Failure of Perturbative DFT-Derived STM Images of Organic Molecules

Aug 17, 2010 - In order to maintain the integrity of the tip crystalline structure, all of the tip must be fixed at scaled ideal coordinates except fo...
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Failure of Perturbative DFT-Derived STM Images of Organic Molecules on Semiconductor Surfaces Robin L. Hayes† and Mark E. Tuckerman*,†,‡ Department of Chemistry and Courant Institute of Mathematical Sciences, New York UniVersity, New York, New York 10003 ReceiVed: March 25, 2010; ReVised Manuscript ReceiVed: June 6, 2010

Tersoff-Hamann and Bardeen perturbation theory derived empty-state STM images of the [4 + 2] intradimer adduct of 1,3-cyclohexadiene (CHD) adsorbed on Si(100)-2 × 1 using a density functional description of the electronic structure appear to capture the π* CdC orbital observed experimentally but ultimately produce images dominated by the CH2 groups. Neither averages over finite temperature structures nor use of W(110) tips with O or Si adsorbed on the apex yield the correct image. Strong tip-CHD interactions substantially lower the energy of the π* orbital relative to the Fermi energy and change the CHD geometry. In addition to perturbing the CdC bond, it is found that the tip pushes aside the CH2 groups. The former electronic effect enhances the prominence of the π* orbital, while the latter geometric effect suppresses contributions from the remainder of the CHD. Introduction Well-ordered organic/semiconductor interfaces could play an important role in molecular electronics,1-3 sensors,4-6 and hybrid materials.7 One such prototypical system used to explore interfacial bonding is 1,3-cyclohexadiene (CHD) adsorbed on the Si(100)-2 × 1 surface. Empty state STM imaging8,9 revealed at least five distinct adducts based on the π* orbital located on the remaining CdC bond. Previous work by us used Car-Parrinello molecular dynamics10 to explain the observed adduct distribution.11 As reported in ref 11, our initial attempts to reproduce the experimental STM images using standard density functional theory (DFT) informed methods, Tersoff-Hamann and Bardeen perturbation theory, yielded erroneous STM images. This paper systematically analyzes the origin of the failure. Prior to our study, Galperin and Beratan12 used a nonequilibruim Green’s function (NEGF) method on a fixed [4 + 2] intradimer adduct of 1,3-CHD adsorbed on a Si10H12 cluster to conclude that the π* on the CdC bond is imaged due to charging at finite voltages. At zero voltage, the π* orbital is far above the LUMO energy. An experimentally derived LDOS on the same system13,14 revealed a significant force between the tip and CdC bond at low biases that produced a new bonding state. Complementary DFT calculations between a small metal cluster above the CdC bond of a CHD adduct on a periodic Si surface also displayed significant tip-surface interactions. A more recent DFT study15 elaborates on the electronic effects: the π* orbital drops closer to the Fermi energy as the tip approaches. Tersoff-Hamann derived STM images have been used to identify pentacene on Si(001)-2 × 116 and Si(111)-7 × 7 surfaces17 and organic molecules on graphite,18 but an increasing number of recent studies have concluded that strong STM tip-surface interactions alter the local atomic and electronic structure on semiconducting surfaces and compromise the reliability of perturbative STM methods. Examples include * To whom correspondence should be addressed. E-mail: mark.tuckerman@ nyu.edu. † Department of Chemistry. ‡ Courant Institute of Mathematical Sciences.

the dangling bond of adatoms on the Si(111)-(7 × 7) surface19 and styrene on hydrogen passivated Si(100).20,21 Similar tip-surface effects have been seen during STM imaging of the TiO2(110) surface.22,23 Furthermore, the ability of DFT to correctly predict conduction through molecules such as substituted styrene chains on Si has been widely questioned (see references within).24,25 The goal of this study was to determine if the effects of finite temperature, tip impurities, time averaging, boundary conditions, and tip-surface interactions including full geometry optimization can improve the ability of Tersoff-Hamann and Bardeen perturbation theory to correctly predict the STM images of CHD on the Si(100)-2 × 1 surface and to delineate criteria that need to be included in future methods.

