Theoretical Study of Work Function Modification by Organic Molecule

Feb 20, 2008 - Tuning of the electronic properties of semiconductors can be achieved by surface modification with organic molecules. In this work, we ...
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J. Phys. Chem. C 2008, 112, 3780-3784

Theoretical Study of Work Function Modification by Organic Molecule-Derived Linear Nanostructure on H-Silicon(100)-2 × 1 Amsalu Y. Anagaw,† Robert A. Wolkow,†,‡ and Gino A. DiLabio*,‡ Department of Physics, UniVersity of Alberta, Edmonton, Alberta, Canada T6G 2G7, and National Institute for Nanotechnology, National Research Council of Canada, 11421 Saskatchewan DriVe, Edmonton, Alberta, Canada T6G 2M9 ReceiVed: October 16, 2007; In Final Form: December 19, 2007

Tuning of the electronic properties of semiconductors can be achieved by surface modification with organic molecules. In this work, we study, by periodic density functional theory, the change in work function that occurs upon the modification of nominally hydrogen-terminated Si(100)-2 × 1 by chemisorption of substituted styrene molecules. Our results show that monolayers derived from 4-X-styrene molecules, with X being electron donating groups or hydrogen, decrease the work function of the system. Conversely, monolayers derived from 4-X-styrene molecules, with X being electron withdrawing groups, increase the work function of the system. For the molecules used in the modeling, the calculations indicate that the work function can be substantially modified from -1.4 eV (XdN(CH3)2) to +1.9 (XdNO2) eV relative to H-Si(100)-2 × 1. Because the direction and magnitude of charge transferred upon chemisorption is the same for all molecules, the work function changes are not the result of band bending. The work function modification comes exclusively from the inherent dipoles of the molecules chemisorbed on the surface. The computed dipoles for the monolayers range from -1.3 (XdN(CH3)2) to +1.4 (XdNO2) Debye. We conclude that substantial local control over some of the electronic properties of silicon can be achieved by the chemisorption of dipole-containing molecules.

Introduction The modification of surfaces with organic molecules represents a promising approach for the incorporation of new functionality into semiconductors.1-3 The unique properties of organic and semiconducting materials and their interfaces may lead to a variety of novel applications in areas of molecular electronics4 and chemical or biological sensing.5 The advantages associated with the use of organic species arise from the ability to easily modify molecular properties via synthesis by the judicious choice of substituent groups. Through chemisorption,1,2 these traits can be used to tune the properties of interfaces between the molecules and their semiconductor substrate or those of the substrate itself. The spatial extent of tuning depends on the degree of coverage, and thus, controlled molecular chemisorption6 offers a means of creating regions on semiconductor surfaces with highly localized, altered electronic properties. The deposition of molecules on a semiconductor surface can tune the substrate electronic properties by two principal mechanisms.7 Bonding of molecules onto a surface may quench gaps states which can result in the elimination of surface charge. Similarly, chemisorption may result in the creation of states residing in the semiconductor band gap which can lead to surface charge localization. In addition, molecular deposition can change surface dipoles as a consequence of the chargetransfer process that accompanies bond formation and by the adsorption of molecules containing an inherent dipole moment. The presence of surface charges generally leads to band bending, an effect which may also be induced, to a smaller extent, by * Author to whom correspondence should be addressed. Phone: +1780-641-1729. E-mail: [email protected]. † University of Alberta. ‡ NRC-NINT.

surface dipoles. Both band bending and the presence of surface dipoles alter the work function of a substrate. Recent studies have demonstrated that the deposition of benzoic8 and dicarboxylic acid derivatives3,9 on compound semiconductor surfaces can modify the substrate work function and that the change in work function depends on the molecular dipole. Much of our own recent work has focused on the creation of organic/silicon hybrid constructs using a growth mechanism that results in the formation of contiguous, linear molecular nanostructures on silicon surfaces.10 While these nanostructures have been described as molecular wires (and their transport properties have been studied theoretically11), they may also modulate transport through the silicon substrate near the molecule attachment sites. There are presently no experimental data on the work function change of H-Si(100)-2 × 1 upon the adsorption of para-substituted styrene (4-X-styrene) molecules. The aim of the present theoretical work is to understand how linear nanostructures created from different para-substituted styrene molecules alter the work function of an otherwise hydrogen-terminated Si(100)-2 × 1 surface. The substituents are chosen such that the molecular dipole moments span a large range. Our analysis involves the decomposition of work function changes according to built-in molecular dipole and chemisorption dipole and demonstrates that work function can be tuned by the choice of substituent. Details of Computational Modeling Calculations were performed within the frame work of a periodic density functional theory (DFT) as implemented in VASP.12 The interaction between ions (nuclei) and electrons were described using the projector augmented wave pseudopotentials.13 Electron-electron exchange and correlation interac-

