1. 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

2. 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.

3. 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

4. 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

5. 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

6. 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, 245407 (2001).

7. 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, 166805 (2008); Y. Ke et al., PRB 79, 155406 (2009); F. Zahid et al., PRB 81, 045406 (2010). NEGF DFT H KS 

8. 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)]

9. 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

10. 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

11. 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.

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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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.

20. 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 ).

21. 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.