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Molecular Orientation in Octanedithiol and Hexadecanethiol Monolayers on GaAs and Au Measured by Infrared Spectroscopic Ellipsometry Dana M. Rosu,*,† Jason C. Jones,‡ Julia W. P. Hsu,‡ Karen L. Kavanagh,§ Dimiter Tsankov,| Ulrich Schade,⊥ Norbert Esser,† and Karsten Hinrichs*,† ISAS-Institute for Analytical Sciences, Department Berlin, Albert-Einstein-Str. 9, 12489 Berlin, Germany, Sandia National Laboratories, Albuquerque, New Mexico 87185-1120, KaVanagh Laboratory, Department of Physics, Simon Fraser UniVersity, 8888 UniVersity DriVe, Burnaby, BC, V5A 1S6, Canada, Institute of Organic Chemistry, Bulgarian Academy of Sciences, Acad. G. BoncheV Str., Block 9, BG-1113 Sofia, Bulgaria, and Berliner Elektronenspeicherring-Gesellschaft fu¨r Synchrotronstrahlung mbH, Albert-Einstein-Str. 15, 12489 Berlin, Germany ReceiVed August 14, 2008. ReVised Manuscript ReceiVed NoVember 6, 2008 Infrared spectroscopic ellipsometry was used for determination of molecular orientation and for lateral homogeneity studies of organic monolayers on GaAs and Au, the organic layer being either octanedithiol or hexadecanethiol (HDT). The laterally resolved measurements were performed with the infrared mapping ellipsometer at the synchrotron storage ring BESSY II. The molecular orientation within the monolayers was determined by optical model simulations of the measured ellipsometric spectra. Different tilt angles were obtained for the monolayers of HDT and octanedithiol on GaAs: 19° and >30°, respectively. The tilt angle of the methylene chains for HDT on Au substrate (22°) is similar to the 19° tilt which was obtained for the HDT monolayers on GaAs, thus suggesting similar molecular ordering of the thiolates on both substrates.
Introduction Research on the properties of n-alkanethiol monolayers is of high relevance due to their potential use in a variety of applications: lubrication in micromechanical systems, passivation in microelectronic devices, and chemical biosensing.1-3 Whereas the adsorption of the n-alkanethiols on metal substrates was intensively studied,4-7 the study of the adsorption of these molecules on GaAs is limited despite the wide potential for such films in electronic and optoelectronic devices. Many surface-sensitive methods have been applied over time to study the packing and orientation of the alkanethiol molecules on different substrates. Typical investigation methods are as follows: reflection infrared absorption spectroscopy (RAIRS),6,8-10 UV-visible ellipsometry, infrared spectroscopic ellipsometry (IRSE),11,12 near-edge X-ray absorption fine struc* Corresponding authors. E-mail:
[email protected];
[email protected]. † ISAS-Institute for Analytical Sciences. ‡ Sandia National Laboratories. § Simon Fraser University. | Bulgarian Academy of Sciences. ⊥ Berliner Elektronenspeicherring-Gesellschaft fu¨r Synchrotronstrahlung mbH.
(1) Dorsten, J. F.; Maslar, J. E.; Bohn, P. W. Appl. Phys. Lett. 1995, 66, 1755. (2) Gooding, J. J.; Hibbert, D. B. TrAC, Trends Anal. Chem. 1999, 18, 525. (3) Lio, A.; Charych, D. H.; Salmeron, M. J. Phys. Chem. B 1997, 101, 3800. (4) Kondoh, H.; Nambu, A.; Ehara, Y.; Matsui, F.; Yokoyama, T.; Ohta, T. J. Phys. Chem. B 2004, 108, 12946. (5) Dubois, L. H.; Zegarski, B. R.; Nuzzo, R. G. J. Chem. Phys. 1993, 98, 678. (6) Laibinis, P. E.; Whitesides, G. M.; Allara, D. L.; Tao, Y. T.; Parikh, A. N.; Nuzzo, R. G. J. Am. Chem. Soc. 1991, 113, 7152. (7) Vericat, C.; Vela, M. E.; Benitez, G. A.; Gago, J. A. M.; Torrelles, X.; Salvarezza, R. C. J. Phys.: Condens. Matter 2006, 18, R867. (8) McGuiness, C. L.; Blasini, D.; Masejewski, J. P.; Uppili, S.; Cabarcos, O. M.; Smilgies, D.; Allara, D. L. ACS Nano 2007, 1, 30–49. (9) Atre, S. V.; Liedberg, B.; Allara, D. L. Langmuir 1995, 11, 3882. (10) Nesher, G.; Vilan, A.; Cohen, H.; Cahen, D.; Amy, F.; Chan, C.; Hwang, J.; Kahn, A. J. Phys. Chem. B 2006, 110, 14363. (11) Hu, Z. G.; Prunici, P.; Patzner, P.; Hess, P. J. Phys. Chem. B 2006, 110, 14824–31. (12) Meuse, C. W. Langmuir 2000, 16, 9483.