10.1021/jp710065t CCC: $40.75 © 2008 American Chemical Society Published on Web 02/20/2008

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tions were described using the gradient corrected PerdewBurke-Ernzerhof (PBE) functional.14 The formation of linear nanostructures derived from organic molecules bonded to nominally hydrogen-terminated Si(100)-2 × 1 has been described in substantial detail elsewhere.10 Briefly, surface dangling bonds (DBs) act as addition sites for certain double-bond containing molecules, such as styrene.10a Addition occurs through the terminal atom of the carbon-carbon double bond of the vinyl group in styrene. The vinyl π bond is broken upon addition, and the central carbon has an unpaired electron. The newly formed carbon-centered radical abstracts a hydrogen atom from a neighboring surface site on the next dimer in the dimer row. The hydrogen atom abstraction process passivates the C-centered radical and stabilizes the chemisorbed species while generating a new DB site juxtaposed with the added molecule. Line growth propagates when another molecule adds to the newly formed DB. In all calculations, nominally hydrogen-terminated Si(100)-2 × 1 was modeled by periodic repeated slabs separated by regions of vacuum into which adsorbed molecules can be added. An asymmetric slab with eight layers of Si atoms and a vacuum thickness of ca. 26 Å was used. The bottom silicon layer was terminated by two fixed-position hydrogen atoms per silicon. The coordinates of the Si atoms in the bottom three layers were kept fixed. Surfaces were modeled with 4 × 1 unit cells to simulate coverages of one molecule for every two silicon dimers in two dimer rows. This degree of coverage is defined in the present work as 0.5 monolayer (ML) coverage. This level of coverage is approximately that arising from a line-growth experiment in which dense nanostructure formation occurs. The projections of the unit cells in the xy plane results in lines of molecules along one side of dimer rows, with lines on every second dimer row. The remainder of the surface sites were capped by hydrogen atoms. The geometries of 10 4-X-styrene (XdN(CH3)2, NH2, OCH3, CH3, H, COOH, CF3, C(O)CF3, CN, NO2) molecules chemisorbed on H-Si(100)-2 × 1 were optimized to their minimum ground state energies by minimizing their Hellmann-Feynman forces until all residual forces on the relaxed atoms were smaller than 0.02 eV/Å.15 The substituents were chosen to span a large range of electron withdrawing (EW) and electron donating (ED) strengths, as reflected by σp+ Hammett parameters.16 The σp+ scale of substituent constants is based on the measured rate constant for the SN1 solvolysis of substituted cumyl chlorides in 90% acetone/water at 25 °C17 and correlates well with a large number of physical properties of substituted benzene systems. A uniform k-point sampling grid in the surface Brillouin zone was used with a Gaussian smearing of 0.08 eV.18 For all calculations, an energy cutoff of 450 eV was used for the plane wave expansion. Brillouin-zone integrations were performed using 3 × 15 × 1 k-point Monkhorst-Pack grids. For isolated molecules, a large super cell size of 20 × 20 × 32 (Å3) and one k point at the gamma center were used. For all calculations, the work function and the dipole moment were converged to within 0.1 eV and 0.1 Debye, respectively. The work function (Φ) was obtained by subtracting the Fermi energy of the system (Ef) from the electrostatic potential in the vacuum gap (Vvac), where it has reached its asymptotic value, according to

Φ ) Vvac - Ef

(1)

The electrostatic potential, V(r b), is the sum of the Hartree potential, VHart(r b), and the ion-electron pseudopotential, Vlocal b) pp (r

V(b) r ) Vlocal r + VHart(b) r pp (b)

(2)

The average, smoothed electrostatic potential along the surface normal (in the z axis direction) was obtained using

V h (z) )

1 A

∫∫ V(x,y,z) dx dy

(3)

