCox (VGS − VT )VDS 2k BTL q I DS = W υT L Cox (VGS − VT )VDS L 2kBTL q υ λ Dn = T 0 2 I DS = 32 I DS µn = Dn υT L µB ≡ k T q 2 k B TL q (B L ) W Cox µ B (VGS − VT )VDS L Lundstrom: SISC 2011 W = Cox µn (VGS − VT )VDS L µn → µ B ballistic MOSFET: on-current ID VGS = VDD f1 >> f2 VDS I DS 33 2q 2q = T ( E ) M ( E ) ( f1 − f2 ) dE → I DS = T ( E ) M ( E ) f1 dE ∫ ∫ h h Lundstrom: SISC 2011 saturated region with MB statistics I DS 2q 2 = h ∞ ∫ T ( E ) M ( E ) f ( E ) dE 2D 1 EC Boltzmann statistics: f0 ≈ e− ( EC − EF ) kB TL 34 π ( ) T E =1 N 2 D ( EF − EC ) kB TL e 2 ⎛ m * ⎞ ( EF − EC ) kB TL = gV ⎜ e 2⎟ ⎝ 2π ⎠ nS = I DS = WqnSυT I DS = WCoxυT (VGS − VT ) ( ) M 2D E = gV W ( 2m* E − EC ✔ υT = 2kBTL π m* = υ x+ Lundstrom: SISC 2011 ) under low VDS I+ E EF1 I + = nS+υT I− + I I EF 2 I − = nS−υT nS+ nS− − nS = nS+ + nS− nS+ nS− ≈ x 35 Lundstrom: SISC 2011 nS 2 Cox nS ≈ (VGS − VT ) q under high VDS E I+ EF1 I − = nS−υT I− ≈ 0 nS− ≈ 0 nS = nS+ + nS− ≈ nS+ EF 2 x 36 I + = nS+υT Lundstrom: SISC 2011 Cox nS ≈ (VGS − VT ) q velocity vs. VDS E I+ I + = nS+υT I− EF1 I υ = D qnS I ( = + − I− ) nS nS = nS+ + nS− EF 2 x nS− −qVDS = e nS+ υ = υT 37 I − = nS−υT k B TL (1 − e (1 + e − qVDS kBT − qVDS kBT ) ) velocity vs. VDS E I+ I− υ → υT υ EF1 EF 2 υ ∝ VDS x VDS Velocity saturates in a ballistic MOSFET but at the top of the barrier, where E-field = 0. 38 Lundstrom: SISC 2011 velocity saturation in a ballistic MOSFET υ = υT ≈ 1.2 × 10 7 cm/s velocity 2007 N-MOSFET saturation VDS = 1.0 V VGS υ = υ sat ≈ 1.0 × 10 7 cm/s 39 (Courtesy, Shuji Ikeda, ATDF, Dec. 2007) Lundstrom: SISC 2011 aside: relation to conventional expression ballistic MOSFET I ON = WCoxυT (VGS − VT ) conventional MOSFET I DS = WCoxυ sat (VGS − VT ) υ sat → υT 40 Lundstrom: SISC 2011 the ballistic IV (Boltzmann statistics) I DS (on) = W υT Cox (VGS − VT ) ID ballistic on-current ( VG − VT ) 1 ballistic channel resistance VDS I DS = GCH VDS 41 υT =W Cox (VGS − VT )VDS ( 2kBTL q ) Lundstrom: SISC 2011 K. Natori, JAP, 76, 4879, 1994. outline 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional Approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10 nm Summary Lundstrom: SISC 2011 42 comparison with experiment: Silicon LG = 40 nm I Dlin I ballistic ≈ 0.2 I ON I ballistic ≈ 0.6 • 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 VDS. 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. 43 Device characterization and simulation: Himadri Pal and Yang Liu, Purdue, 2010. Jesus del Alamo group (MIT) 44 Lundstrom: SISC 2011 outline 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional Approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10nm Summary Lundstrom: SISC 2011 45 transmission and carrier scattering λ0 T= λ0 + L 1 X X X 0 < T <1 R = 1− T L λ0 is the mean-free-path for backscattering I DS → TI DS ? 