ture,4 liquid drop contact angle measurements,9 grazing incidence X-ray diffraction,13 surface plasmon spectroscopy,14 X-ray photoelectron spectroscopy (XPS),6,9,10 and time-of-flight secondary ion mass spectroscopy.15 A recent study16 using a combination of RAIRS and XPS techniques reported a 14° tilt angle of the methylene chains for octadecanethiol on GaAs(001). A tilt angle lower than 15° was determined from XPS measurements by Nesher et al. in a study of the electronic properties of a GaAs-alkylthiol monolayer-Hg junction.10 The ellipsometric methods in the visible (VIS) as well as in the infrared (IR) spectral range are standard methods for structural investigation and thickness determination of thin films.17-20 The ellipsometric experiment is nondestructive and contact-free and does not depend on special requirements such as (ultrahigh) vacuum. Depending on the photon energy, electronic or vibrational properties are probed. Since many organic compounds do not exhibit characteristic electronic transitions in the VIS spectral range, a detailed structural characterization is often not possible from VIS ellipsometric spectra. On the other hand, IR ellipsometry is widely used for this purpose because characteristic IR bands associated with vibrations of specific molecular groups are observed. The band amplitudes and shapes in the IR (13) Fenter, P.; Eberhardt, A.; Liang, K. S.; Eisenberger, P. J. Chem. Phys. 1997, 106, 1600. (14) Ehler, T. T.; Malmberg, N.; Noe, L. J. J. Phys. Chem. B 1997, 101, 1268. (15) Zhou, C.; Walker, A. V. J. Phys. Chem. C 2008, 112, 797. (16) McGuiness, C. L.; Shaporenko, A.; Mars, C. K.; Uppili, S.; Zharnikov, M.; Allara, D. L. J. Am. Chem. Soc. 2006, 128, 5231. (17) Hinrichs, K.; Gensch, M.; Esser, N. Appl. Spectrosc. 2005, 59, 272A. (18) Ro¨seler, A.; Korte, E. H.; Griffiths, P. R.; Chalmers, J. Infrared spectroscopic ellipsometry. In Handbook of Vibrational spectroscopy; Griffiths, P. R., Chalmers, J., Eds.; Wiley: Chichester, 2001; Chapter 2.8. (19) Aspnes, D. E. The Accurate Determination of Optical Properties by Ellipsometry. In Handbook of Optical Constants of Solids; Palik, E. D., Ed.; Academic Press: New York, 1985; pp 89-110L. (20) Rossow, U.; Richter, W. Spectroscopic Ellipsometry. In Optical Characterisation of Epitaxial Semiconductor Layers; Bauer, G. , Richter, W., Eds.; Springer: New York, 1996; Chapter 3, pp 68-128.
10.1021/la8026557 CCC: $40.75 2009 American Chemical Society Published on Web 12/24/2008
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Figure 1. Principle of the ellipsometry measurement.17-20,28
ellipsometric spectra are directly related with the directions of transition dipole moments of specific molecular vibrations, thus enabling determination of the molecular orientation.17,21-23 In recent years, IRSE has proven to be well-suited for analysis of thin functional organic films on metal and semiconductor substrates by providing information about thickness and molecular structure.17 In this paper, the results of orientation analysis of monolayers formed by octanedithiol and hexadecanethiol (HDT) on GaAs and on Au are presented.