A

where A is the area of the surface unit cell normal to z. Results and Discussion As a reference and to assess our theoretical methods, we began by calculating the change of work function that occurs for Si(100)-2 × 1 upon hydrogen termination. The surface of clean Si(100)-2 × 1 is known to be composed of buckled dimers in which charge is distributed in an asymmetric fashion.19 This dimer buckling is eliminated upon hydrogen termination.20 We calculated work functions for clean Si(100)-2 × 1 and H-Si(100)-2 × 1 of 5.0 and 4.6 eV, respectively, on the basis of the differences in the planar averaged electrostatic potential in the middle of the vacuum gap for both models. The decrease in work function, Φ, of 0.4 eV upon fully H terminating the 2 × 1 surface, is within 0.1 eV (the convergence limit of our calculations) of the experimentally determined decreases which range from 0.34 to 0.40 eV.20a,21,22 These results therefore provide some confidence with respect to the prediction of the work function change. We also computed the work functions for Si(100)-2 × 1 surfaces with varying hydrogen coverage. For cases in which the hydrogen coverage is one H atom per dimer and three H atoms on two dimers in two adjacent rows, the work functions were calculated to be 4.73 and 4.67 eV, respectively. We also computed the work function of the dihydrogen-terminated bottom of the silicon slab to be 4.68 eV. That is, the work functions for silicon surfaces with varying hydrogen coverage and surface reconstruction are computed to occur over a small range between 4.63 and 4.73 eV. These results indicate that the reduction in work function of clean Si(100)-2 × 1 upon hydrogenation is largely due to the elimination of the dipole associated with the buckled dimers on clean Si rather than to any minor dipole that may be associated with Si-H bonds at the H-Si surface.20a Surface DBs are involved in the initiation of line growth and line propagation. However, the nature of the growth process ensures that the total number of DBs is constant through out the growth process and small relative to the numbers of molecules and hydrogen atoms occupying surface sites. Therefore, we compute the change in the work function of Si(100)-2 × 1 surface, ∆Φ, upon the adsorption of molecules simply as

∆Φ ) Φmod - ΦH-Si(100)-2×1

(4)

where Φmod is the modified work function of the surface after the adsorption23 of molecules and ΦH-Si(100)-2×1 is the work function calculated for H-Si(100)-2 × 1. Figure 1 shows the planar-averaged electrostatic potential for differently substituted styrene molecules adsorbed on H-Si(100)-2 × 1 as a function of slab position in the direction, z, perpendicular to the surface. The relative potential in the vacuum space on the left side is representative of that of H- Si(100)-2 × 1 and is the same for all models.24 The potential on the right side, in the space above the molecules in the vacuum, is that associated with the molecule-modified surface. It is immediately obvious from the figure that the work functions are decreased

3782 J. Phys. Chem. C, Vol. 112, No. 10, 2008

Anagaw et al. TABLE 1: Difference in the Asymptotic, Planar-Averaged Electrostatic Potentials, ∆VML, and the Left and Right Ionization Potentials (IPleft and IPright) of the Molecular Layers of 4-X-styrene Molecules (eV) with the Dipole Moments of the Molecular Layers, µML (Debye), Obtained from Eq 7 Also Given

Figure 1. Planar-averaged electrostatic potential for 0.5 ML coverage of selected 4-X-styrene molecules adsorbed on H-Si(100)-2 × 1 as a function of position in the direction perpendicular to the surface. The left-most side of the potentials represents the work function of H-Si(100)-2 × 124 and the right side of the potentials indicate how the work function is modified upon the formation of molecular lines on the surface. The inset shows a “ball and stick” representation of the silicon atomic layers and molecules. The red ball indicates where the X substituents are attached to the ring. The vertical dashed line indicates the approximate midpoint of the silicon-molecule bond.

in cases where XdED groups and XdH and work functions are increased with XdEW groups, relative to H-Si(100)-2 × 1. The origin of ∆Φ is the change in the surface dipole upon adsorption of the molecules. If the adsorbed molecules are well oriented, parallel, and close-packed, then they can be considered as a dipole layer and a uniform electrostatic potential change must occur over the width of the layer. To obtain a better understanding of this phenomenon, we turn to classical electrostatics. According to the Helmholtz equation, ∆Φ can be interpreted in terms of change in the surface dipole, ∆µ, due to adsorption of a dense molecular ML according to