Methodology STM Theories. Density functional theory (DFT) derived scanning tunneling microscopy (STM) images have traditionally been calculated by two methods: Tersoff-Hamann26 and Bardeen perturbation theory.27 Several excellent reviews of DFTderived STM methods exist in the literature.28,29 Tersoff-Hamann, the simplest approximation, assumes that the tunneling current is proportional to the electron density above the surface:

I∝

∑ |ψν(rtip)|2δ(Eν - EF)

(1)

ν

where ψν(r) is the νth wave function of the sample with energy Eν, rtip is the location of the probe, and EF is the Fermi energy of the sample. Bardeen perturbation theory27 adds an additional level of complexity by explicitly including the contributions of the tip from a separate DFT calculation, with the current given by

10.1021/jp102692r  2010 American Chemical Society Published on Web 08/17/2010

Organic Molecules on Semiconductor Surfaces

I∝

∑ f(Eµ)[1 - f(Eν + eV)]|Mµν|2δ(Eµ - Eν)

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(2)

µ,ν

Here f(E) is the Fermi function, V is the applied voltage, Eµ and Eν are tip and sample energy levels, and Mµν is the tunneling matrix element between tip and surface states ψµ and ψν, respectively. In both cases, there is the assumption that the tip does not alter either the geometry or the electronic structure of the surface. Once the DFT-derived Kohn-Sham energies and wave functions for the tip and surface are in hand, the STM image over a range of bias and isocurrents can be calculated using the same data set. In this work, we use the STM code developed by Kova´cˆik and Marx30,31 based on the Bardeen perturbation theory implementation given by Hofer et al.28 The spatial resolution of the calculated STM images is 0.14 Å. Computational Setup. We use Kohn-Sham density functional theory (DFT)32,33 as implemented within the Quantum Espresso code34 to calculate the electronic structure. Plane waves are expanded up to 36 Ry, and exchange-correlation is treated at the LDA level.35 The Kleinman-Bylander36 pseudopotential forms are employed. During 0 K geometry optimizations, the total force on each atom is reduced to less than 1.0 × 10-3 au. The initial Si(100)-2 × 1 surface with 1,3-cyclohexadiene (CHD) adsorbed in the [4 + 2] intradimer adduct configuration is extracted from a previous 300 K NVE Car-Parrinello molecule dynamics (CPMD) simulation.11 There are five layers of Si, with the bottom Si layer fixed at the bulk lattice constant and terminated by two H on each Si. The surface area contains eight Si dimers divided equally between two rows. For isolated surface calculations, Lz ) 31.8 Å (21.8 Å vacuum). Separate DFT calculations of the tip are required for the Bardeen perturbation theory derived STM images. Six electrons are included for each W atom. The W(110) bcc tip is comprised of three pyramidal layers on two (2 × 3) bulk layers fixed at the theoretically derived lattice constant (3.12 Å) with Lz ) 26.9 Å. The three pyramidal layers and any adatom on the apex of the tip (Si or O) are allowed to fully relax. Combined tip-surface calculations fix the lateral dimensions at the bulk Si value (15.5 × 15.5 Å) and expand Lz to 34.8 Å. The expanded lateral dimensions require (3 × 5) W-bulk layers (30 atoms/ layer), resulting in a minimum bulk W strain of (0.9% × 16.8%). In order to maintain the integrity of the tip crystalline structure, all of the tip must be fixed at scaled ideal coordinates except for the z-component of the three pyramidal layers. Representative finite temperature and ideal clusters are extracted from the corresponding full surface configurations by taking the positions of the CHD and nearest 10 Si and terminating all 12 broken bonds with H. In all cases, the large unit cell allowed the gamma point approximation to be employed. Results and Discussion Failure of Tersoff-Hamann and Bardeen Perturbation Theory Generated STM Images. Teague and Boland8,9 characterized at least five types of CHD adducts on the Si(100)-2 × 1 surface by identifying unpaired Si dimers and π* orbitals on the CdC bond through empty-state STM imaging. During our CPMD study of the cycloaddition reaction of 1,3-CHD on the Si(100) surface,11 we attempted to generate a comparison of empty-state STM images using DFT-derived Tersoff-Hamann and Bardeen perturbation theory. This straightforward exercise proved to be much more challenging than initially anticipated. The [4 + 2] intradimer CHD adduct is reported here for

