Adsorption-Induced Surface Stresses in ... - Semantic Scholar
PRL 101, 185504 (2008)
PHYSICAL REVIEW LETTERS
week ending 31 OCTOBER 2008
Adsorption-Induced Surface Stresses in Alkanethiolate-Au Self-Assembled Monolayers Varadharajan Srinivasan,1 Giancarlo Cicero,2 and Jeffrey C. Grossman1 1
2
Berkeley Nanoscience and Nanoengineering Institute, University of California, Berkeley, California 94720, USA Materials Science and Chemical Engineering Department, Politecnico of Torino, C.so Duca degli abruzzi 24, 10129, Torino, Italy (Received 30 May 2008; published 31 October 2008) First-principles calculations were employed to elucidate the origin of adsorption-induced surface stresses in alkanethiolate self-assembled monolayers on an Au(111) surface. Our results suggest a mechanism that accounts for the huge relief of the tensile stress compared to the bare surface in terms of a local rearrangement of surface Au atoms accompanying charge removal from the surface towards the Au-S bond. A purely interadsorbate interaction model is shown to be inconsistent with the anisotropy and the magnitude of the calculated stress. DOI: 10.1103/PhysRevLett.101.185504
PACS numbers: 62.23.St, 07.07.Df, 82.47.Rs, 87.85.fk
Self-assembled monolayers (SAMs) of organic molecules on metal surfaces have shown great promise in the development of nanoscale electronic and mechanical devices. Consequently, these systems have received much attention from experiments and theory alike. In particular, the physics and chemistry of alkanethiolate (AT) SAMs on Au have been extensively investigated [1–7]. Their adsorption is known to lead to changes in the surface stress of the metal substrate which can be transduced into either mechanical motion as in a cantilever or capacitance changes of a membrane. The binding of target species ranging from small molecules such as trinitrotoluene [8,9] to large fragments of DNA [10] to the ends of AT SAMs leads to a further change in stress which can be detected in the same way. This property has been shown to be very useful for sensing applications where one uses functionalized AT SAMs on Au as a receptor coating layer to sense a desired target. By varying the chemistry of the target-receptor (T-R) interaction it is possible, in principle, to achieve high selectivities and sensitivities of 1 in 1012 [8]. Systematic tuning of the performance of nanomechanical sensors based on surface stress changes requires complete knowledge of the physical mechanisms governing both the AT adsorption and T-R binding induced stress responses. The surface stress change following SAM formation is in itself a quantity of fundamental interest since it can strongly influence the structure and energetics of interfaces relevant to nanoscale device applications and has been the subject of much experimental [11] and recent theoretical effort [12–14]. However, the origin of adsorption-induced stress, particularly in the AT SAMs, is unknown. The key mechanisms operative have not been elucidated and it remains unclear whether the weak effects arising from interadsorbate interactions can alone account pffiffiffi for the large stress responses. For instance, the 22 3 reconstruction of bare Au(111) and the lifting of the same in the AT covered surface are both thought to be driven by stress relief [15]. However, while the effect has been studied well for the bare surface, the mechanism in the AT covered surface is yet to be completely understood. 0031-9007=08=101(18)=185504(4)
We present in this Letter a first-principles densityfunctional theory (DFT) analysis of the origin of surface stresses in both the bare and alkanethiolate coated Au surface. We first consider the bare unreconstructed Au (111) surface and confirm the existence of a tensile stress which originates from a charge redistribution into the bonds between surface atoms. We then compute the surface stresses on short chain AT SAMs on Au(111) and find a large anisotropic reduction of the stress. We argue that current models of adsorption-induced stress are unable to describe either the magnitude or the anisotropy we observe in our DFT results. Instead, our analysis of the charge distribution and structure of this surface brings to light a simple local stress relief (LSR) model that takes into account a stress-relieving distortion of surface Au atoms promoted by localized charge removal by the Au-S bonds, and can explain consistently both the calculated anisotropy and the large stress relief. The mechanism we propose provides a new handle on the design of surface stress-based nanomechanical sensors that could have an important impact on the sensitivity of these devices. We employed a plane wave DFT framework using the QUANTUM-ESPRESSO package [16]. Core electrons were modeled by ultrasoft pseudopotentials [17]. Semicore d electrons of gold were included explicitly in the calculation as they are crucial for an accurate description of the surfaces considered. Total energies were calculated using a generalized-gradient approximation to the exchangecorrelation functional according to the Perdew-BurkeErnzerhoff [18] scheme and with a plane wave kinetic energy cutoff of 25 Ry. Surfaces were represented by a ˚ vacuum separating 10 atomic layer slab with at least 12 A the two slab surfaces, ensuring a stress convergence of 0:05 N=m. Our calculations on both pffiffiffi thepffiffiffibare and AT coated surfaces were performed in a 3 3R30 surface supercell, which is commensurate with the experimentally observed periodicity for AT SAMs on Au [3,4]. The Brillouin zone of the slabs was discretized by dense meshes of 10 10 1 k points. All slabs were relaxed fully until the forces on each atom were less than 3 meV=A.