∆Φ )

eµ cosθ eµz ) oA oA

(5)

where o is the permittivity of vacuum and A is the surface area taken by one molecule in a full monolayer.25 Note that µz corresponds to the component of the dipole moment directed along the surface normal, since this is the only component that affects the work function. We can further express µz as a sum of the z components of the dipole moment of the molecular ML (µML), that is the dipole of the ML in the absence of the silicon substrate and the dipole moment created through the charge-transfer that accompanies chemical bond formation between the molecules and the surface (µchem) according to

∆Φ )

eµz e(µML + µchem) ) oA oA

(6)

For a close-packed layer of molecules, depolarization effects in the molecular layer are taken into account in the periodic boundary DFT calculations. Calculations involving the substratefree ML were performed on the ML geometry obtained from optimized structure of the ML on the H-Si(100)-2 × 1 surface.26

X

∆VML

IPleft

IPright

µML

N(CH3)2 NH2 OCH3 CH3 H COOH CF3 OC2F3 CN NO2

-1.6 -1.7 -0.9 -0.7 -0.6 0.2 0.8 1.3 1.6 1.7

5.1 5.2 4.9 4.9 4.9 5.0 5.0 5.1 5.0 5.1

3.5 3.5 3.9 4.1 4.3 5.2 5.8 6.4 6.6 6.8

-1.3 -1.3 -0.8 -0.6 -0.5 0.1 0.7 1.1 1.3 1.4

By using the Helmholtz principle, µML can be related to the difference in the electrostatic potential across the molecular ML as

∆VML ) Vright - Vleft )

eµML oA

(7)

where Vright and Vleft are the asymptotic, planar-averaged electrostatic potentials on both sides of the molecular layer. Table 1 summarizes the ∆VML values obtained from our calculations and the results of the application of eq 7 to substrate-free MLs derived from styrene molecules with different para substituents. Data are ordered according to the strength of the substituent group, from strongest ED group to strongest EW group. The ∆VML values are also reflected in the differences between the left and the right side ionization potentials (IP) of the molecular ML. The IPs are obtained by subtracting the highest occupied molecular orbital (HOMO) energy of the molecular ML from the left and right sides of the asymptotic electrostatic potentials, respectively. The value of IP depends upon from which side of the ML the electron is ejected. The left side IP corresponds to the side of the molecular ML associated with the ethyl moiety26 and is the same for all molecular layers regardless of substituent. The right side IP corresponds to the side of the molecular MLs with differing ring substituents. The ∆VML and IP values vary monotonically according to the EW or ED strength of the substituent groups (as indicated by σ+ p ) on the molecules comprising the ML. These variations can be understood from the perspective of perturbative molecular orbital (PMO) theory: EW groups pull electron density out of the benzene ring through σ bonds (raising IP) while ED groups push electron density into the benzene ring via π overlap (lowering IP).27 Note that ∆VML and µML for the 4-carboxy ML are nearly zero, indicating that the EW effect of the COOH group is effectively cancelled by the ED effect of the ethyl group. As is shown in Table 1, the values for µML calculated using eq 7 strongly depend on the nature of the substituents and vary over a range of more than 2.5 Debye. The calculated ∆Φ values for 10 4-X-styrene-derived MLs on H-Si(100)-2 × 1 are compiled in Table 2, along with the values for µML from Table 1. The z component of µML and µchem, obtained from eqs 5 and 6, respectively, are also given in Table 2. There is a nearly monotonic progression of ∆Φ values (ranging from -1.4 to +1.9 eV) with σ+ p . However, the differences in the ∆Φ values obtained for the ML with the strongest ED (-NH2, -N(CH3)2) and EW (-CN, -NO2) groups are essentially zero. This may indicate that substituent effects on the molecules have saturated, that is, that electron

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TABLE 2: Calculated Change in the Work Function (∆Φ/eV) of H-Si(100)-2 × 1 upon the Adsorption of 4-X-syrene, Surface Dipole (µz), Molecular Dipole (µML), and the Chemisorption Dipole Moment (µchem) where Dipole Moments Are in Debye X

