One-Dimensional Pattern Formation of Adsorbed Molecules on the Ge

Article pubs.acs.org/JPCC

One-Dimensional Pattern Formation of Adsorbed Molecules on the Ge(100)‑2 × 1 Surface Driven by Nearest-Neighbor Effects Bonggeun Shong and Stacey F. Bent* Department of Chemical Engineering, Stanford University, 381 North−South Mall, Stanford, California 94305, United States S Supporting Information *

ABSTRACT: Formations of distinct one-dimensional patterns along the dimer row have been reported in methanol and ethylene adsorption on the germanium(100)2 × 1 surface. A theoretical investigation is carried out in this study to provide a unified explanation of the pattern formation. Density functional theory calculation results show that an existing adsorbate affects the adsorption kinetics of the adjacent dimer, an effect that is mostly confined to the nearest neighbor. Kinetic Monte Carlo simulations are performed with the calculated kinetic parameters. The simulation results agree well with the experimental observations of ethylene and methanol adsorption on Ge(100), showing that the nearest-neighbor effect leads to longerrange pattern formation. The modeling is extended to the Si(100) surface where a similar pattern as on Ge(100) was formed with ethylene but not with methanol, and it can be further applied to spontaneous adsorbate patterning on ordered surfaces.

1. INTRODUCTION Controlled self-assembly on solid surfaces has been attracting great interest because it produces unprecedented properties and enables possibilities for fabrication of subnanoscale devices.1 The 2 × 1 reconstructed (100) surfaces of group IV semiconductors possess ordered arrays of dimers, which can serve as a template for spontaneous patterning upon adsorption of organic molecules.2−5 Linear molecular nanostructure formation on semiconductor surfaces has mostly been studied on hydrogen-terminated Si(100), where the Si−H bond cleavage step is important in the growth of adsorbate patterns.6,7 Only a handful of works have suggested onedimensional (1D) patterns of molecular adsorbate on pristine Si or Ge (100) surfaces,8−11 many of which were perpendicular to the dimer rows. The adsorption of small molecules such as methanol12−14 and ethylene15−23 on Ge(100) has been studied extensively. Though the detailed mechanisms differ, reactions of the two molecules on Si or Ge surfaces bear many similarities. For example, their adsorptions are both precursor-mediated, and product formations are irreversible at room temperature (Figure 1). However, in recent scanning tunneling microscopy (STM) studies, distinct 1D adsorption patterns (ordered in the [011̅] direction, i.e. parallel to the rows, and random in the [011] direction, i.e. perpendicular to the rows) emerged on Ge(100).13,18 Whereas methanol formed successive arrays of adsorbates along the rows, ethylene adsorbates occupied every second dimer, skipping the nearest-neighbor (NN) sites (Figure 2). Interestingly, on the closely related Si(100) surface, similar self-assembly was observed with ethylene but was not significant with methanol.24,25 The formation mechanism of these patterns has not been fully understood so far. © 2012 American Chemical Society

Figure 1. Schematic potential energy diagram of precursor-mediated adsorption during reaction of methanol and ethylene on Ge(100). Formation of the chemisorption product is stable and irreversible at room temperature, while the precursor in the shallow well is metastable and short-lived.

It is known that clustering of adsorbates on Si(100) is energetically favored in order to minimize the disruption of dimer buckling that exists on the bare surface.26 This effect can nominally explain the positioning of adsorbed methanol on adjacent dimer sites. However, the adsorption pattern of ethylene does not appear to follow this trend. Moreover, to understand the origin of this spontaneous pattern formation, it is important to consider a kinetic driving force: while thermodynamic equilibrium can be reached when the adsorbates are allowed to diffuse, diffusion of chemisorbed methanol or ethylene on Ge(100) is not observed or expected at room temperature.13,18 On the other hand, it is known that interdimer interactions alter the reactivity of adjacent dimers upon successive adsorption.27,28 Meanwhile, the covalent Received: August 7, 2012 Revised: November 12, 2012 Published: December 27, 2012 949

