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Comparison of full-band Monte Carlo and Non-equilibrium Green’s function simulations

Comparison of full-band Monte Carlo and Non-equilibrium Green’s function simulations Ranganathan Ravishankar, Gulzar Kathawala, Umberto Ravaioli University of Illinois, Urbana-Champaign Collaboration with Sayed Hasan and Mark Lundstrom Purdue University. strengths:

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Comparison of full-band Monte Carlo and Non-equilibrium Green’s function simulations

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  1. Comparison of full-band Monte Carlo and Non-equilibrium Green’s function simulations Ranganathan Ravishankar, Gulzar Kathawala, Umberto Ravaioli University of Illinois, Urbana-Champaign Collaboration with Sayed Hasan and Mark Lundstrom Purdue University

  2. strengths: - advanced scattering models - band structure readily included - moderate computational cost • strengths: • - quantum coherence • tunneling and evanescent • behavior at barriers Semi-classical transport Ballistic quantum transport particle wave inclusion of: - quantum corrections - quantum sub-band details inclusion of: - scattering models - band structure details Motivation • There is still a considerable separation between semi-classical and quantum models in terms of physical detail

  3. tox S D tSI tox S1 S1 u LG u LT Benchmark Model • We have considered a 2-D device model for the double-gate MOSFET performing simulations with MOCA 2-D (UIUC) NanoMOS (Purdue). Device parameters tox   = 1.0 nm ( k = 1.0 ) tSi   = 4.0 nm, 3.0 nm, 2.0 nm S1   = 6.0 nm u   = underlap = 4.0 nm LG = 9.0 nm (-4.5nm to 4.5nm) LT = 17.0 nm (-8.5nm to 8.5nm) NS/D = 1020 cm-3 (gradient 1.0 nm/decade) Nbody = 1010 cm-3

  4. tSi = 4nm, Vds = 0.05V, Vg = 0.05V tSi = 4nm, Vds = 0.05V, Vg = 0.20V

  5. tSi = 4nm, Vds = 0.05V, Vg = 0.35V tSi = 4nm, Vds = 0.05V, Vg = 0.50V

  6. tSi = 4nm, Vds = 0.20V, Vg = 0.35V tSi = 4nm, Vds = 0.20V, Vg = 0.50V

  7. tSi = 4nm, Vds = 0.35V, Vg = 0.35V tSi = 4nm, Vds = 0.35V, Vg = 0.50V

  8. tSi = 4nm, Vds = 0.50V, Vg = 0.35V tSi = 4nm, Vds = 0.50V, Vg = 0.50V

  9. tSi = 3nm, Vds = 0.35V, Vg = 0.35V tSi = 3nm, Vds = 0.35V, Vg = 0.50V

  10. tSi = 3nm, Vds = 0.50V, Vg = 0.35V tSi = 3nm, Vds = 0.50V, Vg = 0.50V

  11. tSi = 2nm, Vds = 0.35V, Vg = 0.35V tSi = 2nm, Vds = 0.35V, Vg = 0.50V

  12. tSi = 2nm, Vds = 0.50V, Vg = 0.35V tSi = 2nm, Vds = 0.50V, Vg = 0.50V

  13. tSi = 4.0 nm tSi = 3.0 nm tSi = 2.0 nm Velocity Profiles Vds = 0.50V, Vg = 0.50V

  14. Long Channel benchmark tSi= 3.0 nm LG = 50 nm, Vds = 0.50V, Vg = 0.50V

  15. Velocity comparison for a ballistic device tSi= 4.0 nm LG = 9 nm, Vds = 0.50V, Vg = 0.50V

  16. Conclusions • The present benchmark comparison indicates that Monte Carlo and NEGF simulations give potential and density profiles that agree well in a range of conditions and silicon slab thicknesses. • Discrepancies are noticed at low bias, explained by the granular nature of Monte Carlo as opposed to the continuum nature of NEGF. • For thinner silicon slab thickness, size quantization is emphasized, and we are looking for the limits of validity of the quantum correction potential approach in Monte Carlo. • At high fields, NEGF tend to give a much more prominent velocity overshoot. This is understood by considering that the present model of nanoMOS has parabolic bands, where velocity is not constrained as in a realistic band.

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