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Structural and Electronic Properties of the Methyl-Terminated Si(111) Surface Antonio Aliano,† Yan Li,*,§ Giancarlo Cicero,‡ and Giulia Galli§,| Departments of Physics and Material Science and Chemical Engineering, Polytechnic of Torino, Torino 10129, Italy, and Departments of Chemistry and Physics, UniVersity of California, DaVis, DaVis, California 95616 ReceiVed: March 5, 2010; ReVised Manuscript ReceiVed: May 13, 2010
We have investigated the structural and electronic properties of the methyl-terminated Si(111) surface using first-principles calculations at the semilocal density functional theory level, inclusive of semiempirical dispersion forces between the methyl groups. In agreement with previous ab initio studies and consistent with lowenergy electron diffraction measurements, we find that the most stable geometry corresponds to a (1 × 1), symmetric pattern, with methyl groups vertically bound to the Si substrate. Therefore, our computed scanning tunneling microscopy (STM) images exhibit three-fold symmetry at variance from those reported by recent experiments. The main contribution to the tunneling current comes from surface resonant states close to the Fermi level that are very weakly affected by self-energy corrections within many body perturbation theory. Our computed current-voltage profiles are in qualitative agreement with experiment. We suggest that the differences between computed and measured STM patterns may arise from tip-substrate interactions. Introduction Functionalized silicon surfaces have many applications in photoelectrochemistry, and some of those (e.g., the use of Si rods as photocathodes in solar cell applications1,2) require the development of chemical protection strategies to prevent uncontrolled oxidation.3 Recently, a full methylation of Si(111) surfaces has been achieved,4,5 which constitutes a promising protection from oxidation. However, the apparently simple atomic structure of the methyl-terminated surface [CH3-Si(111)] is still under debate. In particular, low-temperature scanning tunneling microscopy (STM) images6 suggest a H-C-Si-Si torsion angle of θ ) 23 ( 3°, whereas firstprinciples structural optimizations find θ ≈ 38-40°.7-10 Most importantly, STM images show an asymmetric pattern with broken three-fold symmetry, raising the question of whether the methyl group is vertically adsorbed on Si(111) or instead tilted with respect to the atop site. Recent transmission infrared spectroscopy (TIRS) measurements show that both the C-H symmetric bending mode, or the “umbrella” mode, and the Si-C stretching mode are polarized in the direction perpendicular to the surface, indicating that the methyl groups are oriented normal to the substrate plane.11 To understand measured STM images and to address the controversy on the structural properties of CH3-Si(111), we have carried out an analysis of the structural and electronic properties of this surface; in particular, we have computed STM images, after structural optimizations at the semilocal density functional theory (DFT) level, inclusive of semiempirical dispersion forces between the methyl groups. Our calculations confirm previous ab initio structural data and therefore yield images with three-fold symmetry, whose main contribution comes from surface resonant states close to the Fermi level. * To whom correspondence should be addressed: E-mail:
[email protected]. † Department of Physics, Polytechnic of Torino. ‡ Department of Material Science and Chemical Engineering, Polytechnic of Torino. § Department of Chemistry, University of California, Davis. | Department of Physics, University of California, Davis.
The electronic structure of CH3-Si(111) is found to be very similar to that of the hydrogen-terminated Si(111).12 The rest of the article is organized as follows. We first describe the method and geometrical models used in our calculations. Then, we present our results for structural, electronic, and spectroscopic properties of the CH3-Si(111) surface. A summary of our findings concludes the article. Method We carried out DFT calculations with the Quantum ESPRESSO package13 using norm-conserving pseudopotentials, the localdensity approximation (LDA) and generalized gradient approximation (GGA/PBE14) for the exchange-correlation functionals, and plane wave basis sets with a kinetic energy cutoff of 55 Ry. A (12 × 12 × 1) Monkhorst-Pack15 k-point grid was used to sample the Brillouin zone. Fully functionalized, methyl-terminated Si(111) surfaces were modeled by symmetric slabs at the calculated bulk equilibrium lattice constant (5.47 and 5.40 Å using PBE and LDA, respectively). A vacuum region of 10 Å between periodically repeated supercells was used to avoid spurious interactions between replicas. We included long-range van der Waals (vdW)-type forces between the methyl groups by using the so-called DFT+D approach,16 where a semiempirical dispersion (D) energy correction (Edisp), expressed as a sum over atomic pair contributions, is added to the DFT total energy N-1
Edisp ) -s6
N
∑ ∑
i)1 j)i+1
Cij6 Rij6
fdamp(Rij)
(1)
Here s6 is a functional-dependent scaling factor, N is the total number of atoms in the system, C6ij are the dispersion coefficients, and Rij are the interatomic distances. The damping function fdamp(Rij) has the form [1 + e-R(Rij/R0-1)]-1, where R0 is the sum of the atomic vdW radii and R ) 20.16 The values of the coefficients C6ij ) (C6i C6j )1/2 are obtained from atomic firstprinciple calculations.16
10.1021/jp102028z 2010 American Chemical Society Published on Web 06/18/2010
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Figure 1. Top-view (left) and side-view (right) of the optimized geometry of the fully covered (1 × 1) CH3-Si(111) surface. The H-C-Si-Si torsion angle is indicated by θ. White, green, and yellow spheres denote H, C, and Si atoms, respectively.