dx.doi.org/10.1021/jp3078503 | J. Phys. Chem. C 2013, 117, 949−955

The Journal of Physical Chemistry C

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set, while a LANL2DZ pseudopotential was used for the bulk Ge atoms, and a 6-31G(d) basis set for the terminating H atoms. This level of theory yielded a bond length and a tilt angle of the Ge dimer of 2.47 Å and 18.7°, which are close to the experimental values of 2.5 ± 1 Å and 19° ± 1°.34 Following the default settings of Gaussian 03, a pruned grid with 75 radial shells and 302 angular points per shell and the weighting scheme of Stratmann et al.35 were used in all numerical integrations. The transition state geometries were confirmed after optimization by having an imaginary vibrational mode along the reaction coordinate. All reported energies were zeropoint corrected. In our KMC simulations, the Ge(100) surface was modeled as a 1D chain of reactive sites. Each collision was assumed to be independent, since the STM experiments were done in ultrahigh vacuum conditions13,18 conducive to a low impingement rate. This condition keeps the surface concentration of the precursor low and allows us to ignore precursor−precursor interactions. Upon further exposure to gaseous molecules, the trapping coefficient toward the precursor state on unreacted dimers was assumed to be independent of the local environment,36−38 while reacted dimers with product adsorbates were assumed to have a sticking probability of 0. Therefore, a dimer that forms precursor at each KMC step was randomly selected with a uniform probability from among unreacted dimers. Then, the probability P for a physisorbed precursor to chemisorb is site-specifically given by eq 1, whose detailed derivation is given in ref 39 for a similar precursor-mediated reaction of acetylene/Si(100).39,40 rrxn P= rrxn + rdes (1)

Figure 2. Experimental STM images of Ge(100) (16 × 16 nm2) after exposure to (a−c) methanol (where dark = adsorbate) and (d−f) ethylene (where bright = adsorbate), with coverages of (a) 0.08, (b) 0.34, (c) 0.68, (d) 0.12, (e) 0.53, and (f) 0.68 ML. One monolayer (ML) = 1 molecule per dimer. Adapted with permission from refs 13 and 18. Copyright 2007, 2004 American Chemical Society.

nature of the group IV materials restricts the effective range of nonlocal interaction.4 For example, surface-mediated interaction on Si(100) is effective within the same row, whereas interrow effects are small.27 Ignoring interrow interactions reduces the problem into that of 1D cooperative sequential adsorption. In this work, we show that the distinct patterns formed with methanol and ethylene adsorbates on Ge(100)-2 × 1 can be collectively explained by local changes in the kinetic parameters. Density functional theory (DFT) calculations show that the adsorption energies and kinetic barriers of the precursors are altered when placed adjacent to an adsorbate. We hypothesize that the interaction between buckled dimers, the inductive effect of the adsorbate, and the steric hindrance by the adsorbate modify the potential energy surface along the reaction channel. This interadsorbate interaction is most effective at nearest-neighbor sites. Kinetic Monte Carlo (KMC) simulations based on the local kinetic parameters closely reproduce the coverage-dependent evolution of the experimentally observed 1D patterns for both methanol and ethylene. Our discussion is extended to selective pattern formation on Si(100) to show the importance of surface reactivity in spontaneous patterning across different semiconductor surface systems.

Here rrxn describes the rate of reaction from the precursor to the chemisorbed state and rdes describes the rate of desorption back to the gas phase from the precursor state. The conversion rate r of a precursor is defined according to the local NN occupation (0, 1, and 2 NN adsorbates) and calculated by the Arrhenius equation: r = Γexp[−Ea /RT ]

(2)

The vibrational frequencies of the adsorbate−surface bond accompanying the motion of the precursor along the relevant coordinates were adopted as the attempt frequencies Γ, which were Γdes ≈ 9 × 1012 s−1 for desorption and Γrxn ≈ 2−3 × 1012 s−1 for reaction. The activation energies Ea are defined as Ea,des = −Eads(precursor) for desorption and Ea,rxn = Eads(transition state) − Eads(precursor) for chemisorption (Figure 1). The temperature T was 298.15 K for all calculations, and the effect of quantum tunneling was ignored. The simulations were terminated when certain coverages were achieved.

