Towards Atomistic Simulations of the Electro-Thermal Properties of Nanowire Transistors Mathieu Luisier and Reto Rhyner

Transcription

1 Towards Atomistic Simulations of the Electro-Thermal Properties of Nanowire Transistors Mathieu Luisier and Reto Rhyner Integrated Systems Laboratory ETH Zurich, Switzerland

2 Outline Motivation Electron Transport Simulation Approach Mobility Calculation in Si NW Phonon Transport Simulation Approach Anharmonic Ph-Ph Scattering Thermal Conductivity in Si NW Outlook and Conclusion

3 Motivation

4 Motivation: Transistor Evolution Source: Intel Source: Intel Source: IBM Planar to 3-D CS Scaling Ultimate FET? d 5nm L g 10nm

5 Motivation: Ballistic Transport? Si GAA NWFET d=3nm L g =5nm 5nm 5nm source Ballistic spectral current drain Spectral current with e-ph scatt. e-ph scattering still matters in L g <10nm Si FETs

6 Electron Transport

7 Electron/Hole Bandstructure Model Empirical Nearest-Neighbor Tight-Binding Method GOOD: Si Electron Bandstructure bulk CB and VB fitted extension to nanostructures atomistic description BAD: high computational effort empirical parametrization U Γ X Γ

8 Electron Transport Solve 1D/2D/3D Schrödinger equations Modified form to account for open boundary conditions Solution ingredients Atomic Orbitals s/s* Numerical Methods Non-equilibrium Green s Function (NEGF) or Wave Function (WF) Massive Parallelization p x d z 2 -r 2

9 GAA NW FET Simulation Objective: Electron-Phonon in Si NW FETs, extract e-ph limited mobility µ ph Approach: Tight-binding (sp 3 d 5 s*) description of the electron/hole properties Equilibrium phonon population Quantum transport with NEGF Model returns electron mobility of 1630 cm 2 /Vs for bulk (no fitting parameter) Results and Impacts: Drain current reduction (larger in transistor ON-state) Change in the shape of the electrostatic potential x=<100> d=3nm L g =15nm

10 Mobility Extraction Technique R(L)=ΔV/I d (L) µ eff (top) N inv (top) Calculation Method R(L)=ΔV/I d (L) R(L)=R 0 +R ph (L) ρ 1D =dr(l)/dl µ ph =1/(q*ρ 1D *N inv ) 1. Perform self-consistent simulation of nanowire FET including electron-phonon scattering at a small drain voltage ΔV 2. Calculate the channel resistance R(L) for different gate lengths 3. Extract the 1-D inversion charge N inv at the top-of-the-barrier

11 Phonon-limited Channel Resistance <100> <110> R(L)=R 0 +R ph (L) ρ 1D =dr(l)/dl µ ph =1/(q*ρ 1D *P inv ) µ ph =1/(q*ρ 1D *N inv ) <111> Phonon-limited Channel resistance mobility of of d=3nm Si NW Si NW FETs FETs Mobility Comparison extraction of p-type based and on n-type dr/dl devices method <110>: Crystal best orientations electron <100>, and hole <110>, compromise <111>

12 Phonon Transport

13 Phonon Bandstructure Model Valence Force Field (VFF) Method with Empirical Potential Features: modified Keating Model 4 bond interactions extension to nanostructures Δr ΔΘ Δr Δr Si Phonon Bandstructure Sim. Exp. ΔΘ ΔΘ 4 1. bond stretching 2. bond bending 3. cross bond stretching 4. coplanar bond bending

14 Phonon Transport Model Solve 1D/2D/3D lattice dynamics equations Modified form to account for open boundary conditions Solution ingredients Bond Interactions Δr ΔΘ Numerical Methods Non-equilibrium Green s Function (NEGF) or Wave Function (WF) Massive Parallelization ΔΘ ΔΘ

15 Anharmonic Phonon Decay In the case of ballistic transport, each phonon enters and leaves a simulation domain with the same energy: Energy x In reality, high energy phonon can decay into two particles with lower energy (ph-ph scattering): Energy E+E E E x

16 Anharmonic Model Verification Requirement: phonon transport model should be able to reproduce available experimental data Test: lattice thermal conductivity and mean free path for scattering of bulk Si

17 Application: Si NW Structures d 3 nm L The thermal current flowing through Si nanowires with a diameter d=3 nm, varying lengths L, a n d d i f f e r e n t c r o s s sections is simulated. <100> <110> <111>

18 Ballistic vs. Dissipative Thermal Current Thermal current through L=50 nm Si nanowires at different temperatures and for different transport directions. 1.7x 4x

19 Nanowire Thermal Conductivity Since phonon transport in the presence of anharmonic phonon decay is diffusive, a thermal resistivity ρ th and ph-ph limited conductivity κ th can be extracted.

20 Outlook and Conclusion

21 Coupled Electron-Phonon Transport Current status: electron/phonon transport solver Separate, but implemented in the same tool Electron Transport OMEN Phonon Transport Coupling through scattering self-energies Numerical implementation very complicated

22 Conclusion Important of e-ph scattering Even in ultra-short Si devices Electron transport Good reproduction of bulk µ e Modification of NW electrostatics 30% reduction of NW ON-current Phonon transport Good reproduction of bulk κ th Change in thermal current shape Reduction of thermal conductivity