Experimental Section Sample Preparation. Molecular monolayers on GaAs substrates were prepared according to well-established protocols.24 The 1,8octanedithiol (Aldrich, 97%) or hexadecanethiol (HDT, Fluka, >95%) monolayers were deposited from solution (5 mM in ethanol) onto bulk n+-GaAs wafers (Si-doped, 3 × 1018 cm-3), previously etched with a combination of 1:20 NH4OH:deionized water and 1:10 HCl: ethanol solutions to remove the native oxide. Octanedithiol and HDT were used as received without any further purification. Exactly the same deposition procedure was used to form monolayers on Au films (50 nm) that were e-beam evaporated on Si substrates with a Ti adhesion layer (2.5 nm). Prior to thiol deposition, the Au films were cleaned with UV ozone for 20 min and rinsed with ethanol to remove possible hydrocarbon contaminations. The root-mean-square roughness of the cleaned GaAs substrates was determined by AFM measurements over an area of 1 µm2 to be 0.5 nm. Ellipsometry. The samples were investigated using IRSE. We used an ellipsometer attached to a BRUKER 55 located in our laboratory18 and a mapping ellipsometer25-27 attached to a BRUKER IFS 66/v located at the IR beamline at the BESSY II synchrotron facility, both operating in the mid-IR spectral range. The mapping system provided a lateral resolution below 1 mm226 using a photovoltaic mercury-cadmium-telluride detector. Both systems enable investigation of thin film samples with monolayer sensitivity. For defined reflectance measurements the incidence angle was set either to 60° or to 65° for the following reasons. First, these incidence angles ensure in the laboratory experiments that the probed spots are definitely smaller than the sample size (7 × 19 mm2). We refrained from using an incidence angle of 80° because at the same experimental settings the irradiated spot would become larger than the actual sample size. Second, the lower incidence angles of 60° and 65° reduce the error due to the opening angle (for our externally attached (21) Hinrichs, K.; Tsankov, D.; Korte, E. H.; Ro¨seler, A.; Sahre, K.; Eichhorn, K.-J. Appl. Spectrosc. 2002, 56, 737–743. (22) Parikh, A. N.; Allara, D. L. J. Chem. Phys. 1992, 96, 927. (23) Debe, M. K. J. Appl. Phys. 1984, 55, 3354. (24) Jun, Y.; Zhu, X.; Hsu, J. W. P. Langmuir 2006, 22, 3627. (25) Gensch, M.; Esser, N.; Korte, E. H.; Schade, U.; Hinrichs, K. Infrared Phys. Technol. 2006, 49, 39. (26) Roodenko, K.; Mikhaylova, Y.; Ionov, L.; Gensch, M.; Stamm, M.; Minko, S.; Schade, U.; Eichhorn, K.-J.; Esser, N.; Hinrichs, K. Appl. Phys. Lett. 2008, 92, 103102. (27) Roodenko, K.; Gensch, M.; Heise, H. M.; Schade, U.; Esser, N.; Hinrichs, K. Infrared Phys. Technol. 2006, 49, 74.
Figure 2. Schematic of the geometric model of HDT molecules used for the simulations. The tilt angle γ and the twist angle δ are marked. To account for the uniaxial symmetry (nx ) ny) of the studied samples, the angle φ (rotation in the x, y plane) was set to 45°. The directions of the transition dipole moments of the symmetric and asymmetric stretching vibrations of the CH2 group are shown in the inset.
ellipsometer it is limited to about (3.5°). Setting the incidence angle at 80° or above would increase the error due to nonlinearity of the p-polarized reflectance. As shown schematically in Figure 1, the incident linearly polarized radiation is reflected from the sample surface as elliptically polarized radiation and the resulting change in the state of polarization is quantified via the ellipsometric parameters: tan Ψ and ∆. tan Ψ stands for the amplitude ratio and ∆ for the phase shift difference of the two orthogonally polarized components of the reflected wave (rs and rp). The ellipsometric parameters are defined by the quantity F, which is the ratio of the complex reflection coefficients rp and rs:
F)
rp ) tan Ψ · ei∆ rs
(1)
The s- and p-polarized reflectances are defined by Rp ) |rp|2 and Rs ) |rs|2. The reflection absorbance of a thin film is defined by -log(R/R0), where R0 is the reflectance of the clean substrate. Optical Simulation. Central to the quantitative evaluation of thin film characteristics is a true optical simulation of the measured spectra. For well-defined organic film-on-a-substrate, a three-phase optical layer model is most frequently used.21,28,29 In our simulations21,29 the vibrational bands are represented as Lorentzian oscillators with wavenumber (ν˜ i0), parameters for the oscillator strengths (Fi), and full-width at half-maximum (fwhm) (Γi) to yield the complex dielectric function εˆ ) ε′ + ιε′′ with
ε ′ ) ε∞ +
∑ (ν˜
2 ˜ 2)2 + (Γiν˜ )2 i0 - ν
i
ε )
FiΓiν˜ 2 ˜ 2)2 + (Γiν˜ )2 i0 - ν
∑ (ν˜ i
Fi(ν˜ i02 - ν˜ 2)
(2) (3)
Uniaxial symmetry was assumed for the samples studied which requires isotropic properties in directions parallel to the surface plane (x, y plane in Figure 2). The dielectric function components in the (28) Azzam, R. M. A.; Bashara, N. M. In Ellipsometry and Polarized Light; North-Holland Publishing Co.: Amsterdam, 1977; Chapter 4. (29) Ro¨seler, A. In Handbook of Ellipsometry; Tompkins, H. G., Irene, E. A., Eds.; William Andrew Publishing: Springer, 2005; p 779.