2. METHODS DFT calculations were performed with the Gaussian 03 package.29 The Ge(100)-2 × 1 surface was represented by a Ge33H28 cluster with four layers of Ge atoms, consisting of 5 dimers in a row and 23 subsurface atoms, in which the bottom two layers were frozen at the ideal lattice positions and the top two layers and adsorbates were allowed to relax. A buckled dimer geometry was used for all calculations. We found in a previous study that the intensity of the π-complex on Ge(100) is dependent on the exchange−correlation functional.30 In this work, the B3PW91 functional incorporating Becke’s threeparameter hybrid exchange31 and the nonlocal part of PW91 correlation32 was used to reproduce the critical energy values that were experimentally estimated for ethylene16 and B3LYPcalculated for ethanol33 on Ge(100). The Ge dimers and the adsorbates were modeled with a triple-ζ 6-311++G(d,p) basis

3. RESULTS AND DISCUSSION Four different local environments for the adsorption were considered in the calculation of adsorption energetics (Figure 3): on the bare surface (A), adjacent to one NN adsorbate (B), between two NN adsorbates (C), and at the next nearest neighbor of an adsorbate (D). For a single chemisorption of both molecules, only the on-top configuration (adsorption on one dimer) was considered, because it was the only observed configuration for methanol13 and the major configuration that forms the distinct NN skipping pattern for ethylene.18 The optimized geometries of the Ge dimer and the adsorbates 950



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In contrast to the similar trends in chemisorption energies, the precursor adsorption energies, Eads(precursor), of the two molecules show an important dissimilarity. Whereas the dativebonded methanol precursor does not experience a significant change in Eads for the different environments, the π-complex precursor of ethylene is destabilized by 9−10 kJ/mol per NN adsorbate. We attribute this change in Eads(precursor) to a combination of the following effects. First, when the buckling of a Ge dimer is broken by an on-top adsorbate, the resulting symmetric dimer loses its ability to delocalize the donated electron density from an adjacent precursor.27 On the other hand, an O−H dissociated methanol adsorbate becomes an electron-withdrawing group through its covalent Ge−O bond,28 which then can inductively stabilize the electron density donation. The small electronegativity difference in the Ge−C bond of an adsorbed ethylene cannot provide such an effect. Furthermore, neighboring ethylene adsorbates would impose steric hindrance to the precursor in a similar way as they do to the cycloaddition product, while the hindrance imposed by a NN methanol adsorbate is minimal. The inductive effects of adjacent adsorbates are manifested in the atomic charges of the down atoms to which the precursor binds (Table 1). The down atom of the bare Ge(100) cluster is positively charged by 0.33 e, and the electronic density of this Ge atom for different local environments can be measured by means of the variations in the atomic charges. Adding each NN dissociated methanol increases the charge of the down atom by about 0.1 e, making it more prone to accept dative bonding. Therefore, we speculate that the inductive effect of a NN methoxy almost offsets the loss of charge density delocalization of the bare surface from disruption of dimer buckling. In contrast, each NN ethylene adsorbate decreases the down atom charge by about 0.1 e, which could be caused by either an inductive effect or isolation of the dimer π orbital from the buckled neighbors.44 As a result, the reduced positive charge of the down atom, the loss of ability to delocalize donated charge density, and the steric hindrance collectively destabilize the ethylene π-complex precursor near another adsorbate. At the transition states for chemisorption, the dimer is partially flattened, resembling the symmetric geometry of the product. Therefore, we believe that the transition states are also

Figure 3. Schematic description of local adsorption environments considered in this study, shown with ethylene as an example: A, on bare surface; B, adjacent to one adsorbate; C, between two adsorbates; and D, next nearest neighbor of an adsorbate.

corresponding to the precursor, transition state, and product at A (bare surface) are summarized in Table S1, Supporting Information. The calculated adsorption energies (Eads) and activation energies (Ea) are listed in Table 1. First to note is that the chemisorption products are more stable at B (adjacent to one NN adsorbate) and C (between two NN adsorbates) than at A (on the bare surface). The additional stabilization for occupying a NN was 11−14 kJ/mol for methanol, close to the magnitude of the Ge(100) interdimer interaction estimated around 10 kJ/ mol.2 When an additional molecule is adsorbed at B or C, it saves one and two dimer−dimer interactions from breaking compared to adsorption at A. For ethylene, the stabilization effect is weakened to 3−6 kJ/mol, possibly by interadsorbate Pauli repulsion between the C−H groups.16,41,42 The C−C axis of the ethylene cycloaddition product on Ge(100) becomes more rotated with respect to the dimer axis with increasing coverage, which is evidence of this effect (Table S2, Supporting Information). The rotation increases from 3.6° at A to 8.2° at C, comparable to the estimated rotation of 7.4°−11.4° at saturation on Si(100).41,42 On the other hand, the C−O axes of methanol adsorbates are rotated less than 2° regardless of the coverage, owing to smaller overlap between adjacent H adatoms and methoxy adsorbate. While a recent theoretical study on ethylene/Ge(100) predicted a slight decrease in Eads upon coverage increase,22 we note that there is a disagreement in the literature on the direction of the coverage dependence of Eads(ethylene) on Si(100), where more severe surface crowding exists.43 Either way, the change in Eads is small compared to the magnitude of Eads itself, and the chemisorption of ethylene is always exothermic regardless of the environment.

