Electronic transport properties of nano-scale Si films: an ab initio study

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

3. 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 SiO2 Charge traps Surface states SiO2 University of Wisconsin-Madison SiO2 Si Vacuum

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

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

6. Theoretical method • Density functional theory (DFT) combined with nonequilibrium Green’s functions (NEGF)1 • Two-probe geometry under finite bias DFT  HKS NEGF Simulation Box - + Device Left lead Right lead Buffer Buffer University of Wisconsin-Madison 1Jeremy Taylor, Hong Guo and Jian Wang, PRB 63, 245407 (2001).

7. Theoretical method • DFT: Linear Muffin-Tin Orbital (LMTO) formalism2 • Large-scale problems (~1000 atoms) • Can treat disorder, impurities, dopants and surface roughness DFT  HKS NEGF 2Y. 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). University of Wisconsin-Madison

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

9. || dimers  dimers  dimers || dimers 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) University of Wisconsin-Madison

10. || dimers  dimers  dimers || dimers 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) University of Wisconsin-Madison

11. 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. University of Wisconsin-Madison

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

13. n++ i n++ n++ n++ i 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 L = 3.8 nm L = 19.2 nm University of Wisconsin-Madison

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

15. 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 EF i VB n++ University of Wisconsin-Madison

16. 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 EF i VB n++ University of Wisconsin-Madison

17. 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  TOP VIEW i n++ n++  University of Wisconsin-Madison

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

19. 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. University of Wisconsin-Madison

20. 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 ~104 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). University of Wisconsin-Madison

21. 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. University of Wisconsin-Madison