Figure 1. (a) Experimental empty-state STM image [Vsurf ) 1.3 V] of the [4 + 2] intradimer CHD adduct on the Si(100)-2 × 1 surface (from ref 9). The prominent dumbbell-shaped feature was attributed to the π* of the single remaining CdC double bond. Both the (b) Tersoff-Hamann and (c) Bardeen perturbation theory derived emptystate STM images [Vsurf ) 0.2 V, I ) 1.0 × 10-10 A] of the [4 + 2] intradimer CHD adduct adsorbed on the Si(100) surface, taken 3.75 ps into a 300 K Car-Parrinello molecular dynamics simulation,11 exhibit a similar dumbbell shape. Pink corresponds to peaks and blue to troughs. (d) Superimposing the molecular structure on the DFT-derived STM image reveals that the Si surface dimers (silver ball and sticks) match the experimental results but that the dumbbell shape is due to the CH2 groups, not the CdC π* orbital.

simplicity, but similar results hold for the other adducts. Figure 1 illustrates the danger of accepting appearances without questing the underlying assumptions. Figure 1a shows the characteristic experimental STM signature of the [4 + 2] CHD adduct: a dark square containing a dumbbell-like protrusion corresponding to the CdC π* orbital with a smaller contribution at the bottom due to the remainder of the CHD. Both (b) Tersoff-Hamann and (c) Bardeen perturbation theory derived STM images share striking similarities with the experimental image, but for the wrong reasons. Superimposing the Si surface dimers and CHD adduct (d) on top of the isosurface reveals that the even through the Si dimers are correctly described, the dumbbell-like protrusions correspond to the CH2 groups, not the CdC bond! A number of alternative explanations were explored. Sometimes tips are either intentionally or accidentally decorated28,37 with either surface atoms when the tip hits the surface or oxygen when the vacuum is not complete. For comparison, Figure 2 shows Bardeen perturbation theory derived STM images with a W(110) tip that has no impurities, a single Si, or an O atom on the apex. Oxygen slightly sharpens the image but does not change the fundamental character. The experimental images were taken at room temperature where the Si dimers flip and the CH2 groups and C in the CdC bond move up and down with respect to the surface. Indeed, configurations taken at 500 fs intervals do produce different STM images, but neither individual snapshots nor the average even qualitatively capture the experimental results. Comparison of STM images in Figure 3 for several surface biases and isocurrents is revealing. In all cases, blue is a depression and red a protrusion. Thin black lines go through CH2 groups (upper) or CdC groups (lower). For small isocurrents (10-9-10-10 A), all surface biases lead to protrusions only on the CH2 groups. This can be understood by analyzing the low-energy Kohn-Sham orbitals. For instance, the LUMO + 1 orbital in the upper right-hand portion of Figure 3 displays clear contributions on the CH2 groups. While a

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Figure 2. Bardeen perturbation theory derived empty-state STM images [Vsurf ) 0.2 V, I ) 1.0 × 10-10 A] using structures taken at 500 fs intervals during a 300 K CPMD simulation. Each row used a W(110) tip with either (top) no, (middle) a silicon, or (bottom) an oxygen atom adsorbed on the tip. The same color scale is used in Figure 1. The last column is the average over all sampled configurations. Although the shape in the CHD region changes, it never exhibits a nodal structure over the CdC double bond.

