Molecular Modeling of Alkyl Monolayers on the Si(111) Surface

© Copyright 2000 American Chemical Society

APRIL 4, 2000 VOLUME 16, NUMBER 7

Letters Molecular Modeling of Alkyl Monolayers on the Si(111) Surface Alexander B. Sieval, Bram van den Hout, Han Zuilhof,* and Ernst J. R. Sudho¨lter* Laboratory of Organic Chemistry,Wageningen University, Dreijenplein 8, 6703 HB Wageningen, The Netherlands Received August 20, 1999. In Final Form: November 9, 1999 A computational approach has been delineated to model alkyl monolayers on hydrogen-terminated silicon (111) surfaces by molecular mechanics calculations. The monolayers can be properly described by making use of two-dimensionally repeating boxes with minimally ∼30 alkyl chains. For two different substitution patterns on the Si surface, both with an overall substitution percentage of 50%, good agreement between the computational and the available experimental data (FT-IR, X-ray, ellipsometry) was found. It is shown that the thus formed layers are nearly stress-free and that different orientations of individual alkyl chains exist, which combined yield an overall uniformly ordered monolayer.

Introduction Covalently bonded, well-ordered alkyl monolayers on hydrogen-terminated silicon surfaces get increasing attention,1 because of their interesting properties2-4 and possible applications thereof.5-7 These monolayers can be easily formed by a reaction between a 1-alkene and a * To whom correspondence may be addressed. E-mail: [email protected]: [email protected]. (1) Buriak, J. M. Chem. Commun. 1999, 1051-1060. (2) Linford, M. R.; Fenter, P.; Eisenberger, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc. 1995, 117, 3145-3155. (3) Sieval, A. B.; Demirel, A. L.; Nissink, J. W. M.; Linford, M. R.; van der Maas, J. H.; de Jeu, W. H.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 1998, 14, 1759-1768. (4) (a) Boukherroub, R.; Morin, S.; Bensebaa, F.; Wayner, D. D. M. Langmuir 1999, 15, 3831-3835. (b) Stewart, M. P.; Buriak, J. M. Angew. Chem., Int. Ed. Engl. 1998, 37, 3257-3260. (c) Bateman, J. E.; Eagling, R. D.; Worrall, D. R.; Horrocks, B. R.; Houlton, A. Angew. Chem., Int. Ed. Engl. 1998, 37, 2683-2685. (d) Effenberger, F.; Go¨tz, G.; Bidlingmaier, B.; Wezstein, M. Angew. Chem., Int. Ed. Engl. 1998, 37, 24622464. (e) He, J.; Patitsas, S. N.; Preston, K. F.; Wolkow, R. A.; Wayner, D. D. M. Chem. Phys. Lett. 1998, 286, 508-514. (f) Buriak, J. M.; Allen, M. J. J. Am. Chem. Soc. 1998, 120, 1339-1340. (g) Sung, M. M.; Kluth, J.; Yauw, O. W.; Maboudian, R. Langmuir 1997, 13, 6164-6168. (5) (a) Bansal, A.; Lewis, N. S. J. Phys. Chem. B 1998, 102, 10671070. (b) Bansal, A.; Lewis, N. S. J. Phys. Chem. B 1998, 102, 40584060.

hydrogen-terminated silicon surface (Figure 1).2-4,8 In the case of an octadecyl monolayer on the H-terminated Si(111) surface, a possible structure of the molecules in the monolayer has been proposed.2 It was concluded that (a) 50% of the Si surface atoms are bound to an alkyl chain, whereas the other 50% of the Si-H groups do not react, and that (b) the alkyl chains are in an all-trans conformation, except for the first C-C bond at the surface, which is considerably twisted (torsion angle Si-C-C-C ≈ 37°). Although these monolayers have been characterized using a variety of different techniques, relatively little is still known about the structure of the monolayers on a molecular level. For example, the results from IR spectroscopy, contact angle measurements, ellipsometry, and X-ray reflectivity measurements show that densely packed, well-ordered monolayers are formed and also provide information about the overall structure of the monolayer, (6) Sieval, A. B.; Zuilhof, H.; Sudho¨lter, E. J. R.; Schuurmans, F. M.; Sinke, W. C. Proceedings of the 2nd World Conference on Photovoltaic Solar Energy Conversion (Vienna, 1998); European Commission: Ispra, Italy, 1998; pp 322-325. (7) Currie, E. P. K.; Sieval, A. B.; Avena, M.; Zuilhof, H.; Sudho¨lter, E. J. R.; Cohen Stuart, M. A. Langmuir 1999, 15, 7116-7118. (8) Sieval, A. B.; Vleeming, V.; Zuilhof, H.; Sudho¨lter, E. J. R. Langmuir 1999, 15, 8288-8291.