185504-1
Ó 2008 The American Physical Society
PRL 101, 185504 (2008)
PHYSICAL REVIEW LETTERS
The stress tensor in every case was obtained using the Nielson-Martin stress theorem [19] which represents the stress as a functional of the ground-state density. This approach directly yields the stress along with the energy at the end of standard DFT ground-state calculation. The surface stress for a fully relaxed surface was obtained as [20,21] ij ¼ 12 ij Lz , where and are, respectively, the surface and the supercell stress tensors and Lz is the length of the supercell along the surface normal. The factor of 1=2 accounts for the two equivalent surfaces in all our slab calculations. As our reference system, we first computed the surface stress for the bare Au(111) surface and obtained an isotropic tensile stress of 2:88 N=m. The origin of the tensile stress on bare Au(111) has been discussed previously [12– 14], and our analysis confirms the prevalent picture. As shown in Fig. 1, we find that the electronic charge in the surface layer is redistributed in between the Au-Au bonds leading to an increased pffiffiffi pffiffiffiattraction between the bonded Au atoms. For the 3 3 surface used in the calculations, the surface Au-Au distances are more than the equilibrium distance dictated by the charge redistribution, leading to a large tensile stress on this surface. We confirm this picture by a Lo¨wdin population analysis which gave a reduced contribution to the charge density from surface Au sp orbitals relative to those in the bulk and a slightly increased contribution from surface d orbitals. This charge redistribution between the sp and d orbitals has been correlated to the tensile stress in the case of d-block metals [13], in good agreement with our results. The above rationalization of the tensile stress allows us to anticipate the effect of adsorbates on the surface stress in terms of further charge redistribution promoted by chemical bonding with the adsorbate. Electron donating adsorbates are expected to lead to tensile stresses whereas
FIG. 1 (color online). Electron density differences between the surface and bulk layers of bare Au(111) projected on the h111i surface. Filled black circles represent the Au atoms and the boundaries of the 1 1 surface unit cell are indicated with dashed lines. Note that the density increases in the Au-Au bonds along ½211 and ½110 leading to the calculated tensile stress.
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electron acceptors would lead to compressive stresses [14]. STM-coupled electrochemical measurements of the charge response of the Au(111) surface also yield compressive stresses that increase linearly with the positive charge density of the surface [22,23]. These observations point to a charging-induced surface stress model [14] whereby one can even lift the reconstruction of the Au (111) surface with adequate charging [15]. Interadsorbate interactions could also contribute to the observed surface stress changes and, in fact, were used to account for compressive stresses seen in AT adsorption on Au [24]. However, our DFT results presented below indicate a large anisotropic tensile stress relief upon AT-SAM formation. We demonstrate that neither the charging model nor interadsorbate interactions can satisfactorily capture all the aspects of the ab initio results. The actual response is due to an interplay between the charge redistribution and structural rearrangements on the surface. Alkanethiolate-adsorbed Au surfaces were optimized starting from an adsorption site close to the fcc hollow and allowing all atoms to fully relax. The resulting energetic and structural parameters are in good agreement with previous work [25]. The optimized structure for methanethiolate on Au, shown in Fig. 2, has the sulfur atom located in the region between the bridge and the fcc site and above ˚ away from the twofold bridge the surface (about 0.30 A site). The S-C bond is tilted by an angle of 54 away from the surface normal over the bridge site towards the hcp site. Table I summarizes our calculated adsorption-induced changes on the stress. Unlike the bare surface the stress tensor is now anisotropic with a tensile (positive) stress (v1 ) and compressive (negative) stress along along ½011 ½211 (v2 ). These directions are equivalent to the ones marked in Fig. 1. Our results also indicate that the magnitudes of these stresses are much smaller than that of the bare surface, indicating a large tensile stress relief. Similar features are also observed in the stress for ethanethiolate on Au (Table I). A decrease in tensile stress would lead to the deflection of a cantilever away from the receptor layer based on this adsorption system as is observed in experiments [24]. Hence, our results are in good agreement with the experimental trend. However, the adsorption response has been suggested to be due to dipolar repulsion between the molecular dipoles. The magnitude of stresses due to such repulsive interactions can be shown to be at least an order of magnitude smaller than those calculated here. It can also be shown that the anisotropy obtained from such a molecular dipole model is entirely inconsistent with that predicted by our DFT results. If we imagine the adsorbate layer as a 2-dimensional hexagonal lattice of point dipoles, then the strength of the interaction, restricted only to nearest neighbors, is given by