Figure 3. (Top) Tersoff-Hamann and (bottom) Bardeen perturbation theory derived empty-state STM images of CHD adsorbed on Si(100)-2 × 1, taken 3.75 ps into a 300 K CPMD simulation, at Vsurf ) 0.2, 0.4, 0.6, 0.8, and 1.0 V and I ) 1.0 × 10-x A; x ) 7, 8, 9, 10. Conditions used in Figures 1 and 2 are highlighted in yellow and red, respectively. The upper thin black lines go through the CH2 groups and the lower lines through the CdC atoms. The Tersoff-Hamann images are significantly more structured. The smaller isocurrent values, which correspond to tip heights of 4.7-6.0 Å where the Bardeen perturbation theory is typically valid, give rise to incorrect STM images at all sample biases. The (top) LUMO + 1 Kohn-Sham wave function of the surface confirms that CH2 groups in low-energy states have significant electron density, which ultimately gives rise to the false STM images. In contrast, the Bardeen perturbation theory-derived image at Vsurf ) 0.6 V and I ) 1.0 × 10-7 A is plausible, but the corresponding tip height is only 1.7-3.2 Å: the region where the theory no longer applies due to likely tip-surface interaction. Indeed, the LUMO + 3 Kohn-Sham wave function in a combined tip + surface DFT calculation reveals significant interaction. STM images (right blue box) from the optimized CHD + surface are qualitatively the same as the finite temperature results.

portion of the problem may lie with DFT’s inability to properly describe unoccupied orbitals 4.7-6.0 Å into the vacuum region,

the full answer is more complicated. The first orbital with π*like character is at the LUMO + 3 level (lower right-hand side

Organic Molecules on Semiconductor Surfaces

Figure 4. Lowest energy π* Kohn-Sham orbital for finite temperature (a, c) and geometry optimized (b, d) structures using either the full CHD + Si surface (a, b) or an CHD + Si10H12 cluster. The ordering of Kohn-Sham orbitals is sensitive to surface vs cluster and 0 K vs finite temperature configurations. In general, geometry optimized structures yield clearer π* orbitals, but only the 0 K cluster (d) displays textbook π* character.

of Figure 3 and Figure 4a). Furthermore, several orbitals at similar and higher biases (0.6-1.0 V) have contributions on the CH2 groups. As a consequence, the π* character is obscured under most conditions. The exception appears to be at Vsurf ) 0.6 V and I ) 1.0 × 10-7 A (yellow box in the bottom part of Figure 3), but this corresponds to a tip-CHD distance of only 1.7-3.2 Å; the region where the assumption that the tip and surface do not interact breaks down. Indeed, strong tip-surface interaction can be seen in the LUMO + 3 Kohn-Sham orbital in a combined tip + surface DFT calculation. If the surface is allowed to relax fully to a 0 K configuration (right blue box in bottom of Figure 3), the Bardeen perturbation theory STM image does sharpen slightly but does not qualitatively change. The degree to which the underlying Kohn-Sham orbitals conform to the expected orbital character and ordering depends on the system configuration. Figure 4 shows the first virtual orbital that displays significant CdC π* character for the periodic surface (a, b) and an isolated cluster taken directly from the surface (c, d) for a finite temperature configuration (a, c) and the fully optimized surface (b, d). As one might anticipate, the π* character is clearer in the fully optimized, 0 K, case. Somewhat more surprising is the lack of a textbook π* orbital in both surfaces. Over time, the asymmetry in the π* will average out as the CHD tilts from side to side. Only the 0 K Si10H12 cluster displays the expected orbital symmetry. This idealized picture of the more complicated system serves as a caveat for studies that use clusters rather than periodic surfaces to obtain STM images and other Kohn-Sham-based properties.12 The other notable feature in Figure 4 is that the π* orbital is not the LUMO, but rather occurs (a) 0.65, (b) 0.63, (c) 2.85, and (d) 2.79 eV above the Fermi energy. This behavior has been previously observed by Boland and co-workers15 and Galperin and Beratan.12 As shown above, the tip interacts with the CHD at typical STM imaging distances. As a consequence, the distance between the CdC bond and the tip decreases and the π* orbital shifts to smaller energies. For instance, when the W(110) tip is placed 3.3 Å above the midpoint of the CdC

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Figure 5. Initial vs final tip-CHD z-distance when the tip is positioned either above CH2-CH2 or CdC during a DFT geometry optimization. If there were no difference, the symbols would fall on the solid diagonal line. Once the initial distance drops below about 4.5 Å, the tip-CHD distance decreases primarily by CHD being pulled closer to the tip. The effect is greater for CdC tip positions but still present for CH2-CH2.