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Figure 1. Schematic representation of the reaction between a hydrogen-terminated silicon surface and a 1-alkene.

like the average tilt angle of the molecules.2,3 However, as these methods measure only overall properties of the monolayer, it is not possible to get detailed information about the geometry of individual molecules. Molecular modeling provides a unique way to atomistic information on these monolayers, specifically by using the approach of two-dimensionally repeating boxes to mimic the surface.9 This method provides a rapid tool to obtain properties of the wide variety of monolayers that can be formed on Si surfaces.3 In this Letter, the detailed setup and initial results of the first molecular simulations on such alkyl monolayers on H-terminated Si surfaces are reported. The H-terminated Si(111) surface was chosen, as it displays a well-defined two-dimensional structure, in which only one hydrogen atom is bound to each Si surface atom, and because alkyl substitution of this surface has been characterized in most detail.2,4a,4d,10 This not only simplifies modeling of this surface compared to that of other H-terminated Si surfaces11 but also allows for a more direct comparison with experiment. The above-mentioned octadecyl monolayer was investigated, as a large amount of experimental data are available for this layer.2,3,10 Computational Approach General. All calculations were performed with the MSI program Cerius2 (version 3.5).12 The structures were optimized using the “Smart Minimizer” with “highconvergence” criteria,13 which were shown to yield significantly different results from (faster) “standardconvergence” criteria. Two different force fields were used: universal force field (UFF)14 and polymer consistent force field (PCFF),15 both as implemented in Cerius2. In the case of PCFF, the “ignore undefined terms” program option was used, as this force field does not contain inversion parameters for the Si atoms with a dangling (9) Li, T.-W.; Chao, I.; Tao, Y.-T. J. Phys. Chem. B 1998, 102, 29352946. (10) (a) Terry, J.; Linford, M. R.; Wigren, C.; Cao, R.; Pianetta, P.; Chidsey, C. E. D. J. Appl. Phys. 1999, 85, 213-221. (b) Schenkel, T.; Schneider, M.; Hattass, M.; Newman, M. W.; Barnes, A. V.; Hamza, A. V.; Schneider, D. H.; Cicero, R. L.; Chidsey, C. E. D. J. Vac. Sci. Technol., B 1998, 16, 3298-3300. (c) Terry, J.; Linford, M. R.; Wigren, C.; Cao, R.; Pianetta, P.; Chidsey, C. E. D. Appl. Phys. Lett. 1997, 71, 10561058. (d) Henry de Villeneuve, C.; Pinson, J.; Bernard, M. C.; Allongue, P. J. Phys. Chem. B 1997, 101, 2415-2420. (11) See for an overview of the various structures of hydrogenterminated Si surfaces: Dumas, P.; Chabal, Y. J.; Jakob, P. Surf. Sci. 1992, 269/270, 867-878. (12) (a) Cerius2, version 3.5, Molecular Simulations Inc., September 1997. (b) Terms that are specific to the Cerius2 program have in the text been put between quotes. (13) The criteria for the high-convergence minimizations are: Atom root mean square force 1 × 10-3 kcal mol-1 Å-1; atom maximum force 5 × 10-3 kcal mol-1 Å-1; energy difference 1 × 10-4 kcal mol-1; root mean square displacement 1 × 10-5 Å; maximum displacement 5 × 10-5 Å. (14) (a) Rappe´, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024-10035. (b) Castongauy, L. A.; Rappe´, A. K. J. Am. Chem. Soc. 1992, 114, 58325842. (c) Rappe´, A. K.; Colwell, K. S.; Casewit, C. J. Inorg. Chem. 1993, 32, 3438-3450. (15) (a) Sun, H.; Mumby, S. J.; Maple, J. R.; Hagler, A. T. J. Am. Chem. Soc. 1994, 116, 2978-2987. (b) Sun, H. J. Comput. Chem. 1994, 15, 752-768. (c) Sun, H. Macromolecules 1993, 26, 5924-5936. (d) Sun, H. Macromolecules 1995, 28, 701-712. (e) Sun, H.; Mumby, S. J.; Maple, J. R.; Hagler, A. T. J. Phys. Chem. 1995, 99, 5873-5882. (f) Hill, J.-R.; Sauer, J. J. Phys. Chem. 1994, 98, 1238-1244.