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EðÞ ¼
2 ½1 3sin2 cos2 ð Þ; 40 R3
(1)
PRL 101, 185504 (2008)
week ending 31 OCTOBER 2008
PHYSICAL REVIEW LETTERS
FIG. 2 (color online). (a) Structure of methylthiolate adsorbed on Au(111) (top view). The different kinds of Au atoms on this surface are shown by the letters T, B, F, and H for on-top, bridge, fcc, and hcp hollows, respectively. Arrows indicate the principal axes direction parallel to a line of bridge atoms while v2 is along the tilt of the anisotropic surface stress tensor. v1 is along the ½011 direction ½211 of the molecules. (b) Side view of the same system indicating isosurfaces of the charge-density difference upon adsorption. Charge is removed from the bond between the bridge Au atoms. Arrows indicate the displacements of the bridge Au atoms. (c) Stress anisotropy from a hexagonal lattice of tilted point dipoles. The signs in the circles in the top panel indicate attraction () or repulsion (+). The sign of the corresponding stress is opposite. The magnitude of the energy (force) is plotted as a function of the location of the neighbor in units where , R, and 40 are 1. (d) Electron density difference arising in the h111i surface plane upon methanethiolate adsorption. Depletion occurs between bridge atoms where the thiol binds. Black circles indicate the location of the Au atoms in the surface unit cell (dashed lines).
where and are, respectively, the polar and azimuthal angles of the molecular dipole moment vector and is the angle describing the distance vector between the nearest neighbor dipoles in the lattice plane. For dipoles normal to the surface one expects isotropic repulsion and hence compressive stresses. However, the AT molecules on Au (111) are found to be tilted at an angle of ¼ 54 to the surface normal. The sign of the nearest neighbor interaction energy and the corresponding force as a function of the location of the neighbor () is depicted in Fig. 2(c). It is clearly seen that the interaction is anisotropic and it is unreasonable to expect uniform compressive stresses. However, according to this model, the stress along v1 must be compressive and that along v2 tensile, inconsistent with the values in Table I. Hence, the molecular dipoles cannot be the sole contributors to the observed stress. The charging-induced stress models also cannot account for this anisotropy as a uniform charging of metal surfaces would preserve the symmetry of the bare neutral surface. Moreover, the maximum change induced in the stress in such a case is 0:3–0:4 N=m in the compressive direction, as seen in experiments [23] and predicted by DFT [28], for surface charge densities similar to those induced upon ATSAM formation. This strongly suggests that there is an entirely different mechanism at play. In order to probe the cause of the large stress reduction we performed a charge-density analysis similar to that for the bare Au surface discussed earlier. Our results [Figs. 2(b) and 2(c)] indicate a removal of electronic charge from the Au surface and the S atom towards an Au-S bond. This removal of charge from the metal surface is, in fact, localized between the two bridge Au atoms bonded to the S as depicted in the contour plot in Fig. 2(d).
Concomitantly, the spacing between bridge Au atoms ˚ ) compared to the or v1 increases (by 0.17 A along ½011 bulk value causing the two bonds to an on-top site in the [29]. same row to shrink (by 0:05 A) Based on the observation above we propose a local stress relief mechanism to be operative: bare Au(111), as discussed earlier, has a tensile stress because of charge buildup between Au atoms as compared to bulk. The adsorption of the thiol molecule near every fourth bridge site along v1 results in a depletion of this charge from the bond between Au atoms constituting the bridge. The repulsion resulting from this charge depletion causes the bridge Au atoms (bonded to the S) to move apart, thereby also shrinking the bond to the adjacent (on-top) atom on either side of the bridge. This relaxation pattern, indicated by the short arrows in Fig. 2(b) for a row of atoms belonging to the surface, allows for the large relief in tensile stress not possible on the bare surface. A localized removal of charge is crucial for this mechanism to hold and is possible on a metal surface only via adsorption of molecules at specific sites. Merely charging the Au surface would lead to a uniform removal of charge and hence a uniform expansion of the surface [28] preservpffiffiffi pffiffiffi TABLE I. Adsorption-induced stress changes at the 3 3 Au(111) surface. 1 and 2 (Nm1 ) are principal stresses in directions 30 and 60 of the x axis, respectively (see Fig. 2).