Table 1. Calculation Results for Adsorption Energy, Activation Energy, Probability of Adsorption, and Mulliken Charge of the Ge Dimer Down Atom for Reactions of Methanol and Ethylene on Ge(100)a A Eads(precursor), kJ/mol Eads(transition state), kJ/mol Eads(chemisorption), kJ/mol Ea,rxn, kJ/mol P down atom charge, e

−53.5 13.7 −121.9 67.2 1.0 × 10−3 0.33

Eads(precursor), kJ/mol Eads(transition state), kJ/mol Eads(chemisorption), kJ/mol Ea,rxn, kJ/mol P down atom charge, e

−33.9 5.6 −105.2 39.5 2.9 × 10−2 0.33

B Methanol −53.0 8.0 −132.8 61.0 9.6 × 10−3 0.43 Ethylene −25.2 11.4 −111.3 36.6 3.0 × 10−3 0.26

C

D

−53.7 0.1 −147.2 53.8 0.18 0.57

−54.5 15.1 −118.9 69.6 5.8 × 10−4 0.35

−15.2 19.3 −114.1 34.4 1.3 × 10−4 0.17

−36.3 4.3 −103.8 40.6 4.9 × 10−2 0.32

Ea,des = −Eads(precursor) by definition. A, on bare surface; B, adjacent to one NN adsorbate; C, between two NN adsorbates; and D, two dimers away from an existing adsorbate.

a

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Figure 4. Simulated coverage-dependent adsorption patterns on Ge(100) (16 × 16 nm2) of methanol and ethylene, and site-nonspecific adsorption. Gray spot, empty dimer; white spot, adsorbate-occupied dimer.

surfaces at θ > 0.5 ML.16,40 At a high coverage of θ > 0.5 ML, most empty dimers would statistically be C sites with a small fraction of B sites. Therefore, P and consequently s would encounter a decrease of more than 2 orders of magnitude at θ > 0.5 ML, an effect amplified by the decrease in the number of available reaction sites. Adsorption energetics at two dimers away from an existing adsorbate (D) are also calculated (Table 1) to estimate the next-NN interactions. Changes in Eads and the down atom charges at D are small compared to those at B or C, such that the deviation may even be within the error of the calculation. In terms of P, the critical parameter in our model, the variations at D are less than ×2±1, much smaller than nearly 10-fold and more than 100-fold changes at B and C, respectively. We expect that the effect of a nearby adsorbate is mostly limited to NN because the chemical bonding in group IV materials is covalent and local.4 In this sense, only NN occupations were considered in the simulations as the local environment of a precursor. KMC simulations of adsorption patterns on Ge(100) were performed with the DFT-calculated site-specific adsorption probabilities. Figure 4 shows the simulated patterns for methanol and ethylene, compared with a random sitenonspecific adsorption where P is uniformly equal. Clear differences are seen between the three cases. Our simulations closely reproduce not only the morphology of the experimental adsorption patterns but also their coverage-dependent evolution (Figure 2). At a very low coverage (0.03 ML), there are few adjacent adsorbate sites, and therefore no adsorption pattern is expected regardless of the adsorbate species. The chainlike array formation of methanol is noticeable with coverage as low as 0.1 ML, and these clusters continue to grow with some additional initiations on “bare” areas. The apparent morphology at higher coverages resembling 2D islands that exist both in simulated and experimental images of methanol adsorption may originate from the smaller number of new adsorbate chain initiations compared to the case of random adsorption at the same coverage. On the other hand, the NN skipping pattern of the ethylene adsorbates becomes most prominent at θ = 0.5 ML. At coverages exceeding a half monolayer, the dimers between existing ethylene adsorbates are forced to adsorb another molecule and some successive arrays are formed. Two-dimensionally, local p(2 × 2) and c(4 × 2)