When simulating STM images, we approximated the calculation of the tunneling current I at an applied sample bias V by a simple integral of the surface local density of states (LDOS) at the tip position, without taking into consideration the shape and charge density of the tip
I∝
∫EE +eV dE Fs(r, E) F
F
(2)
where Fs(r, E) ) Σi|Ψi(r)|2δ(Ei - E) is the unperturbed (zero applied bias) surface LDOS at energy E and tip position r and Ψi(r) and Ei are the one-electron wave function and eigenvalue. The Fermi level EF is defined as EF ≡(EVBM + ECBM)/2, where VBM and CBM denote the valence band maximum and conduction band minimum, respectively. At large bias, the electronic structure of the surface is modified by the presence of the tip, and effects from the electric field of the tip should be explicitly taken into consideration in the expression of Fs(r, E) as a function of the applied bias. At low bias, following eq 2, we obtain the normalized conductance as (dI/dV)/(I/V) ) VFs(r, E)/∫EEFF+eV dE Fs(r, E). The sampling of the integrated LDOS, which mimics the scanning of the tip, was performed at a plane 1 Å above the top of the adsorbate, and we verified that increasing the vertical distance between the sampling plane and the surface up to 5 Å does not affect the qualitative features of the simulated STM images. Results At the PBE and LDA levels, we find a C-Si bond length of 1.9 Å, in agreement with experiments (1.85 ( 0.05 Å).17,18 The equilibrium H-C-Si-Si torsion angle θ (see Figure 1) is not in agreement with that inferred from measured STM images6 (θ ) 23°), but it is in accord with calculations reported in the literature:7-10 in our calculations, it varies between 38 and 39°, depending on the number of layers used in our supercell (varied between 6 and 30) and on whether the LDA or PBE approximations are used. We note that similar to bond distances and torsion angles, total energy differences are insensitive to the slab thickness and to the choice of the LDA or PBE approximation: for example, the difference between the optimized geometry and the one corresponding to the experimentally proposed angle (θ ) 23°) varies between 23 and 26 meV per methyl group. We also carried out optimizations using (2 × 2) and (3 × 3)
supercells, starting from a variety of initial configurations for the methyl groups. Such configurations all relaxed to the wellordered (1 × 1) arrangement with θ = 38 to 39°, and the methyl groups vertically bound to the top silicon atoms. These findings are consistent with the evidence of the vertically oriented methyl groups inferred from TIRS measurement11 and with recent lowenergy electron diffraction (LEED) measurements showing sharp patterns that exhibit a three-fold symmetry corresponding to a well-ordered (1 × 1) structure with relatively few defects.19 We note that the equilibrium H-C-Si-Si angle is determined by the interplay between the steric repulsion among the methyl groups and the underlying Si substrate and the repulsion between close-packed methyl groups, favoring θ ) 60 and 30°, respectively. Our optimized value of 38° falls within the expected interval, unlike the one inferred from measured STM images. The inclusion of semiempirical dispersion forces changed energy differences computed at the PBE level by few millielectronvolts and yielded the same results as PBE calculations for the most stable surface structure. We used the optimized geometry described above and shown in Figure 1 to carry out electronic structure calculations and compute STM images. Although finite size effects (number of layers included in the slab) were found to be negligible in the determination of structural and stability properties of CH3-Si(111), slabs with at least 30 layers are necessary to converge the electronic properties of the surface. For example, the PBE band gap (Eg) calculated with slabs of 6, 12, and 30 silicon layer is 1.1, 0.87, and 0.70 eV, respectively, to be compared with Eg ) 0.64 eV found for bulk silicon using the same equilibrium lattice constant (5.47 Å). Similar results were found for the H-Si(111) surface.12 Of course, the agreement with the experimental value (Egexp ) 1.2 eV) for the band gap of Si, as obtained using a six-layer slab, is accidental because of error cancellations between an overestimate of the band gap due to size effects and an underestimate originating from the use of DFT/PBE. In the calculations described below, we adopted a 30-layer slab. In Figure 2a, we show the PBE band structure of j -K j -M j . These CH3-Si(111) along the high symmetry line Γ 12,20 VBM results are very similar to those found for H-Si(111). and CBM states remain bulk-like, and there are no states in the gap induced by the presence of the adsorbate. This is important for explaining the observed surface passivation character of the methyl groups.5,19 Despite different adsorbate-substrate bonds
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Figure 3. Simulated constant height scanning tunneling microscopy (STM) images of the CH3-Si(111) surface at sample bias of (a) -2.0 and (b) -1.0 V.