Bare Au CH3 S-Au CH3 CH2 S-Au
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Eads (eV)
1
2
1
2
1.73 1.73
2.88 0.86 0.95
2.88 0:07 0.00
2:02 1:93
2:95 2:88
PRL 101, 185504 (2008)
PHYSICAL REVIEW LETTERS
ing the hexagonal symmetry. Since the on-top site does not move much relative to its position on the bare surface, the stress along v2 originates simply from the repulsion that persists along that direction following the charge induced on the surface. As a result the stress in this direction is compressive and results from a different mechanism. An alternative but equivalent point of view is that the induced charge produces compressive stresses in both directions but is relieved along v1 by the LSR mechanism. In either point of view, the overlayer structure formed upon adsorption dictates the anisotropic stress relief. The proposed mechanism has fundamental as well as practical implications. The stress-charge response of (111)-textured Au electrodes under specific adsorption conditions has been recently measured [30] by in situ dilatometry experiments. The experiments indicate a lowering of the response coefficient (=q) compared to direct metal-electrolyte interfaces. A similar effect is anticipated upon alkanethiolate adsorption as well. This could be explained using the second point of view presented above. Unlike the bare surface, any charge removed from the thiolated surface would originate from the bridge sites where the molecules are bound. Hence, the compressive stress, that would otherwise be induced by charging, is relieved along one of the directions by LSR rearrangements bringing down the average response [31]. This illustrates the power of the LSR mechanism and may provide a new handle on sensor design. AT molecules are needed in the preparation of receptor layers and when appropriately functionalized they can bind to targets with high specificity. Our results suggest that it would then be extremely beneficial to design organic thiols where target binding can be conveyed as a charge response down to the Au-S bond instead of relying on weak interchain interactions as is currently done. This would constitute a design challenge but would not be beyond the reach of present-day synthetic chemistry techniques. The resulting high sensitivities could enable detection even in the presence of competing environmental factors such as humidity, rendering nanomechanical sensing a more practical technology. We are grateful to E. Schwegler for helpful discussions. This work was supported by the LDRD program of Lawrence Livermore National Laboratory, and under the auspices of the National Science Foundation, by U.C. Berkeley under Grant No. 0425914. G. C. acknowledges partial support by MIUR through FIRB LATEMAR.
[1] F. Schreiber, Prog. Surf. Sci. 65, 151 (2000). [2] M. H. Dishner, J. C. Hemminger, and F. J. Feher, Langmuir 13, 2318 (1997). [3] H. Kondoh and H. Nozoye, J. Phys. Chem. B 103, 2585 (1999). [4] V. De Renzi, R. Di Felice, D. Marchetto, R. Biagi, U. del Pennino, and A. Selloni, J. Phys. Chem. B 108, 16 (2004). [5] P. Maksymovych, D. C. Sorescu, and J. T. Yates, Jr., J. Phys. Chem. B 110, 21 161 (2006).
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[6] M. C. Vargas, P. Gianozzi, A. Selloni, and G. Scoles, J. Phys. Chem. B 105, 9509 (2001). [7] R. Mazzarello, A. Cossaro, A. Verdini, R. Rousseau, L. Casalis, M. F. Danisman, L. Floreano, S. Scandolo, A. Morgante, and G. Scoles, Phys. Rev. Lett. 98, 016102 (2007). [8] L. A. Pinnaduwage, V. Bioadjiev, J. E. Hawk, and T. Thundat, Appl. Phys. Lett. 83, 1471 (2003). [9] S. Satyanarayana, D. T. McCormick, and A. Majumdar, Sens. Actuators B Chem. 115, 494 (2006). [10] J. Fritz, M. K. Baller, H. P. Lang, H. Rothuizen, P. Vettiger, E. Meyer, H.-J. Gu¨ntherodt, C. Gerber, and J. K. Gimzewski, Science 288, 316 (2000). [11] W. Haiss, Rep. Prog. Phys. 64, 591 (2001). [12] V. Fiorentini, M. Methfessel, and M. Scheffler, Phys. Rev. Lett. 71, 1051 (1993). [13] J. Kolla´r, L. Vitos, J. M. Osorio-Guille´n, and R. Ahuja, Phys. Rev. B 68, 245417 (2003). [14] H. Ibach, J. Vac. Sci. Technol. A 12, 2240 (1994). [15] C. E. Bach, M. Giesen, H. Ibach, and T. L. Einstein, Phys. Rev. Lett. 78, 4225 (1997). [16] http://www.q-espresso.org. [17] D. Vanderbilt, Phys. Rev. B 41, 7892 (1990). [18] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). [19] O. H. Nielsen and R. M. Martin, Phys. Rev. B 32, 3792 (1985). [20] R. J. Needs, Phys. Rev. Lett. 58, 53 (1987). [21] Vanderbilt, Phys. Rev. Lett. 59, 1456 (1987). [22] R. J. Nichols, T. Nouar, C. A. Lucas, W. Haiss, and W. A. Hofer, Surf. Sci. 513, 263 (2002). [23] W. Haiss, R. Nichols, J. Sass, and K. Charle, J. Electroanal. Chem. 452, 199 (1998). [24] R. Berger, E. Delamarche, H. P. Lang, C. Gerber, J. K. Gimzewski, E. Meyer, and H.