Special Issues on Nanodevices1 Special Topics in Nanodevices 3 rd Lecture: Nanowire MOSFETs Byung-Gook Park

Special Issues on Nanodevices2 Nanowire MOSFETs  MOSFET Scaling and Issues  Evolution of MOSFET Device Structure  Double Gate Structures  Multiple Gate Structures  Ballistic Electron Transport in Nanowires  Effect of Scattering – Landauer ’ s Formula Ref : H.S. Min, Y.J. Park, B.G. Park, H.C. Shin, Semiconductor Devices with NANOCAD, Ch. 8 S. Datta, Electronic Transport in Mesoscopic Systems, Ch. 2

Special Issues on Nanodevices3 MOSFET Scaling - The Grand View D.R. = 20e (Y-1960)  ~ 3 yrs : 2 -1/2 reduction  ~ 20 yrs : reduction ITRS Roadmap (’05) 2016 : 9 nm (MPU L phy ) 2019 : 6 nm (MPU L phy )

Special Issues on Nanodevices4 Short Channel Effects (1)  Phenomenon : roll-off of V T as a function of gate length L  Cause : charge sharing

Special Issues on Nanodevices5 Short Channel Effects (2)

Special Issues on Nanodevices6  Number of dopants in the depletion region : - The number of dopant atoms in the depletion region decreases as the device dimension decreases. - As the number of dopants decreases, the statistical fluctuation of the number of dopants becomes more important.  Example : L = W = 50 nm, N a = cm -3  W dm = 35 nm  N = N a LWW dm = 87.5  s N = N 1/2 = 9.35 (~ 10.7%)  Threshold voltage variation due to dopant number fluctuation : Dopant Number Fluctuation and V T

Special Issues on Nanodevices7 Evolution of Device Structure (1)  Tightness of gate control over the channel SiO 2 Double gate SOI Bulk

Special Issues on Nanodevices8 Evolution of Device Structure (2)  Tightness of gate control over the channel

Special Issues on Nanodevices9 Short Channel Effects  Design guideline SG: t si  L channel /3 DG: t si  2L channel /3 NW: t si  L channel

Special Issues on Nanodevices10 Various Double Gate Structures L: horizontal W: horizontal L: vertical W: horizontal L: horizontal W: vertical Type IType IIType III

Special Issues on Nanodevices11 FinFETs G S D L G t SOI W fin G S D L G SOI W fin SD G G G G SD  FinFET Schematic  FinFET Issue H fin =t SOI W fin <L G

Special Issues on Nanodevices12 Electric Field and Charge Distribution  Electric Field  Charge V G >V T V G <V T

Special Issues on Nanodevices13 Basic Equations for DGMOSFETs  Due to symmetry  Voltage, electric field, and channel charge

Special Issues on Nanodevices14 Threshold Voltage and Drain Current  Threshold voltage  Drain current * Usually, Q b  0 to suppress the dopant # fluctuation effect  negative threshold voltage for n-channel  work function engineering required * Two devices in one!

Special Issues on Nanodevices15 Inversion Charge in the Channel  Charge distribution : - assumption: Charge distribution is dominated by the ground state. Surface inversion – two channels are separated Bulk inversion – two channels are merged

Special Issues on Nanodevices16 V T vs. Channel Thickness VTVT T ch  Threshold voltage for thicker channel :  Threshold voltage for thin channel : - dominated by the energy level quantization - higher for thinner body

Special Issues on Nanodevices17 MG MOSFETs and Corner Effects Gate Oxide Channel Gate Oxide Channel  Quadruple gate MOSFET - The gate surrounds the channel.  Corner effect : - Field concentration at corners.

Special Issues on Nanodevices18 Coaxial Gate MOSFETs Gate Oxide Channel  Ideal shape for NW MOSFET - No corner effect - 2D analysis with cylindrical coordinates

Special Issues on Nanodevices19 Carbon Nanotube FETs  CNT FETs -Schottky contact at S/D junction -High  dielectric for gate insulator

Special Issues on Nanodevices20 Ballistic Transport in Nanowire (1) Contact 1Contact 2 W L Ballistic Conductor x y  Large conductor (L >> mean free path): G =  W/L (Ohmic scaling)  G   for L  0?  Ballistic conductor (L << mean free path): G  G c for L  0 G c   “contact” resistance

Special Issues on Nanodevices21  Assumption : ‘reflectionless contacts’ Electrons can enter a wide contact from a narrow conductor without suffering reflections. => +k states : occupied by electrons originating in the left contact  k states : occupied by electrons originating in the right contact  Quasi-Fermi levels :  Dispersion relation : N : transverse mode number  N : cut-off energy for mode N k E N = 11 22 33  eV 1  eV 2 Ballistic Transport in Nanowire (2)

Special Issues on Nanodevices22  Number of transverse modes :  Current by a single transverse mode : +k states are occupied according to the function f(E  E f + ) Ballistic Transport in Nanowire (3)

Special Issues on Nanodevices23  Current by multiple transverse modes :  Total current :  At low temperature : Ballistic Transport in Nanowire (4)

Special Issues on Nanodevices24 Landauer ’ s Formula (1) Contact 1Contact 2 Conductor x y T Lead 1 Lead 2

Special Issues on Nanodevices25 Landauer ’ s Formula (2) Contact 1Contact 2 Conductor x y T Lead 1 Lead 2