∆Φ

µza

µMLb

µchema

N(CH3)2 NH2 OCH3 CH3 H COOH CF3 OC2F3 CN NO2

-1.4 -1.4 -0.7 -0.5 -0.4 0.3 1.0 1.5 1.9 1.9

-1.1 -1.1 -0.6 -0.4 -0.3 0.3 0.8 1.2 1.5 1.5

-1.3 -1.3 -0.8 -0.6 -0.5 0.1 0.7 1.1 1.3 1.4

0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.2 0.1

a

Calculated using eq 6. b Calculated using eq 7.

donation (withdrawal) to (from) the benzene rings by the ED (EW) groups has reach a maximum. Of course, the trend in ∆Φ is perfectly mirrored by the trends in µML and µz, with asymptotic values of dipoles being reached for the strongest ED and EW groups. It is interesting to note that the values for µchem, the dipole associated with the chemical bond between the silicon surface and the molecules, are in the range of 0.10.2 D for all of the MLs. This indicates that the dipole-induced changes in work function are due primarily to the inherent dipole moments of the individual molecules comprising the ML and not due to the charge transfer associated with covalent bonding of the molecules to the surface. This finding is consistent with the fact that para-substituents have very little effect on, for example, the C-H bond dissociation enthalpies of 4-Xtoluenes.28 Overall, the changes in work function can be described as being a result of the formation of dipole arrays arising from the dipoles of individual molecules, on the surface. MLs with Φ-lowering ED substituents have the negative ends of their dipoles closest to the surface and MLs with Φ-increasing EW groups have the positive ends of their dipoles closest to the surface. The details of the charge rearrangement that occurs upon chemisorption to the surface can be examined by computing planar-averaged, electron density differences, ∆F(r b). For these calculations, ∆F(r b) is obtained by subtracting both the densities of the clean substrate, FSubstrate(r b), and the ML FML(r b) from the density of the adsorbate-substrate system FSubstrate + ML(r b)

∆F(b) r ) FSubstrate+ML(b) r - FSubstrate(b) r - FML(b) r

(8)

Planar averaged electron densities can be obtained from

∆F(z) )

1 A

∫∫ ∆F(x,y,z) dx dy

(9)

A

The charge rearrangement calculated according to eq 8 is plotted as a function of position in Figure 2 for three representative examples, styrene- and 4-N,N-dimethylamino- and 4-nitrostyrene-derived MLs. As expected, the largest values of ∆F(rb) occur at the interface between the silicon substrate and the chemisorbed MLs. For all of the substituents, ∆F(r b) in the interface region are within (0.003 electrons. This is consistent with the fact that the substituents do not significantly change µchem. Because the direction and magnitude of the charge transferred is the same for all molecules, the computed work function changes are not the result of band bending. It is also interesting to note how the perturbations in F(r b) diminish very quickly as a function of distance from the interface. Values for ∆F(r b) are

Figure 2. Planar averaged electron density differences for selected 4-X-styrene molecular monolayers on H-Si(100)-2 × 1 as a function of position in the direction perpendicular to the surface. The inset shows a “ball and stick” representation of the silicon atomic layers and molecules. The red ball indicates where the X substituents are attached to the ring. The vertical dashed lines indicate position of the siliconmolecule bond.

Figure 3. Change in work function vs free molecule net dipole moment for 4-X-styrene molecules.

essentially zero at five Si layers away from the surface and near the center of the benzyl rings.29 The direction of charge transfer can be understood by comparing the work function for H-Si(100)2 × 1 with the IPleft values of the molecular MLs. As described earlier, all of the MLs have IPleft values of approximately 5.0 eV while ΦH-Si(100)-2×1 is computed to be 4.6 eV. Thus, charge transfer must occur from the surface to the ML. This is also consistent with the electronegativity difference between the Si and C atoms, namely, χ(Si) ) 1.90, χ(C) ) 2.55. The linear relationship between ∆Φ and µML and µz is clear from eqs 5 and 6. As a final point, we examine how ∆Φ is related to the dipole of the free molecules (µmol) in Figure 3. Perfectly linear behavior is not observed in Figure 3 largely because the net molecular dipoles are plotted and not the value that would represent the component along a direction perpendicular to the surface, if the molecules were surface bound. Nevertheless, and as expected, there is an excellent correlation between ∆Φ and µmol, with an r2 of 0.99.