-J. Gu¨ntherodt, Science 276, 2021 (1997). [25] We find an adsorption energy of 40 kcal=mol and an Au-S ˚ . See Refs. [5,26,27] for bond length of about 2.5 A comparison with theory and experiment, respectively. We also confirmed the lower binding energies at the other high-symmetry sites predicted, for instance, in Ref. [26]. [26] Y. Yourdshahyan and A. M. Rappe, J. Chem. Phys. 117, 825 (2002). [27] F. P. Cometto, P. Paredes-Olivera, V. A. Macagno, and E. M. Patrito, J. Phys. Chem. B 109, 21 737 (2005). [28] Y. Umeno, C. Elsa¨sser, B. Meyer, P. Gumsch, M. Nothacker, J. Weissmu¨ller, and F. Evers, Europhys. Lett. 78, 13 001 (2007). [29] Note that the total change in the bond lengths across 4 atoms along this row is not zero but positive. This is due to an out-of-plane buckling of the bridge atoms [6] enabling them to expand laterally even further than allowed by the lattice periodicity. [30] M. Smetanin, R. N. Viswanath, D. Kramer, D. Beckmann, T. Koch, L. A. Kibler, D. M. Kolb, and J. Weissmu¨ller, Langmuir 24, 8561 (2008). [31] Our calculation (not shown here) indicates that it is, indeed, energetically easier (by 3 meV=surface atom for q ¼ 72 C=cm2 ) to charge the 10 layer Au slab considered here if the adsorption geometry is used instead of the bare unreconstructed Au(111) surface.
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PHYSICAL REVIEW LETTERS
week ending 31 OCTOBER 2008
Adsorption-Induced Surface Stresses in Alkanethiolate-Au Self-Assembled Monolayers Varadharajan Srinivasan,1 Giancarlo Cicero,2 and Jeffrey C. Grossman1 1
2
Berkeley Nanoscience and Nanoengineering Institute, University of California, Berkeley, California 94720, USA Materials Science and Chemical Engineering Department, Politecnico of Torino, C.so Duca degli abruzzi 24, 10129, Torino, Italy (Received 30 May 2008; published 31 October 2008) First-principles calculations were employed to elucidate the origin of adsorption-induced surface stresses in alkanethiolate self-assembled monolayers on an Au(111) surface. Our results suggest a mechanism that accounts for the huge relief of the tensile stress compared to the bare surface in terms of a local rearrangement of surface Au atoms accompanying charge removal from the surface towards the Au-S bond. A purely interadsorbate interaction model is shown to be inconsistent with the anisotropy and the magnitude of the calculated stress. DOI: 10.1103/PhysRevLett.101.185504
PACS numbers: 62.23.St, 07.07.Df, 82.47.Rs, 87.85.fk
Self-assembled monolayers (SAMs) of organic molecules on metal surfaces have shown great promise in the development of nanoscale electronic and mechanical devices. Consequently, these systems have received much attention from experiments and theory alike. In particular, the physics and chemistry of alkanethiolate (AT) SAMs on Au have been extensively investigated [1–7]. Their adsorption is known to lead to changes in the surface stress of the metal substrate which can be transduced into either mechanical motion as in a cantilever or capacitance changes of a membrane. The binding of target species ranging from small molecules such as trinitrotoluene [8,9] to large fragments of DNA [10] to the ends of AT SAMs leads to a further change in stress which can be detected in the same way. This property has been shown to be very useful for sensing applications where one uses functionalized AT SAMs on Au as a receptor coating layer to sense a desired target. By varying the chemistry of the target-receptor (T-R) interaction it is possible, in principle, to achieve high selectivities and sensitivities of 1 in 1012 [8]. Systematic tuning of the performance of nanomechanical sensors based on surface stress changes requires complete knowledge of the physical mechanisms governing both the AT adsorption and T-R binding induced stress responses. The surface stress change following SAM formation is in itself a quantity of fundamental interest since it can strongly influence the structure and energetics of interfaces relevant to nanoscale device applications and has been the subject of much experimental [11] and recent theoretical effort [12–14]. However, the origin of adsorption-induced stress, particularly in the AT SAMs, is unknown. The key mechanisms operative have not been elucidated and it remains unclear whether the weak effects arising from interadsorbate interactions can alone account pffiffiffi for the large stress responses. For instance, the 22 3 reconstruction of bare Au(111) and the lifting of the same in the AT covered surface are both thought to be driven by stress relief [15]. However, while the effect has been studied well for the bare surface, the mechanism in the AT covered surface is yet to be completely understood. 0031-9007=08=101(18)=185504(4)