bond and the system is allowed to relax, the π* orbital drops to 0.05 eV above the Fermi energy consistent with previous studies.12,15 Floppy Molecules. Figure 5 shows the initial vs final tip-CHD z-distance when the W(110) tip is placed above either the atoms or the midpoint of the CdC or CH2-CH2, and the three layers of the tip, the CHD, and the top four layers of Si are allowed to relax. If there were no interactions, all the points should fall along the diagonal line. Like previous studies,13,15 the distance decreases above any point along the CdC when the initial separation is below 4.3 Å. There is a minor downward expansion of the tip (0.1 Å) (not accounted for in pervious studies), but the majority of the relaxation arises from an upward expansion of the CdC. What has not been analyzed before is the effect of the tip on the CH2 groups. When above the CH2-CH2 midpoint, the vertical separation can be reduced by at least 0.3 Å, including the 0.1 Å downward expansion of the tip. Figure 6 estimates the CHD-tip forces by plotting the (a) x, (b) y, and (c) z component of the force on the atom at the apex of the tip vs the actual tip-CHD z-distance in a single point energy DFT combined W(110) tip + surface calculation where the tip and surface positions have been optimized independently. The insets plot the same results against a universal frame that uses the vertical distance between the tip and the CdC as the reference. Six positions are considered: C1, C2, and the midpoint of C1dC2; C4, H4 (in CH2), and the midpoint of CH2-CH2. Fz in Figure 6c confirms that there is an attractive force between the tip and CHD that is stronger for CdC than CH2. The significant repulsion between the tip and CH2 group seen in Figure 6a might not be surprising, but it has profound implications that have not been reported in the literature to our knowledge. During the STM scan, the tip will push away the CH2 groups. Even if low-energy empty states remain on the CH2 groups, they will not contribute to the STM picture because they do not fulfill the spatial requirement. Figure 7 shows flexibility of the [4 + 2] intradimer CHD adduct to avoid the tip when above the CH2 groups if the system is allowed to relax. The ease with which the tip pushes aside the CH2 portion of the adduct may increase the depth and breadth of the depression around the dumbbell-shaped protrusion. This

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Figure 6. Tip-CHD z-distance vs (a) x-, (b) y-, and (c) z-force (Ry/au) when the W(110) tip is positioned either over C1 (red), C1dC2 midpoint (black), C2 (blue), H4 (green), C4 (orange), and CH2-CH2 (purple) midpoint. Each DFT calculation uses the structure from separate geometry optimized Si(100) surface + CHD and W(110) + W bulk calculations. The insets show the same data, but with the corresponding tip-CdC midpoint z-distance. In (a) there is a strong drive to push the CH2 groups away from the tip. The reduced tip-CHD z-distance in Figure 5 can be seen as a strong force in (c).

Figure 7. W(110) tip over the [4 + 2] intradimer cyclohexadiene (CHD) adduct adsorbed on the Si(100) reconstructed surface. The geometry optimized tip is initially placed 3.0 Å vertically (relative to the CdC midpoint) above the independently optimized CHD at the left C in CH2 (right, top), midpoint of CH2-CH2 bond (right, middle), and right C in CH2 (right, bottom) as marked by the red, orange, and blue dots, respectively, in the far right sketch. The purple spheres highlight which Si are at least the same height as the Si connected to the CHD. The CH2 groups move away from the tip after the z-component of the three W-tip pyramid layers and all components of the CHD and top four Si layers are fully optimized. Perturbative methods to calculate STM images based on a single snapshot of the surface + adduct might generate spurious contributions from the CH2 groups because they do not account for floppy adducts that move away from the tip during imaging. For comparison, the three snapshots are concatenated into one picture in the middle panel.

floppiness poses a particular problem for theoretical perturbative STM methods like Tersoff-Hamann and Bardeen perturbation theory that assume the adduct remains fixed. Challenges for Nonperturbative STM Image Calculations. Given the failures of perturbative methods, an interesting alternative is to employ the NEGF formalism38-40 to compute STM images. NEGF methods, which include tip-surface interactions in the calculated I-V curve, can circumvent the problems with perturbative methods encountered above. They do so, however, at a substantial increase in computational

overhead, particularly for empty-state imaging. In a NEGF calculation, the current is computed according to