Figure 2. Band structure computed within DFT using the PBE approximation (left) and projected density of states (PDOS) (right) of the CH3-Si(111) surface. Energy positions of representative j and M j are indicated by surface states at high symmetry points K arrows, with red and blue arrows corresponding to type I and type II surface states, respectively. (See the text.) Orange and cyan curves correspond to PDOS of first-layer Si atoms and that of methyl groups, respectively. The PDOS of a free-standing CH4 selfassembled monolayer is also plotted by comparison, with the lowest PDOS peak aligned with the corresponding peak in the CH3-Si(111) surface.
(i.e., C-Si and H-Si), for both the CH3-Si(111) and H-Si(111) surface, we find three surface state bands located in local gaps of the bulk continuum at about 3, 4, and 8 eV below the VBM, as indicated by the red arrows in Figure 2. Corresponding peaks are observed in the projected density of states (PDOS) of the methyl groups and the first layer Si atoms, which are absent in bulk Si. A close inspection of these states shows that the square moduli of their wave functions are localized on the first two Si layers and exhibit small hybridization with the adsorbate. The properties and energy positions of such surface states (which we denote as type I) are therefore not sensitive to the type of adsorbate (H or CH3). However, the CH3-Si(111) surface has additional surface states with respect to H-Si(111) at about 5-7 eV and 13 to 14 eV below the VBM, as indicated by the blue arrows in Figure 2. These bands, denoted as type II, correspond to molecular orbitals of the methyl group, as can be inferred by comparing their corresponding PDOS with that of a free-standing methane monolayer with the same molecular spacing as in CH3-Si(111). These surface states are weakly hybridized with the silicon substrate and therefore maintain most of their molecular character. Although both type I and type II surface states are located at least 3 eV below VBM, the PDOS contributed by the methyl group extends to the VBM edge, exhibiting a slow-decaying tail. Computed constant height STM images of CH3-Si(111) are shown in Figure 3a,b for sample bias of -2.0 and -1.0 V, respectively. They show the characteristic triangular shape of the methyl groups. An analysis of the integrated LDOS isosurface indicate that the simulated tunneling currents are dominated by contributions from electronic charges on the adsorbate in the range of the applied bias between -2.5 and 2.5 V. Note that the theoretical position of the Fermi level is defined as EF ≡(EVBM + ECBM)/2. As shown in Figure 2b, the PDOS from surface silicon atoms is a few times larger than that from the adsorbate in the vicinity of VBM and in the vicinity of CBM (now shown). However, it is the local DOS that contributes to the tunneling current, and the LDOS decays exponentially with the tip-sample distance. The difference in PDOS between the Si and methyl contributions
is not large enough to modify significantly the signal determined by the difference in their distance from the tip (dSi-C ) 1.9 Å). The STM patterns in Figure 3 exhibit threefold symmetry, consistent with vertically oriented methyl groups, as predicted by DFT/PBE geometry optimizations and inferred from TIRS measurements.11 The STM image measured at 4 K instead shows an asymmetric pattern.6 This symmetry breaking may come from tip-surface interactions present experimentally but not explicitly included in our calculations, as recently indicated by our study of the hydrogen-terminated Si(111) surface.12 Another possible reason for the symmetry breaking could come from a different geometry adopted by the adsorbate, under the nonequilibrium conditions induced by STM imaging. Such conditions might also be responsible for a torsion angle different from that found in the absence of the (dynamical) tip perturbation. It is interesting to discuss the possible influence, on simulated STM images, of self-energy corrections to the eigenvalues obtained at the PBE level.12 In the case of the H-Si(111) surface, photoemission experiments21 and manybody perturbation theory calculations at the G0W0 level20 yield surface states that are