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L.Selmi , P.Palestri, D.Esseni, L.Lucci, M.De Michielis

An efficient, mixed semiclassical/quantum mechanical model to simulate planar and wire nano-transistors. L.Selmi , P.Palestri, D.Esseni, L.Lucci, M.De Michielis DIEGM-IUNET, University of Udine luca.selmi@uniud.it. Gate. Drain. Source. Current. Substrate.

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L.Selmi , P.Palestri, D.Esseni, L.Lucci, M.De Michielis

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  1. An efficient, mixed semiclassical/quantum mechanical model to simulate planar and wire nano-transistors L.Selmi, P.Palestri, D.Esseni, L.Lucci, M.De Michielis DIEGM-IUNET, University of Udineluca.selmi@uniud.it

  2. Gate Drain Source Current Substrate FET switches: the workhorse of electronics L.Selmi, University of Udine

  3. FET Technology Boostersin the ITRS roadmap [public.itrs.net] High-K STRAIN high μ BULK Materials &Architec. Alternative Materials Alternative Architectures L.Selmi, University of Udine

  4. VG2 VS VD VG1 L Decoupling lateral transport and transverse quantization ky kx S D E VS x Strong size and bias induced quantization in the vertical direction (z) Little or no quantization in the transport plane (x-y) but ….. L.Selmi, University of Udine

  5. Carrier motion in the channel Quasi ballistic transport: few scatterings determine the current Ballistic transport Source ITRS 2005 Edition Modeling and simulation needs to be enhanced to deal with the key innovations requested by the PIDS section, including enhanced mobility, high-k dielectrics, metal gate electrodes, non classical CMOS […] Ideal device Real device L.Selmi, University of Udine

  6. nano-FET modeling approaches • Drift Diffusion or Hydrodynamic models • commercial tools • inadequate for nano-FETs • Monte Carlo solver of the 3D BTE • far from equilibrium transport • no vertical or lateral quantization effects • N.E.G.F. • 2D quantization in real space • computationally heavy • difficult to include all relevant scattering mech. • Multi-Subband Monte Carlo (MSMC) • accurate treatment of vertical quantization • efficient semiclassical treatment of far from equilibrium transport • computationally affordable L.Selmi, University of Udine

  7. Multi subband Monte Carlo x VG2 z • Boltzman Transport Equationin transport directionSchrödinger Equationin quantization direction • Solve 1D Schrödinger equation in each section of the device • Solve the BTE in each subband • The solution of the BTEs are coupled by scatterings VS VD VG1 z L.Selmi, University of Udine

  8. y x X z Schroedinger equation VG2 Subband “j” VD Subband “i” VG1 • SchrÖdinger-like equation: • Energy dispersion versus k: • my, mx, mz expressed in terms of mt and mlof bulk crystal • Force: L.Selmi, University of Udine

  9. Band Structure (electrons) Effective mass approximation • Non-parabolic elliptical bands: • Any number of , L,  valleys • Strain: additional valley splitting • Arbitrary crystal orientation: • Subbands with different quantization and transport masses • Various semiconductor materials implementedSi, Ge … L.Selmi, University of Udine

  10. Extraction of band parameters • For a given device: • parametric representation of the bands at a given bias • extraction of eff. masses UTB silicon (Tsi=5nm), (001) Full Band LCBB calculation L.Selmi, University of Udine

  11. BTE in quantized systems • A BTE for each sub-band: : sub-band index Dim(K) <3 • Sub-bands are coupled by inter-subband scattering • Degeneration implemented by rejecting the scattering according to the occupation of the final state L.Selmi, University of Udine

  12. Scattering Theory of the 2D gas • Phonons (Price, 1980) • Ionized impurities (Ando, 1983) • Surface roughness (Esseni, 2003) • S.O.phonons in high-k materials • Matrix elements and scattering rates computed from eigenvalues and wave-functions • Fermi Golden Rule • Anisotropic scattering (SR, II) is screened with the dielectric function of the 2D electron gas L.Selmi, University of Udine

  13. Model flowchart Poisson Equation (2D) electron density n(x,z) Potential V(x,z) MonteCarlo (BTE) Schrödinger equation (1D) Eigenstates Yn,n,i(z) En,n,i Scattering Rates Scattering Theory 2D elecron gas L.Selmi, University of Udine

  14. x VG2 z VS VD VS VG1 ky k kx Degeneration in thin film SOI • degeneration plays a major role UTB MOSFETs L.Selmi, University of Udine

  15. Ballistic transport ky DG SOI, NS/D=5 1020, EOT 0.7nm, Lg=14nm, Tsi=4nm kx S D Phonon scattering in source and drain, no scattering in the channel transport plane (x-y) L.Selmi, University of Udine

  16. Transport with scattering ky DG SOI, NS/D=5 1020, EOT 0.7nm, Lg=14nm, Tsi=4nm kx S D Phonon scattering in source and drain, Phonon, Surface roughness and Tsi Fluctuations in the channel transport plane (x-y) L.Selmi, University of Udine

  17. Mobility: effect of surface orientation [Lucci, IEEE T-ED, p.1156, 2007] • Same model parameters of (001) and (111) orientations • Adjustment of SR spectrum for (110) L.Selmi, University of Udine

  18. Transport in biax. strained-Si devices QUANTIZATION DIRECTION TRANSPORT DIRECTION L.Selmi, University of Udine 18

  19. Mobility in biax. strained-Si devices CB=0.67x [eV] [Rashed, IEDM 1995] L.Selmi, University of Udine 19

  20. Extension to nanowire FETs L.Selmi, University of Udine

  21. drain 3 nm gate oxide source source What are we missing ? • Surface roughness / interface effects • Tunneling through the Source barrier • Scattering mechanisms • Atomistic effects L.Selmi, University of Udine

  22. Conclusions • A new Monte Carlo code based on the theory of the two dimensional carrier gas has been developed for n- and p-type MOSFETs • Quasi ballistic transport in ultra thin body DG SOI devices has been investigated • Importance of a correct modeling of scattering in the channel and of carrier degeneration has been highlighted • The modularity of the code and the parametric description of the band structure make the simulator suitable for extensions to devices with different channel material and crystal orientation L.Selmi, University of Udine

  23. Acknowledgements • EU Nestor (5FP), SiNano (6FP), PullNano (6FP) projects • Italian FIRB 2001 and PRIN 2004 projects • MS and PhD students: Nicola Barin, Marco Braccioli, Simone Eminente, Andrea Ghetti, Davide Ponton, Ivan Riolino, Massimiliano Zilli and all the IU.NET – ARCES partners L.Selmi, University of Udine

  24. Device modeling approaches Fundamental Theory of transport Ballistictransport Velocity overshoot Verticalquantization Lateralquantization Scattering Degeneration Full Band Sub-threshold Availability (Densitygradientcorrection) Near Equilibrium m, vs NO Drift Diffusion Possible NO NO YES Possible Comm (Densitygradientcorrection) DisplacedMaxwellian Possible m, vsT Possible Hydrodynamic NO YES NO YES Comm (Effectivepotentialcorrection) (S/D tunnelingcorrection) Classical (3D) Monte Carlo Univ / Comm Boltzmann Transport eq. Possible YES YES YES YES NO (S/D tunnelingcorrection) Multi Sub Band Monte Carlo BTE 2D +SE 1D YES YES YES YES NO Possible Univ Included Green’s Function YES YES YES YES YES Phon Univ Schrodinger eg. Included Included L.Selmi, University of Udine

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