Electronic and optical properties of graphene- and graphane-like SiC layers

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1 Electronic and optical properties of graphene- and graphane-like SiC layers Paola Gori, ISM, CNR, Rome, Italy Olivia Pulci, Margherita Marsili, Università di Tor Vergata, Rome, Italy Friedhelm Bechstedt, IFTO, Friedrich-Schiller- Universitat, Jena, Germany ESF Workshop on Polaritonics, March 20-23, Marino (Rome), Italy

2 Outline Graphene and graphane-like SiC based 2D sheets: structure Electronic properties: face-dependent behaviour Optical properties: polarizability, bound excitons Conclusions and outlook

3 Theoretical tools: ab-initio methods MBPT c hn c hn EXC wcv c W v DFT ground state v GW Band structure, I, A v BSE Optical properties

4 Theoretical tools: ab-initio methods MBPT c hn c hn EXC wcv c W v DFT v GW v BSE 1) 2) 3)

5 Quasiparticle equation Lars Hedin 1965 igw G: single particle Green s function 1 W V W: screened Coulomb interaction

6 Optical properties: Bethe Salpeter equation MBPT c hn c hn EXC wcv c W v DFT v GW v BSE 1) 2) 3)

7 hn Bethe Salpeter equation c v Absorption spectra A photon excites an electron from an occupied state to a conduction state e h 4 P 4 P IQP 4 P IQP 4 4 P Bethe Salpeter Equation (BSE) Kernel: v W GW BSE e-h exchange bound excitons

, JACS 124, 14464 (2002) Applications for hydrogen

8 SiC-based nanostructures SiC nanotubes SiC nanowires Pan et al., Adv. Mater. 12, 1186 (2000) Sun et al., JACS 124, (2002) Applications for hydrogen storage, nanoelectronics, microelectromechanical systems

79 Å intermediate between graphene (C-C = 1.42 Å) and silicene (Si-Si = 2.

9 Graphene and graphane-like 2D SiC layers Silicongraphene Silicongraphane Flat honeycomb structure (sp 2 +p z ) C-Si bond length = 1.79 Å intermediate between graphene (C-C = 1.42 Å) and silicene (Si-Si = 2.28 Å) Buckling ( z) = 0.58 Å (sp 3 hybridization) C-Si bond = 1.9 Å intermediate between graphane (C-C = 1.54 Å) and silicane (Si-Si = 2.36 Å)

10 2D SiC:H from a SiC surface? Is it possible to obtain 2D SiC:H form a slab of hydrogenated C-terminated 3C-SiC(111)? [E tot (SiC:H 5bil_slab ) + E tot (2D-SiC:H)]-[E tot (SiC:H 6bil_slab ) + E tot (H 2 )] = ev, E tot (SiC:H 5(6)bil_slab ) = total energy of a 5(6)-bilayer 1x1 SiC(111) slab E tot (H2) = total energy of an hydrogen molecule An hydrogenated slab of 3C-SiC(111) in presence of hydrogen can give rise to a stable 2D hydrogenated sheet of SiC

11 Quasiparticle band structures SiC SiC:H

12 Quasiparticle band gaps 2D sheet SiC SiC:H C:H Si:H GW direct gap (ev) 3.7 (K) 5.3 (G) 5.4 (G) 3.6 (G)

13 SiC:H band edge density of states The fundamental gap of SiC:H approaches the value found for graphane: near the gap the DOS is dominated by C and H(C) states.

14 SiC:H - Electrostatic potential

15 SiC:H - Electrostatic potential Two vacuum levels appear as a consequence of the sheet polarity. A dipole discontinuity V=1.7 ev occurs, related to the electron transfer Qe between Si and C. According to Gauss law, 4 Qe V A s 0 where s =2.03, A 0 =8.48 Å 2, =0.58 Å. This gives Q=0.25, smaller than expected for ionic bonding significant covalent bonding contribution. Possible application of 2D SiC:H as electron/hole filter in LED or solar cells P. Gori, O. Pulci et al., APL 100, (2012)

16 Other systems with orientation-dependent ionization energy a-sexithiophene/ag(111) Standing 6T molecules Ionization potential varied of 0.6 ev Duhm et al., Nature Mat. 7, 326 (2008) Lying 6T molecules

17 Optical properties (RPA) SiC SiC:H

18 Bound excitons in 2D SiC, SiC:H

19 2D SiC: first exciton in k-space Holes in the last valence band, Electron in the first conduction band

20 2D SiC: third exciton in k-space Holes in the last valence band, Electron in the first conduction band

21 2D SiC:H: first exciton in k-space Holes in the two last valence bands, Electron in the first conduction band

22 2D SiC:H: third exciton in k-space Holes in the last valence band, Electron in the first conduction band

23 Bound excitons in 2D hydrogenated C, Si, Ge Ge:H Si:H C:H

24 Excitons in 2D systems Exciton size and/or binding energies are heavily influenced by confinement In particular, screening is hindered and binding energies are consequently very large Rough estimate of the binding energy and excitonic radius for the lowest bound exciton through a simplified model similar to a 2D hydrogenic model of the excitons

25 2D Screened Coulomb potential For vanishing sheet thickness, the screened Coulomb potential is W r 2 e r r H 0 N0 4a 2D 2 a 2D 2 a 2 With the two limits: D r = in-plane radius H 0 = Struve function N 0 = Neumann function 2D electronic polarizability: a 2D L L = distance between sheets W r 2 e for 2 a2d r 2D hydrogen atom r W r 2 e 2 a r ln 4 a for 2 a 2D 2D D r Log e-h attraction

26 2D Screened Coulomb potential Log e-h attraction 2D hydrogen atom

27 2D Screened Coulomb potential Log e-h attraction 2D-C:H 2D-Si:H 2D-Ge:H 2D-SiC 2D-SiC:H 2D hydrogen atom

28 Bound excitons in 2D systems SiC, Si:H, Ge:H Large oscillator strength Short radiative lifetime No possibility of BEC C:H, SiC:H Vanishing dipole matrix element Not so small radiative lifetime BEC? SiC, Si:H, Ge:H Large oscillator strength AND Possible significant RT exciton-polariton effects Large exciton binding energy

29 Conclusions and outlook 2D-based SiC and SiC:H: interesting properties + possibilities of integration with Si technology Side-dependent electronic behaviour in SiC:H applicability for hole/electrons filters Strongly bound excitons both in SiC and in SiC:H. Similarities with 2D-C:H, Si:H, Ge:H Laboratory for studies of fundamental physics, e.g. bosonic effects at room temperature Possible applications for polaritons lasers

Modeling of optical properties of 2D crystals: Silicene, germanene and stanene

Modeling of optical properties of 2D crystals: Silicene, germanene and stanene Friedhelm Bechstedt 1 collaboration: L. Matthes 1 and O. Pulci 2 1 Friedrich-Schiller-Universität Jena, Germany 2 Università