We present in this Letter a first-principles densityfunctional theory (DFT) analysis of the origin of surface stresses in both the bare and alkanethiolate coated Au surface. We first consider the bare unreconstructed Au (111) surface and confirm the existence of a tensile stress which originates from a charge redistribution into the bonds between surface atoms. We then compute the surface stresses on short chain AT SAMs on Au(111) and find a large anisotropic reduction of the stress. We argue that current models of adsorption-induced stress are unable to describe either the magnitude or the anisotropy we observe in our DFT results. Instead, our analysis of the charge distribution and structure of this surface brings to light a simple local stress relief (LSR) model that takes into account a stress-relieving distortion of surface Au atoms promoted by localized charge removal by the Au-S bonds, and can explain consistently both the calculated anisotropy and the large stress relief. The mechanism we propose provides a new handle on the design of surface stress-based nanomechanical sensors that could have an important impact on the sensitivity of these devices. We employed a plane wave DFT framework using the QUANTUM-ESPRESSO package [16]. Core electrons were modeled by ultrasoft pseudopotentials [17]. Semicore d electrons of gold were included explicitly in the calculation as they are crucial for an accurate description of the surfaces considered. Total energies were calculated using a generalized-gradient approximation to the exchangecorrelation functional according to the Perdew-BurkeErnzerhoff [18] scheme and with a plane wave kinetic energy cutoff of 25 Ry. Surfaces were represented by a ˚ vacuum separating 10 atomic layer slab with at least 12 A the two slab surfaces, ensuring a stress convergence of 0:05 N=m. Our calculations on both pffiffiffi thepffiffiffibare and AT coated surfaces were performed in a 3 3R30 surface supercell, which is commensurate with the experimentally observed periodicity for AT SAMs on Au [3,4]. The Brillouin zone of the slabs was discretized by dense meshes of 10 10 1 k points. All slabs were relaxed fully until the forces on each atom were less than 3 meV=A.
185504-1
Ó 2008 The American Physical Society
PRL 101, 185504 (2008)
PHYSICAL REVIEW LETTERS
The stress tensor in every case was obtained using the Nielson-Martin stress theorem [19] which represents the stress as a functional of the ground-state density. This approach directly yields the stress along with the energy at the end of standard DFT ground-state calculation. The surface stress for a fully relaxed surface was obtained as [20,21] ij ¼ 12 ij Lz , where and are, respectively, the surface and the supercell stress tensors and Lz is the length of the supercell along the surface normal. The factor of 1=2 accounts for the two equivalent surfaces in all our slab calculations. As our reference system, we first computed the surface stress for the bare Au(111) surface and obtained an isotropic tensile stress of 2:88 N=m. The origin of the tensile stress on bare Au(111) has been discussed previously [12– 14], and our analysis confirms the prevalent picture. As shown in Fig. 1, we find that the electronic charge in the surface layer is redistributed in between the Au-Au bonds leading to an increased pffiffiffi pffiffiffiattraction between the bonded Au atoms. For the 3 3 surface used in the calculations, the surface Au-Au distances are more than the equilibrium distance dictated by the charge redistribution, leading to a large tensile stress on this surface. We confirm this picture by a Lo¨wdin population analysis which gave a reduced contribution to the charge density from surface Au sp orbitals relative to those in the bulk and a slightly increased contribution from surface d orbitals. This charge redistribution between the sp and d orbitals has been correlated to the tensile stress in the case of d-block metals [13], in good agreement with our results. The above rationalization of the tensile stress allows us to anticipate the effect of adsorbates on the surface stress in terms of further charge redistribution promoted by chemical bonding with the adsorbate. Electron donating adsorbates are expected to lead to tensile stresses whereas
FIG. 1 (color online). Electron density differences between the surface and bulk layers of bare Au(111) projected on the h111i surface. Filled black circles represent the Au atoms and the boundaries of the 1 1 surface unit cell are indicated with dashed lines. Note that the density increases in the Au-Au bonds along ½211 and ½110 leading to the calculated tensile stress.
