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Electronic transport properties of nano-scale Si films: an ab initio study Jesse Maassen, Youqi Ke, Ferdows Zahid and Hong Guo Department of Physics, McGill University, Montreal, Canada

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University of Wisconsin-Madison Motivation (of transport through Si thin films) As the thickness of a film decreases, the properties of the surface can dominate.

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University of Wisconsin-Madison Motivation (of transport through Si thin films) The main motivation for our research was the experimental work by Pengpeng Zhang et al. with silicon-on-insulators. Nature 439, 703 (2006) SiO 2 Si SiO 2 Vacuum Charge traps Used STM to image 10 nm Si film on SiO 2 Surface states

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University of Wisconsin-Madison First-principles study of electronic transport through Si(001) nano-scale films in a two-probe geometry Our goal Current Electrode

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University of Wisconsin-Madison First-principles study of electronic transport through Si(001) nano-scale films in a two-probe geometry Our goal Length Thickness Surface Current Electrode Doping level (lead or channel) Orientation

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University of Wisconsin-Madison Theoretical method Device Left lead Right lead Density functional theory (DFT) combined with nonequilibrium Green’s functions (NEGF) 1 Two-probe geometry under finite bias Buffer NEGF DFT H KS -- ++ Simulation Box 1 Jeremy Taylor, Hong Guo and Jian Wang, PRB 63, (2001).

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University of Wisconsin-Madison Theoretical method DFT: Linear Muffin-Tin Orbital (LMTO) formalism 2 Large-scale problems (~1000 atoms) Can treat disorder, impurities, dopants and surface roughness 2 Y. Ke, K. Xia and H. Guo, PRL 100, (2008); Y. Ke et al., PRB 79, (2009); F. Zahid et al., PRB 81, (2010). NEGF DFT H KS

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University of Wisconsin-Madison System under study (surface) Hydrogenated surface vs. clean surface H Si (top) Si Si (top:1) Si (top:2) Si H terminated [2 1:H] Clean [P(2 2)]

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University of Wisconsin-Madison Results (bulk case) Atomic structure & bandstructure H terminated [2 1:H]Clean [P(2 2)] || dimers dimers || dimers dimers Large gap ~0.7 eV (with local density approximation) Small gap ~0.1 eV (with local density approximation) dimers || dimers dimers

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University of Wisconsin-Madison Results (bulk case) Atomic structure & bandstructure H terminated [2 1:H]Clean [P(2 2)] || dimers dimers || dimers dimers Large gap ~0.7 eV (with local density approximation) Small gap ~0.1 eV (with local density approximation) dimers || dimers dimers

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University of Wisconsin-Madison Results (bulk case) Bandstructure : Direct vs. Indirect band gap Up to ~17nm thick, the band gap of a SiNM is direct. Need to calculate for thicker films.

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University of Wisconsin-Madison Band gap values with DFT Recent development solves the “band gap” problem associated with DFT calculations.

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University of Wisconsin-Madison Results (n ++ - i - n ++ system) Two-probe system Channel : intrinsic Si Leads : n ++ doped Si 2 1:H surface Periodic to transport n ++ i i L = 3.8 nm L = 19.2 nm T = 1.7 nm

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University of Wisconsin-Madison Results (n ++ - i - n ++ system) Potential profile (effect of length) Max potential varies with length Screening length > 10nm n ++ EFEF VB i CB

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University of Wisconsin-Madison Results (n ++ - i - n ++ system) Potential profile (effect of doping) Max potential increases with doping Slope at interface greater with doping, i.e. better screening n ++ EFEF VB i CB

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University of Wisconsin-Madison Results (n ++ - i - n ++ system) Potential profile (effect of doping) Max potential increases with doping Slope at interface greater with doping, i.e. better screening n ++ EFEF VB i CB

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University of Wisconsin-Madison Results (n ++ - i - n ++ system) Conductance vs. k-points ( dimers) Shows contribution from k-points to transport Transport occurs near point. Conductance drops very rapidly i n ++ n++n++ TOP VIEW

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University of Wisconsin-Madison Results (n ++ - i - n ++ system) Conductance vs. k-points (|| dimers) i n ++ n++n++ Largest G near point Conductance drops rapidly, but slower than for transport to dimers. TOP VIEW

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University of Wisconsin-Madison Results (n ++ - i - n ++ system) Conductance vs. Length Conductance has exponential dependence on length, i.e. transport = tunneling. Large difference due to orientation. Better transport in the direction of the dimer rows.

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University of Wisconsin-Madison Summary Performed an ab initio study of charge transport through nano-scale Si thin films. Expect to provide a more complete study on the influence of surface states shortly ( H-passivated vs. clean )! This method can potentially treat ~10 4 atoms ( 1800 atoms ) & sizes ~10 nm ( 23.8 nm )! This large-scale parameter-free modeling tool could be very useful for device and materials engineering ( because of it’s proper treatment of chemical bonding at interfaces & effects of disorder ).

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University of Wisconsin-Madison Thank you ! Questions? Thanks to Prof. Wei Ji. We gratefully acknowledge financial support from NSERC, FQRNT and CIFAR. We thank RQCHP for access to their supercomputers.

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