46 Lundstrom: SISC 2011 the quasi-ballistic MOSFET ? I DS VDS ⎛ ⎞ υT I D = T ⎜ WCox (VGS − VT ) VDS ⎟ ( 2kBTL q ) ⎠ ⎝ 47 Lundstrom: SISC 2011 → Tlin ≈ 0.2 on current and transmission + I BALL Qi ( 0 ) = W υT I + + (1 − T ) I + Qi ( 0 ) = W υT + I BALL I = (2 − T ) + I ON 48 (1 − T ) I + EF1 ⎛ T ⎞ + =⎜ I ⎝ 2 − T ⎟⎠ BALL Lundstrom: SISC 2011 I + I D = TI + EF 2 the quasi-ballistic MOSFET I DS ⎛ T ⎞ I D = W υT ⎜ Cox (VGS − VT ) ⎟ ⎝2−T ⎠ → Tsat ≈ 0.7 Tsat > Tlin why? VDS ⎛ ⎞ υT I D = T ⎜ WCox (VGS − VT ) VDS ⎟ ( 2kBTL q ) ⎠ ⎝ 49 Lundstrom: SISC 2011 → Tlin ≈ 0.2 scattering under high VDS λ0 Tlin = λ0 + L E EF1 L→ Tsat EF 2 x λ0 = λ0 + << L Tsat > Tlin 50 Lundstrom: SISC 2011 connection to traditional model (low VDS) ID = W µnCox (VGS − VT )VDS L ⎛ ⎞ υT I D = T ⎜ WCox (VGS − VT ) VDS ⎟ ( 2kBTL q ) ⎠ ⎝ W ID = µnCox (VGS − VT )VDS L + λ0 ID = λ0 T= λ0 + L W µappCox (VGS − VT )VDS L 1 µapp = 1 µn + 1 µ B 51 Lundstrom: SISC 2011 connection to traditional model (high VDS) I D = WCoxυ sat (VGS − VT ) ⎛ T ⎞ I D = WCox (VGS − VT )υT ⎜ ⎝ 2 − T ⎟⎠ −1 ⎡1 1 ⎤ ID = W ⎢ + ⎥ Cox (VGS − VT ) ⎣ υT ( Dn ) ⎦ how do we interpret this result? 52 Lundstrom: SISC 2011 λ0 T= λ0 + the MOSFET as a BJT I D = W υ (0) Cox (VGS − VT ) 1 1 1 = + υ (0) υT Dn “base” E ‘bottleneck’ “collector” EC ( x ) x 53 Lundstrom: SISC 2011 outline 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional Approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10 nm Summary Lundstrom: SISC 2011 54 limits to barrier control: quantum tunneling 55 4) 3) 2) 1) Lundstrom: SISC 2011 / Purdue from M. Luisier, ETH Zurich ultimate limits Limits ES E(eV) min = ln(2) kB T Lmin ≈ 2m ES τ min ≈ ES min min (ΔpΔx = ) (ΔE Δt = ) V. V. Zhirnov, R.K. Cavin III, J.A. Hutchby, and G.I. Bourianoff, “Limits to Binary Logic Switch Scaling— A Gedanken Model,” Proc. IEEE, 91, 1934, 2003. 56 Lundstrom: SISC 2011 32 nm technology 32 nm node Limits ES min (ITRS 2009 ed.) ES ≈ 2, 500 × ES = ln(2) kB T Lmin ≈ 2mEmin =1.5nm(300K) τ min ≈ ES min = 0.04 ps (300K) nmax (at 100W/cm ) =1.5 B/cm 2 57 2 L ≈ 15 × Lmin τ ≈ 17 × τ min n ≈ 1.1 B/cm 2 (minimum size transistor – no parasitics) min Moore’s Law? 58 “Moore’s Law is about lowering cost per function….progress continues at a breathtaking pace, but transistor scaling is approaching limit. When that limit is reached, things must change, but that does not mean that Moore’s Law has to end.” Lundstrom: SISC 2011 outline 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional Approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10nm Summary Lundstrom: SISC 2011 59 physics of nanoscale MOSFETs ID 2) The channel resistance has a lower limit - no matter how high the mobility or how short the channel. 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. VDS 1) Transistor-like I-V characteristics are a result of electrostatics. 60 Lundstrom: SISC 2011 limits of scaling What happens below 10 nm? 61 Lundstrom: SISC 2011 for more information 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 1-8, by Mark Lundstrom, 2011. http://nanohub.org/resources/11872 3) “Electronics from the Bottom Up” http://nanohub.org/topics/ElectronicsFromTheBottomUp 4) “Lessons from Nanoscience,” http://nanohub.org/topics/LessonsfromNanoscience 62 Lundstrom: SISC 2011 nanoHUB-U http://nanoHUB.org/u 63 Lundstrom: SISC 2011 Thank you! 1) 2) 3) 4) 5) 6) 7) 8) Introduction Traditional Approach MOS electrostatics The ballistic MOSFET Comparison to experiments Scattering in nano-MOSFETs MOSFETs below 10nm Summary Lundstrom: SISC 2011 64