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electron acceptors would lead to compressive stresses [14]. STM-coupled electrochemical measurements of the charge response of the Au(111) surface also yield compressive stresses that increase linearly with the positive charge density of the surface [22,23]. These observations point to a charging-induced surface stress model [14] whereby one can even lift the reconstruction of the Au (111) surface with adequate charging [15]. Interadsorbate interactions could also contribute to the observed surface stress changes and, in fact, were used to account for compressive stresses seen in AT adsorption on Au [24]. However, our DFT results presented below indicate a large anisotropic tensile stress relief upon AT-SAM formation. We demonstrate that neither the charging model nor interadsorbate interactions can satisfactorily capture all the aspects of the ab initio results. The actual response is due to an interplay between the charge redistribution and structural rearrangements on the surface. Alkanethiolate-adsorbed Au surfaces were optimized starting from an adsorption site close to the fcc hollow and allowing all atoms to fully relax. The resulting energetic and structural parameters are in good agreement with previous work [25]. The optimized structure for methanethiolate on Au, shown in Fig. 2, has the sulfur atom located in the region between the bridge and the fcc site and above ˚ away from the twofold bridge the surface (about 0.30 A site). The S-C bond is tilted by an angle of 54 away from the surface normal over the bridge site towards the hcp site. Table I summarizes our calculated adsorption-induced changes on the stress. Unlike the bare surface the stress tensor is now anisotropic with a tensile (positive) stress (v1 ) and compressive (negative) stress along along ½011 ½211 (v2 ). These directions are equivalent to the ones marked in Fig. 1. Our results also indicate that the magnitudes of these stresses are much smaller than that of the bare surface, indicating a large tensile stress relief. Similar features are also observed in the stress for ethanethiolate on Au (Table I). A decrease in tensile stress would lead to the deflection of a cantilever away from the receptor layer based on this adsorption system as is observed in experiments [24]. Hence, our results are in good agreement with the experimental trend. However, the adsorption response has been suggested to be due to dipolar repulsion between the molecular dipoles. The magnitude of stresses due to such repulsive interactions can be shown to be at least an order of magnitude smaller than those calculated here. It can also be shown that the anisotropy obtained from such a molecular dipole model is entirely inconsistent with that predicted by our DFT results. If we imagine the adsorbate layer as a 2-dimensional hexagonal lattice of point dipoles, then the strength of the interaction, restricted only to nearest neighbors, is given by
185504-2
EðÞ ¼
2 ½1 3sin2 cos2 ð Þ; 40 R3
(1)
PRL 101, 185504 (2008)
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PHYSICAL REVIEW LETTERS
FIG. 2 (color online). (a) Structure of methylthiolate adsorbed on Au(111) (top view). The different kinds of Au atoms on this surface are shown by the letters T, B, F, and H for on-top, bridge, fcc, and hcp hollows, respectively. Arrows indicate the principal axes direction parallel to a line of bridge atoms while v2 is along the tilt of the anisotropic surface stress tensor. v1 is along the ½011 direction ½211 of the molecules. (b) Side view of the same system indicating isosurfaces of the charge-density difference upon adsorption. Charge is removed from the bond between the bridge Au atoms. Arrows indicate the displacements of the bridge Au atoms. (c) Stress anisotropy from a hexagonal lattice of tilted point dipoles. The signs in the circles in the top panel indicate attraction () or repulsion (+). The sign of the corresponding stress is opposite. The magnitude of the energy (force) is plotted as a function of the location of the neighbor in units where , R, and 40 are 1. (d) Electron density difference arising in the h111i surface plane upon methanethiolate adsorption. Depletion occurs between bridge atoms where the thiol binds. Black circles indicate the location of the Au atoms in the surface unit cell (dashed lines).
