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
Motivation (of transport through Si thin films) As the thickness of a film decreases, the properties of the surface can dominate.
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) Used STM to image 10 nm Si film on SiO 2 Charge traps Surface states SiO 2 SiO 2 Si Vacuum
Our goal First-principles study of electronic transport through Si(001) nano-scale films in a two-probe geometry Electrode Current Electrode
Our goal First-principles study of electronic transport through Si(001) nano-scale films in a two-probe geometry Surface Thickness Electrode Current Electrode Doping level (lead or channel) Length Orientation
Theoretical method Density functional theory (DFT) combined with nonequilibrium Green s functions (NEGF) 1 H KS DFT ρ Two-probe geometry under finite bias NEGF Simulation Box - + Left lead Buffer Device Buffer Right lead 1 Jeremy Taylor, Hong Guo and Jian Wang, PRB 63, 245407 (2001).
Theoretical method DFT: Linear Muffin-Tin Orbital (LMTO) formalism 2 Large-scale problems (~1000 atoms) Can treat disorder, impurities, dopants and surface roughness DFT H KS ρ NEGF 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).
System under study (surface) Hydrogenated surface vs. clean surface H terminated [2 1:H] Clean [P(2 2)] H Si (top) Si Si (top:1) Si (top:2) Si
Results (bulk case) Atomic structure & bandstructure H terminated [2 1:H] Clean [P(2 2)] dimers dimers dimers dimers dimers dimers dimers dimers Large gap ~0.7 ev (with local density approximation) Small gap ~0.1 ev (with local density approximation)
Results (bulk case) Atomic structure & bandstructure H terminated [2 1:H] Clean [P(2 2)] dimers dimers dimers dimers dimers dimers dimers dimers Large gap ~0.7 ev (with local density approximation) Small gap ~0.1 ev (with local density approximation)
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.
Band gap values with DFT Recent development solves the band gap problem associated with DFT calculations.
Results (n ++ - i - n ++ system) Two-probe system Channel : intrinsic Si Leads : n ++ doped Si 2 1:H surface Periodic to transport T = 1.7 nm n ++ i n ++ L = 3.8 nm n ++ n ++ i L = 19.2 nm
Results (n ++ - i - n ++ system) Potential profile (effect of length) Max potential varies with length Screening length > 10nm CB E F n ++ i VB
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 CB E F n ++ i VB
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 CB E F n ++ i VB
Results (n ++ - i - n ++ system) Conductance vs. k-points ( dimers) Shows contribution from k-points to transport TOP VIEW i n ++ n ++ Transport occurs near Γ point. Conductance drops very rapidly
Results (n ++ - i - n ++ system) Conductance vs. k-points ( dimers) TOP VIEW i n ++ n ++ Largest G near Γ point Conductance drops rapidly, but slower than for transport to dimers.
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.
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).
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.