3784 J. Phys. Chem. C, Vol. 112, No. 10, 2008 Summary With a periodic density functional theory approach, we modeled the change in work function that occurs upon the modification of nominally hydrogen-terminated Si(100)-2 × 1 by chemisorption of 4-X-styrene molecules. The substituents used span a large range of electron withdrawing and donating groups. The systems modeled represent monolayers composed of lines of molecules growing on every other dimer row on the surface, an idealized representation of self-direct linear nanostructure formation on H-Si(100)-2 × 1. Our results show that monolayers derived from 4-X-styrene molecules, with X being electron donating groups or hydrogen, decrease the work function of the system. Conversely, monolayers derived from 4-X-styrene molecules, with X being electron withdrawing groups, increase the work function of the system. For the molecules used in the modeling, the calculations indicate that the work function can be substantially modified from -1.4 eV (XdN(CH3)2) to +1.9 (XdNO2) eV relative to H-Si(100)-2 × 1. By using classical electrostatics, the dipole contribution to work function change was decoupled into monolayer dipole and interface dipole terms. The former reflects the inherent dipole of the molecules comprising the monolayer while the latter indicates the degree of charge transfer associated with bond formation as a consequence of chemisorption. This analysis showed that the interface dipole is nearly constant for all molecules, regardless of substituent, and is in the range of 0.10.2 Debye. Upon bond formation, charge is transferred from the Si to the monolayer. Because the direction and magnitude of charge transferred is the same for all molecules, work function changes are not the result of band bending. The variation in work function change comes exclusively from the inherent dipoles of the molecules chemisorbed on the surface. The computed dipoles for the monolayers range from -1.3 (Xd N(CH3)2) to +1.4 (XdNO2) Debye. In the study presented herein, the work function modification of H-Si(100)-2 × 1 is shown to be the result of dipolecontaining molecules chemisorbed on the surface. We conclude that substantial local control over some of the electronic properties of silicon can be achieved by the chemisorption of dipole-containing molecules. Acknowledgment. We are grateful to iCORE, CIAR, and NSERC for funding. G.A.D. thanks the Academic Information and Communication Technologies department of the University of Alberta for access to computational resources. References and Notes (1) Linford, M. R.; Fenter, P.; Eisenberger, P. M.; Chidsey, C. E. D. J. Am. Chem. Soc. 1995, 117, 3145-3155. (2) Wolkow, R. A. Ann. ReV. Phys. Chem. 1999, 50, 413-441. (3) Vilan, A.; Shanzer, A.; Cahen, D. Nature 2000, 404, 166-168. (4) Piva, P. G.; DiLabio, G. A.; Pitters, J. L.; Zikovsky, J.; Rezeq, M.; Dogel, S.; Hofer, W. A.; Wolkow, R. A. Nature 2005, 435, 658-661. (5) Cahen, D.; Naaman, R.; Vager, Z. AdV. Funct. Mater. 2005, 15, 1571-1578. (6) Zikovsky, J.; Dogel, S. A.; Haider, M. B.; DiLabio, G. A.; Wolkow, R. A. J. Phys. Chem. C 2007, 111, 12257-12259.