I)

e πp

∫-∞∞ Tr[G†(E)Γ2(E)G(E)Γ1(E)][f1(E) - f2(E)] dE (3)

where G ) [E - H0 + eV - Σ(E)]-1 is the Green’s function at energy E; the Hamiltonian H0 includes the molecule, the STM

Organic Molecules on Semiconductor Surfaces tip, and the surface region near the molecule treated atomistically. f1(E) and f2(E) are the Fermi functions of the tip and surface, respectively, and Γ1(E) and Γ2(E) are related to the imaginary part of the self-energy operators (Σ(E)) of the tip and surface, respectively. The latter treat the coupling of the atoms included explicitly in H0 to the extended external environment. Since the tip perturbs both the wave function and geometry as a function of the relative tip-surface position, separate NEGF calculations must be done at each point instead of treating the tip and surface separately once and for all. If each NEGF calculation was inexpensive, then generating a 3D map in order to extract a fixed height or isocurrent image would be tedious but not prohibitive. In practice, each individual calculation is costly using standard methods. For illustrative purposes, consider the requirements for this system using the WanT code.39,41 This particular implementation is based on periodic plane wave DFT where Kohn-Sham orbitals are first localized using maximally localized Wannier orbitals so that the required Landuer interaction matrices can be calculated. Implicit in this methodology are two assumptions: the inclusion of enough tip and surface layers in the combined system to approach bulk behavior in the definition of H0 and the ability to map specific localized orbitals in the combined unit cell to equivalent orbitals in separate bulk calculations. Implementations that employ a localized basis trivially meet the second requirement but often require extra basis functions to describe the near surface region.20,37 Since the definition of H0 requires that the tip and surface both be contained in the same simulation cell, either the tip or surface must be strained. The Kohn-Sham energies of the W(110) metallic tip should be less sensitive to strain than those of the semiconductor Si(100) surface, suggesting that the Si surface lattice constant should determine the box size. The smallest Si surface + W(110) tip unit cell with strains less than 13% contains four surface dimers (2 dimers/ row) and 20 W atoms/bulk W layer for a lateral tip strain of -12.4% by -0.9%. K-points would be required due to the small lateral dimensions of the cell. Assuming that five layers of bulk Si (40 atoms) with the bottom layer terminated by H (16 atoms), four layers of bulk W (80 atoms) + two pyramid tip layers (5 atoms), and the CHD (14 atoms) is sufficient, the combined system would have 155 atoms and 359 occupied orbitals. In reality, more bulk Si and W layers may be necessary. The requirement of empty-state STM imaging translates to similar empty-state orbitals on all the bulk Si and at least the π* orbital on the CHD. Calculations reveal that required orbitals can occur up to 5.7 eV above the Fermi energy, at which point many superfluous lower energy W bulk orbitals have appeared. Once even more virtual orbitals have been included to ensure that those of interest are well converged, the total number of virtual orbitals can exceed 170, bringing the total number of orbitals to over 529 for this system. Comparison with the literature reveals this configuration is a factor of 3 larger than previous endeavors using a plane-wave basis.42 While tractable, we have not implemented this due to the high computational cost. We expect that calculation of high-resolution empty-state images for large periodic systems will, however, become routine as computational resources continue to improve. Conclusions DFT-derived Tersoff-Hamann and Bardeen perturation theory empty-state STM images of CHD adducts adsorbed on the Si(100) surface fail to capture the correct physics. Interaction between tip and surface, both of the electronic structure and the geometry, renders these perturbative methods invalid.