lower in energy by 0.5 to 0.9 eV, with respect to those predicted by LDA calculations. However, at low negative bias (-3 < Vbias < 0 V), the main contribution to the tunneling current was found to come from j point, and the bulk-like surface resonant states near the Γ energy positions of these states with respect to the VBM remain almost the same (within a few millielectronvolts) after self-energy corrections are applied.12 Therefore, the H-Si(111) STM images computed at the LDA level are very similar (and qualitatively the same) as those obtained within G0W0. Moreover, within (2.5 eV from the Fermi level of the H-Si(111) surface, the net effect of self-energy corrections is to open up the gap by ∼0.7 eV, whereas the electronic structure of occupied and unoccupied bands remains substantially unaffected with respect to that obtained at the DFT/ LDA level, with variations within 0.1 eV.12 Given the similarity between energy locations of surface states and surface resonant states in the H-Si(111) and CH3-Si(111) surfaces, we expect that also in the case of the CH3-Si(111) surface, low bias STM images and current-voltage characteristics computed using PBE will not be substantially affected by self-energy corrections. Finally, we have calculated I-V characteristics of the CH3-Si(111) surface, and our results for the tunneling current (I), conductance (dI/dV), and normalized conductance (dI/dV/ (I/V)), as functions of the applied sample bias, are presented in Figure 4. As the tunneling conductance directly probes the LDOS at the tip position, its main contribution comes from the charge distribution on the adsorbate due to proximity with the tip, similar to what was observed in the simulated STM images. Indeed, the dI/dV curve displays a wide conductance
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J. Phys. Chem. C, Vol. 114, No. 27, 2010 11901 Summary and Discussion
Figure 4. Simulated current-voltage (I-V) characteristics of the CH3-Si(111) surface. Contributions from the adsorbate (CH3) dominate the tunneling current (I) and conductance (dI/dV), as shown by the wide gap and slowly decaying signal tails in (a) and (b). Contributions from the silicon substrate are enhanced in the normalized conductance (dI/ dV/(I/V)) shown in (c), revealing the fundamental gap of bulk silicon.
gap consistent with the PDOS shape on the methyl group. Instead, in the normalized conductance, contributions from the silicon substrate become dominant near the Fermi level, as clearly shown in Figure 4c. A much narrower and sharp gap is present in the normalized conductance, with a magnitude consistent with the calculated PBE band gap of the CH3-Si(111) slab with 30 layers. The small oscillations in the dI/dV and dI/dV/(I/V) curves arise from corresponding oscillations found in the PDOS of the methyl groups and first-layer Si atoms. We note that computed scanning tunneling spectroscopy (STS) profiles for the hydrogen-terminated surface show features similar to those found for the methyl-terminated surface.12 This finding is consistent with STS measurements on hydrogen-, methyl-, and ethyl-terminated Si(111) surfaces, showing common features despite different terminations, including an apparent band gap of roughly 2 eV and the absence of midgap states.22 The measured tunneling gap, ESTS g , is larger than the intrinsic band gap of bulk Si (Egbulk )1.2 eV), possibly because of tip-induced band bending (TIBB) effects. The penetration of the tip electric field into the semiconductor substrate results in a redistribution of electrons within the substrate and gives rise to an upward (negative bias) or downward (positive bias) bending of the energy bands, yielding an apparent gap larger than the optical one. To model EgSTS correctly, one would need to correct the underestimated PBE band gap (e.g., using GW calculations) and also include TIBB effects. Whereas the former correction may be relatively straightforward to apply, the latter one is more difficult because TIBB effects cannot be estimated by a simple scaling of the measured STS curves by Egbulk/EgSTS; band bending is usually not symmetric with respect to the polarity of the sample bias, especially when the sample is doped, as in the experiments by Yu et al.6,22