partially stabilized at the NN by already broken buckling. However, the change here would be smaller compared to the change in Eads(chemisorption) since the disruption of the dimer tilt is not complete at the transition state. Again for ethylene, the transition state is destabilized by steric hindrance of the C−H group of a neighboring adsorbate. Ea,rxn is thus lowered at NN for both molecules, but the decrease is only by 5−6 kJ/mol for methanol and 2−3 kJ/mol for ethylene. A previous theoretical study for ethylene/Ge(100) also suggested that, at high coverage, Ea,rxn is lowered but the change is less significant than the destabilization of the precursor and resulting decrease of Ea,des, in agreement with the current work.22 Finally, we calculated using eq 1 the probabilities of adsorption (P) from the rates of the reaction and desorption at each environment (r), summarized in Table 1. Recall that P(X) describes the probability for a physisorbed precursor to chemisorb instead of desorb at a local environment X. Since the calculations of P depend largely on the DFT-calculated adsorption energies, the accuracy in P is influenced by errors inherent to the DFT calculations. However, similar DFT cluster calculations from previous studies showed predictive power in differences between Eads values, the most critical factor in determining P, achieving accuracy within a few kilojoules per mole of experimental estimations or QCISD(T) calculations.30,33,45,46 Since values of Eads and therefore Ea,rxn and Ea,des show nontrivial differences with the different local environments, we believe the calculated differences in P are significant. The results show that all r are enhanced at B and C because of the lowered activation barriers. However, for methanol, the increase of rrxn at a NN site is significant while the change of rdes is only slight, and thus P(methanol) is enhanced at B or C. On the contrary, since the NN decrease of Ea,des is more prominent than Ea,rxn for ethylene, rdes is increased far more significantly than rrxn, causing a smaller P(ethylene) at NN sites. The ratio of P(A):P(B):P(C) is 1:9.1:(1.8 × 102) for methanol and 1:0.11: (4.4 × 10−3) for ethylene. The absolute P values are less than 1 /2 for all calculations since the adsorption pathways are activated [Eads(transition state) > 0, Figure 1]. An important implication of the large decrease of P(ethylene) at NN sites is that dramatic diminishments were observed in the sticking coefficient (s) of this molecule on Ge(100) and Si(100) 952



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decreases P of ethylene/Si(100) and can nontrivially lead to formation of adsorbate patterns regardless the magnitude of P(A), as it did on Ge(100). To test these hypotheses, we carried out additional simulations for adsorption of the two molecules on Si(100), assuming a large initial adsorption probability of P(A) = 0.5, together with P(A):P(B):P(C) of (i) 0.5:0.05:0.005 for ethylene, indicating a 10-fold NN suppression of adsorption, and (ii) 0.5:0.95:0.995 for methanol where the probability of desorption is decreased by 10-fold by each NN adsorbate, a reasonable extrapolation of the NN effect on Ge(100). The resulting dependence of nav on coverage on Si surface is shown in Figure 5. nav ≈ 1 for ethylene/Si(100) at θ < 0.5 ML and its overall behavior is close to that on Ge(100), indicating a similar pattern formation. However, nav[methanol/Si(100)] shows only small deviation from the site-nonspecific adsorption, far from the results on Ge(100). Methanol/Si(100) is indeed close to random adsorption in terms of simulated adsorption patterns. If we consider an extreme case of Ea,rxn ≈ 0 and P ≈ 1 already on a bare surface, there is no room for a cooperative effect to direct a chainlike pattern growth by enhancing adsorption at NN sites. Therefore, the lack of patterning during adsorption simulation of methanol/Si(100) is caused by the large P(A) that we assumed. Our results are in qualitative agreement with the experimental STM images of ethylene and methanol on Si(100)24,25 without a precise calculation of the kinetic constants. Now recalling the adsorption patterns of these molecules on Ge(100), while the NN suppression would have sufficed to direct the NN skipping pattern of ethylene, linear chainlike growth of methanol/ Ge(100) is enabled by the low reactivity of the Ge surface combined with the cooperative NN effect.

orderings of ethylene adsorbates coexist, just as in experimental images.18 In contrast, site-nonspecific adsorption does not show any recognizable pattern at all coverage. These excellent agreements with the experimental results, despite the simple construction of the simulation algorithm with the assumption of a 1D surface, suggest that the NN interaction is a key driving force for adsorbate patterning on Ge(100). The agreements also justify the assumption to neglect interaction between neighboring rows for methanol and ethylene, in contrast to halogen adsorbates on Si(100), for which interrow interactions are significant.38,47 The evolution of these 1D patterns with respect to the coverage increase was quantified by the average length of the adsorbate chains (nav), shown in Figure 5. For the site-