J. Phys. Chem. C, Vol. 114, No. 35, 2010 15107 Averaging finite temperature configurations, altering the atom at the apex of the tip, employing 0 K configurations, or extracting idealized clusters all give qualitatively similar results where the CH2 groups, not the π*, appear at low bias and isocurrents. Consistent with previous studies, this behavior can be traced to omission of tip-CHD interactions which lowers the Kohn-Sham energy of the π* orbital and decreases the tip-CdC distance by as much at 0.5 Å. Uncertainty in DFT high-energy unoccupied orbitals at distances several angstroms above the surface further reduces confidence in the DFT-derived images. Previous studies did not account for the floppy nature of the CH2 groups on the CHD adduct when the tip is present. Even if low-energy Kohn-Sham orbitals retain contributions on CH2 groups, they would not contribute to the STM image if the tip was present because the tip pushes them out of the way. This is the likely origin of the large square void surround the [4 + 2] intradimer adduct. Floppy CH2 groups are also consistent with the region of minimal vertical tip-sample interaction force in the CH2 region of the [2 + 2] intradimer CHD adduct experimentally measured (see Figure 2 in ref 13) by Naydenov et al.13 Given the strong tip-CHD interaction in this case, any perturbative STM method will likely fail for conjugated molecules on Si or related semiconductor surfaces. The straightforward application of NEGF methods should capture the correct physics and enable the construction of a valid first-principles empty-state STM image, but the actual implementation is highly nontrivial for larger systems. A new methodology and/or better computational resources will likely be required to treat these systems routinely. Acknowledgment. The authors acknowledge support from NSF CHE-0704036 and the Alexander von Humboldt Foundation. R.L.H. thanks Roman Kova´cˆik and Dominik Marx for stimulating discussions and use of their STM code. References and Notes (1) Heath, J. R. Annu. ReV. Mater. Res. 2009, 39, 1–23. (2) Tao, N. J. Nature Nanotechnol. 2006, 1, 173–181. (3) He, J.; Chen, B.; Flatt, A. K.; Stephenson, J. J.; Condell, D. D.; Tour, J. M. Nature Mater. 2006, 5, 63–68. (4) Faber, E. J.; Sparreboom, W.; Groeneveld, W.; de Smet, L. C. P. M.; Bomer, J.; Olthuis, W.; Zuilhof, H.; Sudholter, E. J. R.; Bergveld, P.; van den Berg, A. ChemPhysChem 2007, 8, 101–112. (5) Cattaruzza, F.; Cricenti, A.; Flamini, A.; Girasole, M.; Longo, G.; Prosperi, T.; Andreano, G.; Cellai, L.; Chirivino, E. Nucleic Acids Res. 2006, 34, e32. (6) Wei, F.; Qu, P.; Zhai, L.; Chen, C.; Wang, H.; Zhao, X. S. Langmuir 2006, 22, 6280–6285. (7) Hamers, R. J. Annu. ReV. Anal. Chem. 2008, 1, 707–736. (8) Teague, L. C.; Boland, J. J. Thin Solid Films 2004, 464-465, 1–4. (9) Teague, L. C.; Boland, J. J. J. Phys. Chem. B 2003, 107, 3820– 3823. (10) Car, R.; Parrinello, M. Phys. ReV. Lett. 1985, 55, 2471–2474. (11) Hayes, R. L.; Tuckerman, M. E. J. Am. Chem. Soc. 2007, 129, 12172–12180. (12) Galperin, M.; Beratan, D. N. J. Phys. Chem. B 2005, 109, 1473– 1480. (13) Naydenov, B.; Teague, L. C.; Ryan, P. M.; Boland, J. J. Nano Lett. 2006, 6, 1752–1756. (14) Naydenov, B.; Ryan, P.; Teague, L. C.; Boland, J. J. Phys. ReV. Lett. 2006, 97, 098304. (15) Ryan, P. M.; Teague, L. C.; Naydenov, B.; Borland, D.; Boland, J. J. Phys. ReV. Lett. 2008, 101, 096801. (16) Suzuki, T.; Sorescu, D. C.; Yates, J. T., Jr. Surf. Sci. 2006, 600, 5092–5103. (17) Yong, K. S.; Zhang, Y. P.; Yang, S. W.; Wu, P.; Xu, G. Q. J. Phys. Chem. C 2007, 111, 4285–4293. (18) Ku¨nzel, D.; Markert, T.; Gross, A.; Benoit, D. M. Phys. Chem. Chem. Phys. 2009, 11, 8867–8878. (19) Jelı´nek, P.; Sˆvec, M.; Pou, P.; Perez, R.; Cha´b, V. Phys. ReV. Lett. 2008, 101, 176101.

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