Letters

bond at the bottom of the Si crystal (vide infra). This reduction of the system does not affect the optimization of the monolayer and yields a welcome reduction of the CPU time (largest computation in this paper: 48 h, on an SGI R4400 Indigo2 workstation). Construction of Starting Structures. All starting structures were obtained from a small unit cell that contains one octadecyl chain and four Si atoms that represent the atoms in the first four layers of the Si surface. This structure was obtained by cleaving the Si crystal structure along the (111) plane. Subsequently, a preoptimized, vertically aligned all-trans octadecyl molecule was attached to the dangling bond of the top Si atom. This new structure was placed in a box, with dimensions a ) b ) 3.840 Å (from the Si bulk unit cell) and c ) 35 Å and angles R ) β ) 90° and γ ) 120° (Figure 2a). Subsequently, this box was copied in the a and b direction by as many times as necessary to obtain a new structure with the dimensions of the required larger repeating box. Finally, alkyl groups were replaced by hydrogen atoms, in such a way that boxesscontaining from 16 to 800 Si atoms, with respectively 2 to 100 alkyl chainsswith either of the two 50% overall substitution patterns (parts b and c of Figure 2, vide infra) were obtained, that were used in the optimizations. To mimic the Si crystal structure, the positions of the two Si layers at the bottom of the box were fixed at their bulk crystal positions; in addition the overall dimensions of the repeating box were fixed. The positions of the other two Si layers, which are closest to the alkyl substituent, were allowed to be optimized. Calculation of the Energy of the Alkyl Chains. After optimization the Si(H) crystal was removed from the structure. Subsequently, the energy of the remaining alkyl chains was obtained from a single point calculation, without adjustment of the number of hydrogen atoms (i.e., without saturation of the dangling bonds of the carbon atoms that were previously attached to the silicon surface). The obtained energies were divided by the number of alkyl chains to allow direct comparison of the results from calculations with different repeating boxes. Results and Discussion As alkylation of the Si-H surface does not occur with 100% substitution, several substitution patterns are possible. Two different substitution patterns of the alkyl chains on the Si surface were investigated: one in which the alkyl chains are placed on the surface in long straight lines (structure 1, Figure 2b), and one in which they form a zigzag pattern (structure 2, Figure 2c). Both structures are feasible on the Si(111) surface at the experimentally observed degree of 50% substitution of the surface Si-H groups.2 The results of the optimizations with UFF and PCFF are rather similar for all unit cells. Therefore only the PCFF results will be discussed.16 First, the minimal dimensions of the repeating box required for accurate modeling of the surface were determined by computation of the energy per alkyl chain in boxes with n alkyl chains and either substitution pattern 1 or 2. As the experimentally observed monolayers display a high degree of ordering, two criteria for a large enough repeating box should be met: (1) Once the minimally required size of the repeating box has been obtained, further enlargement of the box (including proportionally more alkyl chains) should yield a constant average energy (16) This similarity was not found for ω-functionalized monolayers,3 in which the more advanced PCFF computations are preferable. Sieval, A. B.; Zuilhof, H.; Sudho¨lter, E. J. R. Manuscript in preparation.

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Figure 2. (a) Structure of the basis unit (left). (b) Unit cells 1 (right, top) and (c) unit cell 2 (right, bottom) that were used in the construction of the investigated repeating boxes. The unit cells are indicated by the dashed lines. The drawn lines show the top two layers of the Si surface. The C and H indicate the alkylated and hydrogen-terminated Si surface atoms, respectively.

per alkyl chain. For small repeating boxes with only a few alkyl chains (n ) 2 or 8 for structure 1; n ) 4 or 16 for structure 2), the energy per alkyl chain strongly depends on n. In contrast, with larger boxes (n ∼ 30 or more) this energy converges, to become nearly independent of the box size. (2) If the repeating box is large enough, patterns formed by small clusters of alkyl chains should start to occur several times within this box. In other words: it is required that the alkyl chains are not forced in a certain position due to the fact that the method of repeating boxes forces adjacent boxes to be identical. This behavior is only observed with structures of ∼20 alkyl chains onward. Apparently, a small repeating box with only a few alkyl chains9 is insufficient to properly describe all the interactions that take place between alkyl chains in a monolayer, even if it correctly represents the substitution pattern. For an accurate description of a monolayer structure by way of repeating boxes, the use of boxes with a considerable number of alkyl chains is thus required, irrespective of whether this concerns covalently attached monolayers on silicon or, e.g., thiol monolayers on gold. Two representative results for such large repeating boxes are shown in Figure 3. Top and side views are given of (a) a structure with 32 alkyl chains in pattern 1 (Figure 3a, top) and (b) a structure with 64 alkyl chains in pattern 2 (Figure 3b, bottom).17 The structures of the monolayers in the two boxes are strikingly similar. In both structures the alkyl chains form an ordered array of molecules in an all-trans conformation, all oriented in approximately the same direction, in line with the experimentally observed ordering of the monolayers on the Si(111) surface.2,3 The average tilt angle of the molecules with respect to the (17) The starting structures were multiplied by the same integer along the a and b axis. As the initial cell of structure 2 is twice the size of that of structure 1 (Figure 2), this always leads to boxes with twice as many alkyl chains in structure 2 than in structure 1.