Figure 5. Average successive chain length of the simulated adsorbate patterns versus coverage. Solid line: nav = 1/(1 − θ).

nonspecific adsorption, the KMC-simulated dependence of nav on coverage follows the exact relationship of nav = 1/(1 − θ) derived in the literature for an infinite and uniform 1D lattice.48 The growth of nav[methanol/Ge(100)] is conspicuous from small coverages, and it continues to surpass the others at higher coverages. Fast growth of nav can be interpreted as the adsorption at the end of existing chains being more favorable than the initiation of a new adsorption pattern due to the NN effect. On the other hand, ethylene adsorbates on Ge(100) are mostly individually scattered (nav ≈ 1) at low coverages, as their adsorption is suppressed at NN sites. As discussed above, ethylene is forced to form successive chains when θ > 0.5 ML, and thus nav(ethylene) shows a sudden increase at that coverage. A more quantitative analysis was not conducted due to the absence of further experimental statistics. We turn our attention to the related Si(100) surface. As mentioned earlier, on Si(100), ethylene also skipped the NN dimers, while methanol did not show an obvious adsorption pattern.24,25 We suggest that the reactivity of the surface is another key factor in determining whether an adsorption pattern will emerge or not, along with local variations in the kinetics. In general, s of a reactive gaseous molecule and P of a precursor are higher on Si than on Ge due to the higher reactivity of the Si surface.4,5 Adsorption of both methanol and ethylene on the silicon surface is precursor-mediated but nonactivated [Eads(precursor) < Eads(transition state) < 0],40,49 which gives P ≳ 0.5 and a high initial s.40,50 In the case of methanol on silicon, an increase of P at a neighboring site would have a trivial effect in forming an adsorption pattern since P(A) is already high. However, P of methanol on Ge(100) is low enough for a cooperative NN effect to direct the chain growth. On the other hand, a repressive NN effect

4. CONCLUSIONS KMC simulations of methanol and ethylene adsorption on the Ge(100) surface accurately model experimental STM observations of distinct 1D pattern formations according to increasing coverage. Local adsorption probabilities found from DFT calculations are dependent on interadsorbate interactions within the row: ethylene adsorbates hinder NN adsorption, while methanol adsorption prefers the NN site. These changes are caused by a superposition of the buckling nature of the dimers with the inductive effects and the steric hindrances of the adsorbates. Comparison with patterns on Si(100) gives the following generalization for 1D pattern generation during precursor-mediated adsorption: (1) for formation of successive chains of adsorbates, the reaction probability P on the bare surface must not be too high, given a cooperative neighbor effect; and (2) for adsorbates to skip NN sites, having a suppressive neighbor effect that reduces P suffices. These insights into the nearest neighbor effects on chemisorption site preference can be further applied to develop systems for spontaneous surface-templated patterning during irreversible molecular adsorption through a precursor-mediated mechanism.

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ASSOCIATED CONTENT

S Supporting Information *

Two tables, listing optimized adsorption geometries of methanol and ethylene on Ge(100) and calculated rotation angles of molecular axes of adsorbates. This material is available free of charge via the Internet at http://pubs.acs.org. 953