Anagaw et al. (7) Mo¨nch, W. Semiconductor Surfaces and Interfaces, Springer Series in Surface Sciences, Vol. 26; Springer-Verlag: Berlin, 1995. (8) Bastide, S.; Butruille, R.; Cahen, D.; Dutta, A.; Libman, J.; Shanzer, A.; Sun, L.; Vilan, A. J. Phys. Chem. B 1997, 101, 2678-2684. (9) Cohen, R.; Kronik, L.; Shanzer, A.; Cahen, D.; Liu, A.; Rosenwaks, Y.; Lorenz, J. K.; Ellis, A. B.; J. Am. Chem. Soc. 1999, 121, 10545-10553. (10) See, for example, reference 6 and (a) Lopinski, G. P.; Wayner, D. D. M.; Wolkow, R. A. Nature 2000, 406, 48-51. (b) DiLabio, G. A.; Piva, P. G.; Kruse, P.; Wolkow, R. A. J. Am. Chem. Soc. 2004, 126, 16048. (11) (a) Kirczenow, G.; Piva, P. G.; Wolkow, R. A. Phys. ReV. B 2005, 72, 245306. (b) Rochefort, A.; Boyer, P.; Nacer, B. Org. Elec. 2007, 8, 1-7. (12) (a) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 47, 558-561. (b) Kresse, G.; Hafner, J. Phys. ReV. B 1994, 49, 14251-14269. (c) Kresse, G.; Furthmu¨ller, J. Comput. Mater. Sci. 1996, 6, 15-50. (d) Kresse, G.; Furthmu¨ller, J. Phys. ReV. B 1996, 54, 11169-11186. (e) Neugebauer, J.; Scheffler, M. Phys. ReV. B 1992, 46, 16067-16080. (13) (a) Blochl, P. E.; Jepsen, O.; Andersen, O. K. Phys. ReV. B 1994, 49, 16223-16233. (b) Kresse, G.; Joubert, D. Phys. ReV. B 1999, 59, 17581775. (14) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865-3868. (15) The optimized structures of MLs composed of 4-X-styrene molecules are such that the ring moieties of the molecules are not perpendicular to the surface (see, for example, Figure 5b of Pei, Y. and Ma, J. Langmuir 2006, 22, 3040-3048.). In all cases, the substitutent groups were oriented such that maximum conjugation with the ring system was achieved. Molecular and ML properties such as dipole moment and ionization potential are extremely sensitive to the orientation of the substituents. See, for example, Table 4 of reference 28. (16) Hansch, C.; Leo, A.; Taft, R. W. Chem. ReV. 1991, 91, 165-195. (17) Brown, H. C.; Okamoto, Y. J. Am. Chem. Soc. 1958, 80, 49794987. (18) Methfessel, M.; Paxton, A. T. Phys. ReV. B 1989, 40, 3616-3621. (19) (a) Koke, P.; Mo¨nch, W. Solid State Commun. 1980, 36, 10071009. (b) Hamers, R. J.; Tromp, R. M.; Demuth, J. E. Phys. ReV. B 1986, 34, 5343-5357. (c) Wolkow, R. A. Phys. ReV. Lett. 1992, 68, 2636-2639. (20) These calculations utilized 2 × 2 unit cells containing two dimers in one dimer row. (21) Fukiwara, K. Phys. ReV. B 1982, 26, 2036-2040. (22) Souzis, A. E.; Seidl, M.; Carr, W. E.; Huang, H. J. Vac. Sci. Tech. A 1989, 7, 720-723. (23) It should be recognized that, in reality, ∆Φ will be a highly local potential change because line growth occurs in a less regular fashion that is implied by our model. (24) This labeling is used for convenience. In actuality, the potential described here is actually that for the dihydrogen-terminated “bottom” portion of the silicon slab. However, as noted in the text, the work function of this surface was calculated to be within our convergence criterion of 0.1 eV of that for H-Si(100)-2×1. (25) Dipole calculations were performed on 4-X-benzyl species chemisorbed on Si(111) in the following: Natan, A.; Zidon, Y.; Shapira, Y.; Kronik, L. Phys. ReV. B 2006, 73, 193310. These authors evaluated the dipole by integrating the electron density within a slab using µz(z) ) ∫zzcell (z′ - z)F(x, y, z′) dx dy dz′, where µz represents the dipole moment between the vacuum and the plane z. The quantity F(r b) is the charge density and Zcell is the super cell size in the direction perpendicular to the surface. For some representative cases, we verified that the dipole moments we computed with eq 5 gave the same results as those obtained using the more general approach used by Natan et al. (26) It is important to reiterate that, in the process of forming linear nanostructures on silicon surfaces, the vinyl moieties of the styrene molecules become saturated. That is, the carbon-carbon π bond is replaced by one C-Si σ bond and one C-H bond (see Details of Computational Modeling and ref 10). Therefore, in modeling the molecular layer in order to obtain ∆VML, the chemical species comprising these layers are parasubstituted ethylbenzenes. (27) DiLabio, G. A.; Pratt, D. A.; Wright, J. S. J. Org. Chem. 2000, 65, 2195-2203. (28) Pratt, D. A.; DiLabio, G. A.; Mulder, P.; Ingold, K. U. Acc. Chem. Res. 2004, 37, 334-340. (29) Screening effects in intrinsic silicon, the case modeled in the present work, are expected to be smaller than in doped silicon.