Report

Mark Cheung Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22904, USA 1 This lecture will cover: Field-effect transistor (FET) review Motivation for TFET Device design and simulation Literature review Simulation results 2 Field-effect transistor (FET) review Switch On: ID is high Off: ID is low Landauer Formula: 1 2 = ( − )( )[ − 2 ] ℎ −∞ 1 + 2 1 ∞ 3 Motivation "Intel," 2011. Available: http://www.carthrottle.com/why-chemistry-dictates-an-electric-vehiclefuture/ 4 Current-voltage (IV) curve Subthreshold Swing SS (mV/dec): Power P=(1/2)C2 f+VdIloff log( ) = 10 ∗ ( ∗ 1 , log( ) MOSFET IV Curve )−1 Ion ≈ 60 mV/dec ~60 mV/dec Ioff 5 Tunnel Field Effect Transistor (TFET) 6 Tunnel Field Effect Transistor (TFET) 2 = ℎ ℎ − − λ On q∆ Source Off Channel Drain 7 Device design and simulation Gate Source Drain µ1 []1 µ2 [H] []2 Green Function: = ( − − Σ 1 − Σ 2 ) −1 8 Graphene Nanoribbon (GNR) Subbands Transmission 9 Relevant Functions (analytical) SS= log( ) = = = ∗ ( ( ∗ , )− ( ) + ) ∗ − ∆+ = F = ℎ − J. Knoch, S. Mantl and J. Appenzeller, "Impact of dimensionality on the performance of tunneling FETs: Bulk versus one-dimensional devices," ScienceDirect, vol. 51, pp. 572-78, 2007. 10 Literature Review: MOSFET/TFET IV of different material system A. M. Ionescu and H. Riel, "Tunnel field-effect transistors as energy-efficient electronics switches," Nature, vol. 479, pp. 329-337, 2011. 11 Literature Review: varying gate overlap & differential voltage Differential voltage between top and bottom gate for a double gate TFET correlates positively with Ion/Ioff Gate overlap improves SS without degrading Ion and Ioff Fiori, G.; Iannaccone, G., "Ultralow-Voltage Bilayer Graphene Tunnel FET," Electron Device Letters, IEEE , vol.0, no.10, pp.1096,1098, Oct. 2009 doi: 10.1109/LED.2009.2028248 12 Literature Review: varying drainside gate underlap & drain doping X. Yang, J. Chauhan, J. Guo, and K. Mohanram “Graphene tunneling FET and its applications in low-power circuit design,” VLSI, pp. 263-268, 2010 Drain-side gate underlap and drain doping reduce the ambipolar IV characteristics without sacrificing Ion/Ioff and SS 13 Result: varying channel width 2 = ℎ ℎ − − Channel width varies inversely with SS and correlates negatively (exponential) with Ion/Ioff 14 Result: varying channel width 250 1,000,000 100,000 y = 3E+08e-2.043x R² = 0.979 200 150 1,000 100 100 y = 381.85e-0.554x R² = 0.9697 50 10 0 ratio SS(mV/dec) 10,000 SS (mV/dec) Ion/Ioff 1 0 1 2 3 4 5 6 7 8 width (nm) Channel width varies inversely with SS and correlates negatively (exponential) with Ion/Ioff 15 Results: varying channel length λ On q∆ Source Off Channel Drain 16 Results varying channel length 180 100,000 160 y = 30782ln(x) - 70513 R² = 0.7531 140 10,000 1,000 100 Ratio SS (mV/dec) 120 80 100 60 40 SS (mV/dec) Ion/Ioff 10 20 0 1 0 20 40 60 80 100 120 140 160 180 length (nm) Channel length varies inversely with SS and correlates positively (logarithmic) with Ion/Ioff 17 Results: varying doping in contacts λ On q∆ Source Off Channel Drain Channel doping correlates positively with SS (exponential) and positively with Ion/Ioff (exponential) up until doping of around 0.28eV 18 Results: varying doping in contacts 70 1,000,000 60 100,000 y = 20.708e32.662x R² = 0.9263 10,000 40 1,000 30 y = 0.1836e15.587x R² = 0.8899 20 y = 3E+07e-33.01x 100 ratio SS (mV/dec) 50 SS (mV/dec) Ion/Ioff 10 10 0 1 0.2 0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 doping (eV) Channel doping correlates positively with SS (exponential) and positively with Ion/Ioff (exponential) up until doping of around 0.28eV 19 Results: varying drain bias λ On q∆ Source Off Channel Drain Drain bias correlates positively with SS (linear & weak) and negatively with Ion/Ioff (exponential) 20 12 1,000,000 10 100,000 8 10,000 6 1,000 y = 366373e-26.58x R² = 0.9464 4 ratio SS (mV/dec) Results: varying drain bias 100 2 SS (mV/dec) Ion/Ioff 10 0 1 0 0.05 0.1 0.15 0.2 0.25 vd (V) Drain bias correlates positively with SS (linear & weak) and negatively with Ion/Ioff (exponential) 21 Conclusion SS of 6.4 mV/dec and Ion/Ioff of >25,000 were obtained for length=40nm, width=5nm, vd=0.1 V, and doping=0.24eV. Further analysis is required to balance the trade-offs among size, power, and performance. In comparison to a MOSFET, high Ion/Ioff ratio and steep SS over several decades indicate GNR TFET’s superiority for ultra-low-voltage applications. 22 Future direction Link experimental results with analytical equations Adjust simulation to account for experimental challenges Include scattering (inelastic & elastic) Alternative TFET designs 23 Appendix: Simulation Design (continue) Tight-binding Hamiltonian model TFET setup: Channel doping Tri-gate Non-equilibrium green function (NEGF) Assumptions: Room temperature ballistic transport electrodes are infinite electron reservoir steady state 24 Appendix: NEGF = ℎ 2 ℎ − − = ( − − Σ 1 − Σ 2 ) −1 E : energy matrices from the electronic band structure H : hamiltonian matrix Σ 1,2 : self energy matrices from the contacts Σ 1 =Γ1 1 , Σ 2 =Γ2 2 Γ: broadening matrices due to coupling with contacts f: fermi functions describing number of electrons = 1 1 + 2 2 + Electron density per unit energy Γ Γ 25 Appendix: NEGF (continue) T(E)=Trace(Γ1 Γ2 + ) Average transmission at different energy U= + Potential energy effecting the DOS , and hence the transmission T = (− )+ (−q ) = () = 2 ∆N 1 −µ 1+ Probability that an electron will be at an energy state E given the fermi level µ, and temperature T = ℎ 2 ℎ − − 26 Appendix: Relevant functions (continue) SS= log( ) = = = − ( ∗ F = + − = − = ℎ ∗ , )− ( ) + ) = = ∆ = − = ∗ ( − ∗ ∆+ J. Knoch, S. Mantl and J. Appenzeller, "Impact of dimensionality on the performance of tunneling FETs: Bulk versus one-dimensional devices," ScienceDirect, vol. 51, pp. 572-78, 2007. − 27