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(29) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; et al. Gaussian 03, Revision D.01; Gaussian, Inc., Wallingford, CT, 2003. (30) Shong, B.; Bent, S. F. J. Phys. Chem. C 2012, 116, 7925−7930. (31) Becke, A. D. J. Chem. Phys. 1993, 98, 5648−5652. (32) Perdew, J. P. In Electronic Structure of Solids; Ziesche, P., Eschrig, H., Eds.; Akademie Verlag: Berlin, 1991; pp 11−20. (33) Kachian, J. S.; Bent, S. F. J. Am. Chem. Soc. 2009, 131, 7005− 7015. (34) Shirasawa, T.; Mizuno, S.; Tochihara, H. Surf. Sci. 2006, 600, 815−819. (35) Stratmann, R. E.; Scuseria, G. E.; Frisch, M. J. Chem. Phys. Lett. 1996, 257, 213−223. (36) We note that interactions between a gaseous molecule and adsorbates on the surface could change the local potential energy surface during formation of the precursor, as shown in refs 37 and 38. On the following basis, however, we ignore this effect and the possible site-specific inhomogeneity in trapping coefficient that could result, for the simplicity of the simulation. First, to explain a linear chainlike structure of methanol/Ge(100), an attractive interaction, most likely H-bonding, would have to be assumed, as proposed in ref 37 for reaction of NH3 with Si(100). However, H-bonding of methanol and methoxy groups is smaller in number and weaker in intensity than among NH3/Si(100). Second, repulsive interactions, required to skip the NN, may exist between Ge-CH2 and a gaseous ethylene molecule. However, its magnitude would be smaller than that between Si-Cl and gaseous HCl as in ref 38, because the Cl atoms of the latter have bulkier electron clouds and are more negatively charged, and also because Ge has a larger lattice constant than Si, allowing smaller adsorbate−molecule overlap during impingement. Despite the weaker interactions toward the precursor state, the experimentally observed patterns of methanol and ethylene on Ge(100) are more prominent than those of HCl or NH3 on Si(100), requiring an alternative explanation, other than direct adsorbate−molecule interactions, for the phenomenon that dominates the adsorption kinetics. (37) Kim, Y.-S.; Koo, J.-Y.; Kim, H. Phys. Rev. Lett. 2008, 100, 256105. (38) Hsieh, M.-F.; Cheng, J.-Y.; Yang, J.-C.; Lin, D.-S.; Morgenstern, K.; Pai, W.-W. Phys. Rev. B 2010, 81, 045324. (39) Taylor, P. A.; Wallace, R. M.; Cheng, C. C.; Weinberg, W. H.; Dresser, M. J.; Choyke, W. J.; Yates, J. T., Jr. J. Am. Chem. Soc. 1992, 114, 6754−6760. (40) Lipponer, M. A.; Armbrust, N.; Dürr, M.; Höfer, U. J. Chem. Phys. 2012, 136, 144703. (41) Hennies, F.; Föhlisch, A.; Wurth, W.; Witkowski, N.; Nagasono, M.; Piancastelli, M. N. Surf. Sci. 2003, 529, 144−150. (42) Kostov, K. L.; Nathaniel, R.; Mineva, T.; Widdra, W. J. Chem. Phys. 2010, 133, 054705. (43) Marsili, M.; Witkowski, N.; Pulci, O.; Pluchery, O.; Silvestrelli, P. L.; Del Sole, R.; Borensztein, Y. Phys. Rev. B 2008, 77, 125337. (44) Ryan, P. M.; Teague, L. C.; Boland, J. J. J. Am. Chem. Soc. 2009, 131, 6768−6774. (45) Mui, C.; Han, J. H.; Wang, G. T.; Musgrave, C. B.; Bent, S. F. J. Am. Chem. Soc. 2002, 124, 4027−4038. (46) Carman, A. J.; Zhang, L.; Liswood, J. L.; Casey, S. M. J. Phys. Chem. B 2003, 107, 5491−5502. (47) Lin, Y.-H.; Li, H.-D.; Jeng, H.-T.; Lin, D.-S. J. Phys. Chem. C 2011, 115, 13268−13274. (48) Nord, R. S.; Hoffman, D. K.; Evans, J. W. Phys. Rev. A 1985, 31, 3820−3830. (49) Zhang, L.; Carman, A. J.; Casey, S. M. J. Phys. Chem. B 2003, 107, 8424−8432. (50) Tanaka, K.-i.; Xie, Z.-X. J. Chem. Phys. 2005, 122, 054706. (51) Mette, G.; Dürr, M.; Bartholomäus, R.; Koert, U.; Höfer, U. Chem. Phys. Lett. 2012, DOI: 10.1016/j.cplett.2012.11.029.

AUTHOR INFORMATION

Corresponding Author

*Phone 650-723-0385; Fax 650-723-9780; E-mail sbent@ stanford.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This study was supported by the National Science Foundation (CHE-0910717 and CHE-1213879). B.S. acknowledges the Samsung Scholarship for fellowship support. Helpful discussions with A. Wangperawong were also greatly appreciated.

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NOTE ADDED IN PROOF While this article was under review, Mette et al.51 published a relevant work on the adsorption of cyclooctyne on Si(100). Their Monte Carlo simulations of parallel-to-row patterns also resembled the experimental STM observations only when nearest neighbor interactions were assumed between the adsorbates.

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One-Dimensional Pattern Formation of Adsorbed Molecules on the Ge

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