In summary, we have presented a first-principle study of the fully covered methyl-terminated Si(111) surface that has attracted widespread attention lately as a silicon substrate well-protected from oxidation and thus having several potential applications.4,5 Our results on the surface structure confirm previous ab initio calculations,7-10 yielding a stable (1 × 1) geometry, with methyl groups vertically bound to Si atoms. Computed STM images show the methyl groups with three-fold symmetry, and their main contributions come from surface resonant states associated with the adsorbate. Although they were carried out at the DFT level with local and semilocal functionals, we expect our results for STM images to be accurate because self-energy corrections to the states mostly contributing to the tunneling signal are estimated to be on the order of few millielectronvolts relative to valence band edge; therefore, these corrections are not expected to change the qualitative picture found by LDA and PBE calculations. The difference between computed and measured6 STM images, which show a breaking of the threefold symmetry and possibly a pattern not compatible with a (1 × 1) reconstruction, is not due to intrinsic properties of the unreconstructed CH3-Si(111) surface. The computed optimal adsorption geometry, for example, a (1 × 1) coverage with methyl groups oriented perpendicular to the surface, is fully consistent with recent LEED19 and TIRS measurements.11 We ascribe the difference in the STM patterns to tip-surface interactions present experimentally but not in our calculations12 or to geometrical changes (including in the torsion angle) induced by the tip perturbation during imaging. The presence of defects on the surface might influence measured STM images as well, as proposed in ref 8; however, it is unlikely that defects will yield a regular pattern as the one observed experimentally. Acknowledgment. This work was funded by NSF-CHE0802907. Some of our calculations were performed at the NERSC and TeraGrid facilities. A.A. acknowledges NANOLICHT, a project supported by the ERANET initiative “NanoSciERA: NanoScience in the European Research Area” (within the EU FP6). We thank H. Yu, N. S. Lewis, and G. Liu for useful discussions. References and Notes (1) Kelzenberg, M. D.; Boettcher, S. W.; Petykiewicz, J. A.; TurnerEvans, D. B.; Putnam, M. C.; Warren, E. L.; Spurgeon, J. M.; Briggs, R. M.; Lewis, N. S.; Atwater, H. A. Nat. Mater. 2010, 9, 239–244. (2) Boettcher, S. W.; Spurgeon, J. M.; Putnam, M. C.; Warren, E. L.; Turner-Evans, D. B.; Kelzenberg, M. D.; Maiolo, J. R.; Atwater, H. A.; Lewis, N. S. Science 2010, 327, 185–187. (3) Bansal, A.; Lewis, N. S. J. Phys. Chem. B 1998, 102, 4058–4060. (4) Bansal, A.; Li, X.; Yi, S. I.; Weinberg, W. H.; Lewis, N. S. J. Phys. Chem. B 2001, 105, 10266–10277. (5) Webb, L. J.; Lewis, N. S. J. Phys. Chem. B 2003, 107, 5404–5412. (6) Yu, H.; Webb, L. J.; Ries, R. S.; Solares, S. D.; Goddard, W. A.; Heath, J. R.; Lewis, N. S. J. Phys. Chem. B 2005, 109, 671–674. (7) Nemanick, E. J.; Solares, S. D.; Goddard, W. A.; Lewis, N. S. J. Phys. Chem. B 2006, 110, 14842–14848. (8) Solares, S. D.; Yu, H.; Webb, L. J.; Lewis, N. S.; Heath, J. R.; Goddard, W. A. J. Am. Chem. Soc. 2006, 128, 3850–3851. (9) Ferguson, G. A.; Raghavachari, K. J. Chem. Phys. 2006, 125, 154708. (10) Juarez, M. F.; Soria, F. A.; Patrito, E. M.; Paredes-Olivera, P. J. Phys. Chem. C 2008, 112, 14867–14877. (11) Webb, L. J.; Rivillon, S.; Michalak, D. J.; Chabal, Y. J.; Lewis, N. S. J. Phys. Chem. B 2006, 110, 7349–7356. (12) Li, Y.; Galli, G., submitted. (13) Giannozzi, P.; et al. J. Phys.: Condens. Matter 2009, 21, 395502.
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Aliano et al. (20) Blase, X.; Zhu, X.; Louie, S. G. Phys. ReV. B 1994, 49, 4973– 4980. (21) Hricovini, K.; Gnther, R.; Thiry, P.; Taleb-Ibrahimi, A.; Indlekofer, G.; Bonnet, J. E.; Dumas, P.; Petroff, Y.; Blase, X.; Zhu, X.; Louie, S. G.; Chabal, Y. J.; Thiry, P. A. Phys. ReV. Lett. 1993, 70, 1992–1995. (22) Yu, H.; Webb, L. J.; Heath, J. R.; Lewis, N. S. Appl. Phys. Lett. 2006, 88, 252111.
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