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International Workshop on Computational Electronics - 10 Oct 26, 2004 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

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International Workshop on Computational Electronics - 10 Oct 26, 2004 2 There is still a considerable separation between semi-classical and quantum models in terms of physical detail Motivation Semi-classical transport particle inclusion of: - quantum corrections - quantum sub-band details strengths: - advanced scattering models - band structure readily included - moderate computational cost Ballistic quantum transport inclusion of: - scattering models - band structure details strengths: - quantum coherence - tunneling and evanescent behavior at barriers wave

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International Workshop on Computational Electronics - 10 Oct 26, 2004 3 We have considered a 2-D device model for the double-gate MOSFET performing simulations with MOCA 2-D (UIUC) NanoMOS (Purdue). Benchmark Model Device parameters t ox = 1.0 nm ( k = 1.0 ) t Si = 4.0 nm, 3.0 nm, 2.0 nm S 1 = 6.0 nm u = underlap = 4.0 nm L G = 9.0 nm (-4.5nm to 4.5nm) L T = 17.0 nm (-8.5nm to 8.5nm) N S/D = 10 20 cm -3 (gradient 1.0 nm/decade) N body = 10 10 cm -3 SD S1S1 S1S1 uu uu t SI t ox LGLG LTLT

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International Workshop on Computational Electronics - 10 Oct 26, 2004 4 t Si = 4nm, V ds = 0.05V, Vg = 0.05V t Si = 4nm, V ds = 0.05V, Vg = 0.20V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 5 t Si = 4nm, V ds = 0.05V, Vg = 0.35V t Si = 4nm, V ds = 0.05V, Vg = 0.50V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 6 t Si = 4nm, V ds = 0.20V, Vg = 0.50V t Si = 4nm, V ds = 0.20V, Vg = 0.35V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 7 t Si = 4nm, V ds = 0.35V, Vg = 0.50V t Si = 4nm, V ds = 0.35V, Vg = 0.35V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 8 t Si = 4nm, V ds = 0.50V, Vg = 0.50V t Si = 4nm, V ds = 0.50V, Vg = 0.35V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 9 t Si = 3nm, V ds = 0.35V, Vg = 0.50V t Si = 3nm, V ds = 0.35V, Vg = 0.35V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 10 t Si = 3nm, V ds = 0.50V, Vg = 0.50V t Si = 3nm, V ds = 0.50V, Vg = 0.35V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 11 t Si = 2nm, V ds = 0.35V, Vg = 0.35V t Si = 2nm, V ds = 0.35V, Vg = 0.50V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 12 t Si = 2nm, V ds = 0.50V, Vg = 0.50V t Si = 2nm, V ds = 0.50V, Vg = 0.35V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 13 Velocity Profiles V ds = 0.50V, Vg = 0.50V t Si = 4.0 nm t Si = 3.0 nm t Si = 2.0 nm

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International Workshop on Computational Electronics - 10 Oct 26, 2004 14 Long Channel benchmark t Si = 3.0 nm L G = 50 nm, V ds = 0.50V, Vg = 0.50V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 15 Velocity comparison for a ballistic device t Si = 4.0 nm L G = 9 nm, V ds = 0.50V, Vg = 0.50V

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International Workshop on Computational Electronics - 10 Oct 26, 2004 16 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. Conclusions

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