OMEN: a Quantum Transport Modeling Tool for Nanoelectronic Devices Mathieu Luisier and Gerhard Klimeck

Why Quantum Transport Simulator? Motivation Why Quantum Transport Simulator? http://download.intel.com/technology/silicon/silicon_paper_06.pdf 65nm Node Devices LG=35nm Quantum Dots: Self-assembled , InAs on GaAs. Pyramidal or dome shaped R. Leon et al, JPL (1998) Material variations in 3-D on nm-scale! 45nm Node

NEMO 1-D and NEMO 3-D Capabilities => OMEN From NEMO 1-D to OMEN O<-M<-E<-N NEMO 1-D and NEMO 3-D Capabilities => OMEN Features: OMEN: 1D-3D, Parallel, Atomistic, and Full-Band Quantum Transport Simulator (Effective Mass Approx. also Available) OMEN (i) (j) (k) (l) Id-Vgs Electron Density GAA NW 3

Overview Introduction and Motivation Why Quantum Transport? What is OMEN? Application to Devices NW FETs MIT InAs HEMTs Graphene Nanoribbon TFET Summary and Outlook

Overview Introduction and Motivation Why Quantum Transport? What is OMEN? Application to Devices NW FETs MIT InAs HEMTs Graphene Nanoribbon TFETs Outlook

Nearest-Neighbor pz, sp3, sp3s*, sp3d5s* Tight-Binding Method OMEN Physical Models Bandstructure Model Nearest-Neighbor pz, sp3, sp3s*, sp3d5s* Tight-Binding Method GOOD: bulk CB and VB fitted (BTBT) extension to nanostructures atomistic description BAD: high computational effort

(E-H-Σ)·GR = I (E-H-Σ)·C = Inj What is OMEN? Transport Model 1D/2D/3D Schrödinger Equation H | ψE > = E | ψE > Tight-Binding Ansatz for the Wave Function < r | ψE > = ∑ Cij(E,kt)Φσ (r - Rijk)eikt·rt σ σ,ijk,kt (E-H-Σ)·GR = I (E-H-Σ)·C = Inj Matrix Inversion Problem Linear System of Eq.

Overview Introduction and Motivation Why Quantum Transport? What is OMEN? Application to Devices NW FETs MIT InAs HEMTs Graphene Nanoribbon TFETs Outlook

Nanowire Field-Effect Transistors (3D Structures) Application to Devices: NW (1) Nanowire Field-Effect Transistors (3D Structures) Simulation of NW FETs: - any channel shape (square, circular, triangular, …) - any transport direction (<100>, <110>, <111>, …) - any gate configuration (gate-all-around, triple-gate, …) - any material (Si, Ge, III-V Compound, …) - n- and p-doped structures - cross section up to 80 nm2, length>100 nm Triple-Gate FET Gate-All-Around FET

Electron –Phonon Scattering in Si Nanowires Application to Devices: NW (2) Electron –Phonon Scattering in Si Nanowires Gate-All-Around Si Nanowire (d=2.5nm) FET with Scattering Current Reduction : Backscattering and Injection Reduction (ON-Current) Transfer Characteristics Spectral Current

Overview Introduction and Motivation Why Quantum Transport? What is OMEN? Application to Devices NW FETs MIT InAs HEMTs Graphene Nanoribbon TFETs Outlook

MIT HEMT: Device Geometry Effective Mass Simulation of III-V HEMTs (1) MIT HEMT: Device Geometry Experimental Devices: III-V HEMTs for Logic Applications (D.H. Kim et. al, IEDM 07, EDL 08) Objective: Simulation of III-V Devices (HEMTs) Challenge the Experiment Approach: Real-Space EM Simulations Realistic Description of Simulation Domain Injection from Source, Drain, and Gate Contacts Result: Match Experimental Results for Various Gate Lengths

Transfer Characteristics Id-Vgs @ Lg=30, 40, 50 nm Effective Mass Simulation of III-V HEMTs (2) Transfer Characteristics Id-Vgs @ Lg=30, 40, 50 nm All Devices Fitted With One Physical Set of Parameters Lg = 50nm Lg = 30nm Vd=0.5V Vd=0.05V Lg = 40nm Lg = 50nm

Flow Visualization of Gate Leakage Current: Edge Mechanism Effective Mass Simulation of III-V HEMTs (3) Gate Leakage Current Gate Drain Source Flow Visualization of Gate Leakage Current: Edge Mechanism

Overview Introduction and Motivation Why Quantum Transport? What is OMEN? Application to Devices NW FETs MIT InAs HEMTs Graphene Nanoribbon TFETs Outlook

Tunneling Transistor after MOSFET? GNR TFETs (1) Tunneling Transistor after MOSFET? MOSFET: Thermionic Current TFET: B-to-B Tunn. Current

Armchair Graphene Nanoribbon GNR TFETs (2) Armchair Graphene Nanoribbon Graphene Nanoribbon: GOOD: One-Dimensional Structure Compatible to Planar Tech. Low Effective Masses Tunable Band Gap (Width) BAD: Band Gap => Narrow Ribbon Edges => Roughness Bandstructure of 5.1nm GNR Symmetric CB and VB Band Gap Eg = 0.251 eV

GNR TFETs (3) Structure Definition TFET p-i-n Structure: 5.1nm GNR Deposed on SiO2 (N=21) 1nm EOT (2.35nm Al2O3 with εR=9.1) 40nm Gate Length 25nm Source and Drain Extensions Supply Voltage VDD=0.2 V Symmetric Doping Conc. GNR Band Gap Eg=0.251 eV 18

Id-Vgs Transfer Characteristics GNR TFETs (4) Id-Vgs Transfer Characteristics ON-Current: ION=225 μA/μm OFF-Current: IOFF=37 nA/μm Subthreshold Slope SS=12 mV/dec How can we decrease the OFF-Current? How can we increase the ON-Current?

Determination of Supply Voltage GNR TFETs (5) Determination of Supply Voltage ON-Current Increases with VDD (due to Gate Voltage) Condition Vbi+VDD<2*Eg must be Satisfied Condition Broken => Ambipolar Channel Behavior

Summary and Outlook OMEN Simulator Combines NEMO1D and NEMO3D Capabilities 3D, Full-Band, Atomistic, Quantum Transport Features Massively Parallel (Scaling up to 147k Cores) Dedicated to NW, HEMT, or GNR structures Band-to-band Tunneling FETs Outlook and Challenges Dissipative Scattering (Improvement) More Comparison to Experiments Make OMEN available to other Users