surface normal is ∼25°, slightly depending on the box size used. This computed value corresponds well to the tilt angle of 30°, determined from IR dichroism experiments,2 and that of 28° inferred from X-ray reflectivity measurements.3 The all-trans conformation was observed for all C-C bonds in the alkyl chains, apart from the ones closest to the Si surface. The Si-C-C-C twist angle for these bonds in different alkyl chains varies over a wide range, depending on whether substitution pattern 1 or 2 is present. In structure 1 (Figure 3a), this twist angle is close to zero for nearly all alkyl chains, which implies a high degree of commensurability between the Si(111) surface and the packing in structure 1 of the alkyl monolayer. In structure 2 (Figure 3b) this twist angle varies over a wider range: most values range from 0 to 15°, but several alkyl chains have twist angles up to 36°. Despite this difference, the thickness of the monolayer is approximately 19 Å in both cases, pointing to the rather low sensitivity of the layer thickness to slight changes in the molecular structure. This computed thickness agrees within the experimental uncertainties with two measured values: 18 Å, as determined with ellipsometry;2 and 19.7 Å, from X-ray reflectivity measurements.3 Therefore, it can be concluded that molecular modeling via repeating boxes of at least a minimal size yields a good representation of the structure of the octadecyl monolayers on a hydrogenterminated silicon (111) surface.2,3 Our data do not agree with the results of an earlier X-ray measurement, which yielded a monolayer thickness of only 16.0 Å.2 This lower value not only is less likely given the more recent X-ray data3 but also would require the presence of a considerable average twist angle (estimated to be ∼37°).2 From the modeling data presented here, it thus becomes evident that the supposed mismatch between the Si(111) surface and a 50% packing of the surface by octadecyl chains is

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Figure 3. PCFF-optimized structures using (a) substitution pattern 1 with 32 alkyl chains (top) and (b) substitution pattern 2 with 64 alkyl chains (bottom). Note: In the top views (the two pictures on the right), the model is rotated in such a way that the alkyl chains are oriented nearly perpendicular to the plane of the paper. To reveal the substitution patterns, the remaining hydrogen atoms at the Si surface are depicted in the top views by blue balls.

in fact absent, yielding a nearly stress-free contact between the Si(111) surface and the covalently attached monolayer. Interestingly, the energy of patterns 1 and 2 also becomes approximately equal with large boxes, even though the linear and zigzag pattern are different on a molecular level. If the proposed reaction mechanism2 is correct, the substitution pattern that is formed will be determined by the relative rates of the transfer of a hydrogen atom from any of the surrounding Si surface atoms to the intermediary formed alkyl radicals. These kinetics are currently unknown. Both patterns 1 and 2 yield ordered structures in which individual alkyl chains may have substantially different conformations (see specifically both top views in Figure 3). Either of these substitution patterns is consistent with the experimental structural data, but they are not the only possible structures that describe a 50% substituted Si surface. The relative importance of the various substitution patterns is currently under further investigation in our laboratories, using a combination of molecular mechanics and ab initio approaches.18 (18) Sieval, A. B.; Zuilhof, H.; Sudho¨lter, E. J. R. Unpublished results.

Conclusions The experimentally observed data (tilt angle, Si-CC-C twist angle, layer thickness) on the structure of octadecyl monolayers on hydrogen-terminated silicon (111) surfaces (overall 50% substitution of Si-bound H atoms by alkyl chains) can be reproduced by molecular mechanics computations. The use of a two-dimensionally repeating box with a relatively large number of alkyl chains in it (in this case: 30 or more) is required, to mimic all interchain interactions properly. From our computations a near perfect match between the Si(111) surface and the 50% packing of alkyl chains can be inferred. These observations point to the power of modeling techniques in the elucidation of monolayer structures at an atomistic level. Acknowledgment. The authors thank The Netherlands Organization for Scientific Research (NWO) and The Netherlands Agency for Energy and the Environment (NOVEM) for generous funding. LA991131K