where and are, respectively, the polar and azimuthal angles of the molecular dipole moment vector and is the angle describing the distance vector between the nearest neighbor dipoles in the lattice plane. For dipoles normal to the surface one expects isotropic repulsion and hence compressive stresses. However, the AT molecules on Au (111) are found to be tilted at an angle of ¼ 54 to the surface normal. The sign of the nearest neighbor interaction energy and the corresponding force as a function of the location of the neighbor () is depicted in Fig. 2(c). It is clearly seen that the interaction is anisotropic and it is unreasonable to expect uniform compressive stresses. However, according to this model, the stress along v1 must be compressive and that along v2 tensile, inconsistent with the values in Table I. Hence, the molecular dipoles cannot be the sole contributors to the observed stress. The charging-induced stress models also cannot account for this anisotropy as a uniform charging of metal surfaces would preserve the symmetry of the bare neutral surface. Moreover, the maximum change induced in the stress in such a case is 0:3–0:4 N=m in the compressive direction, as seen in experiments [23] and predicted by DFT [28], for surface charge densities similar to those induced upon ATSAM formation. This strongly suggests that there is an entirely different mechanism at play. In order to probe the cause of the large stress reduction we performed a charge-density analysis similar to that for the bare Au surface discussed earlier. Our results [Figs. 2(b) and 2(c)] indicate a removal of electronic charge from the Au surface and the S atom towards an Au-S bond. This removal of charge from the metal surface is, in fact, localized between the two bridge Au atoms bonded to the S as depicted in the contour plot in Fig. 2(d).
Concomitantly, the spacing between bridge Au atoms ˚ ) compared to the or v1 increases (by 0.17 A along ½011 bulk value causing the two bonds to an on-top site in the [29]. same row to shrink (by 0:05 A) Based on the observation above we propose a local stress relief mechanism to be operative: bare Au(111), as discussed earlier, has a tensile stress because of charge buildup between Au atoms as compared to bulk. The adsorption of the thiol molecule near every fourth bridge site along v1 results in a depletion of this charge from the bond between Au atoms constituting the bridge. The repulsion resulting from this charge depletion causes the bridge Au atoms (bonded to the S) to move apart, thereby also shrinking the bond to the adjacent (on-top) atom on either side of the bridge. This relaxation pattern, indicated by the short arrows in Fig. 2(b) for a row of atoms belonging to the surface, allows for the large relief in tensile stress not possible on the bare surface. A localized removal of charge is crucial for this mechanism to hold and is possible on a metal surface only via adsorption of molecules at specific sites. Merely charging the Au surface would lead to a uniform removal of charge and hence a uniform expansion of the surface [28] preservpffiffiffi pffiffiffi TABLE I. Adsorption-induced stress changes at the 3 3 Au(111) surface. 1 and 2 (Nm1 ) are principal stresses in directions 30 and 60 of the x axis, respectively (see Fig. 2).
Bare Au CH3 S-Au CH3 CH2 S-Au
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Eads (eV)
1
2
1
2
1.73 1.73
2.88 0.86 0.95
2.88 0:07 0.00
2:02 1:93
2:95 2:88
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PHYSICAL REVIEW LETTERS
ing the hexagonal symmetry. Since the on-top site does not move much relative to its position on the bare surface, the stress along v2 originates simply from the repulsion that persists along that direction following the charge induced on the surface. As a result the stress in this direction is compressive and results from a different mechanism. An alternative but equivalent point of view is that the induced charge produces compressive stresses in both directions but is relieved along v1 by the LSR mechanism. In either point of view, the overlayer structure formed upon adsorption dictates the anisotropic stress relief. The proposed mechanism has fundamental as well as practical implications. The stress-charge response of (111)-textured Au electrodes under specific adsorption conditions has been recently measured [30] by in situ dilatometry experiments. The experiments indicate a lowering of the response coefficient (=q) compared to direct metal-electrolyte interfaces. A similar effect is anticipated upon alkanethiolate adsorption as well. This could be explained using the second point of view presented above. Unlike the bare surface, any charge removed from the thiolated surface would originate from the bridge sites where the molecules are bound. Hence, the compressive stress, that would otherwise be induced by charging, is relieved along one of the directions by LSR rearrangements bringing down the average response [31]. This illustrates the power of the LSR mechanism and may provide a new handle on sensor design. AT molecules are needed in the preparation of receptor layers and when appropriately functionalized they can bind to targets with high specificity. Our results suggest that it would then be extremely beneficial to design organic thiols where target binding can be conveyed as a charge response down to the Au-S bond instead of relying on weak interchain interactions as is currently done. This would constitute a design challenge but would not be beyond the reach of present-day synthetic chemistry techniques. The resulting high sensitivities could enable detection even in the presence of competing environmental factors such as humidity, rendering nanomechanical sensing a more practical technology. We are grateful to E. Schwegler for helpful discussions. This work was supported by the LDRD program of Lawrence Livermore National Laboratory, and under the auspices of the National Science Foundation, by U.C. Berkeley under Grant No. 0425914. G. C. acknowledges partial support by MIUR through FIRB LATEMAR.
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