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j ) x, y, z directions are represented by εx ) εy * εz. The refractive index is defined as n ) εˆ . A fundamental problem in the case of quantitative spectral interpretation of ultrathin organic films is that the parameters for the oscillator strengths of characteristic vibrational bands are typically unknown. The film thickness and the high-frequency refractive index might be determined from VIS-ellipsometric measurements. A set of oscillator parameters, necessary for IR ellipsometric simulations, is often derived from evaluation of IR or ellipsometric spectra of reference samples. As stated by Parikh and Allara22 for polycrystalline reference samples, the situation of identical inter- and intramolecular interactions, and electronic structure and packing density between the reference and the studied film, is never met exactly, but is still a very useful approximation. In the present work the oscillator parameters are taken from the evaluation of polarized reflectance spectra of a HDT monolayer. The transition dipole moments of the CH2 stretching vibrations are generally used for evaluation of the tilt angle γ of the methylene chains (tilt with respect to the surface normal) and the twist angle δ (rotation about the long axis of the molecule) as shown in Figure 2. The angle φ was set to 45° because this ensures the uniaxial symmetry (nx ) ny) in our simulations. The in-plane isotropy of the prepared alkanethiol films was experimentally verified by comparison of ellipsometric measurements of the same sample rotated by 90°. The parameter F in eqs 2 and 321,29 can be transformed into the dimensionless oscillator strength S (as defined in ref 30) by dividing it by the square of the oscillator position in wavenumbers (∼νi02). The parameters of the oscillator strengths Fi are related to the transition dipole moments Mi by30
Fi ∼ Mi2
(4)
At a particular orientation of the oscillators (νs and νas of CH2 group), the single components of the transition dipole moments in the molecular coordinate system (j ) x, y, z) (Figure 2) are related to the principal transition dipole moment Mmax as
Mix2 ) Mmax2 sin2 θi cos2 φi Miy2 ) Mmax2 sin2 θi sin2 φi Miz2 ) Mmax2
(5)
2
cos θi
where θ and φ are the Euler angles. Since the transition dipole moments of the symmetric and the asymmetric stretching vibrations of CH2 group are mutually orthogonal and both are perpendicular to the chain axis when an all-trans conformation exists, the tilt angle of the chain can be determined from the following equation,30
cos2 θs + cos2 θas + cos2 γchain ) 1
(6)
where θs and θas are the respective tilt angles of the methylene stretching vibrations and γchain is the tilt angle of the methylene chain. Assuming uniaxial orientation cos2 φi ) sin2 φi ) 1/2 holds and the tilt angles (θ1, θ2) can be determined from the ratio of x, y, and z components in eq 5:
sin2 θi Fix Mix2 ) ) Fiz M 2 2 cos2 θ iz
(7)
i
As described at the beginning of this section, the parameters of the oscillator strengths are determined from simulation of the measured ellipsometric or polarization dependent reflection spectra within optical layer models. (30) Handbook of Infrared Spectroscopy of Ultrathin Films; Tolstoy, V. P., Chernyshova, I. V., Skryshevsky, V. A., Eds.; Wiley & Sons, Inc.: New York, 2003. (31) Burkert, U.; Allinger, N. L. Molecular Mechanics; American Chemical Society: Washington, DC, 1982.
Figure 3. Simulated (black) and measured (gray) reflection spectra (top, p-polarized reflection absorbance; middle, s-polarized reflection absorbance; bottom, tan Ψ) of a HDT monolayer on GaAs. The incidence angle was set to 60° to ensure defined reflectance measurements in which the probed spot was smaller than the sample size (7 × 19 mm2).
Results and Discussion The analysis of the CH2 stretching bands provides information about the average conformation and orientation of the methylene backbone of alkanethiols. The analysis of the band shapes and amplitudes of the stretching vibrations via optical simulations of IR ellipsometric spectra determines the average molecular orientation of the organic molecules on the substrates. All the measured spectra were baseline-corrected. The weaker bands due to Fermi resonances at about 2890-2900 and 2932 cm-1 were not considered in our calculations. Monolayer of HDT on GaAs. Figure 3 shows measured and simulated polarized reflectance spectra together with the corresponding tan Ψ spectra of a HDT monolayer on GaAs. Within the simulation procedure first the s-polarized and then the p-polarized spectra were fitted. The procedure is described in detail in ref 21. For n∞ ) 1.41 and a monolayer thickness of 2.3 nm (corresponding nearly to the extended length of HDT) a tilt angle of γ ) 19° and a twist angle of δ ) 45° was determined following the evaluation discussed in the previous section. The band frequencies 2851 cm-1 νs(CH2) and 2919 cm-1 νas(CH2) are characteristic of a well-packed all-trans zigzag conformation. These data support the assumption that the HDT film is highly ordered and comparable to a self-assembled monolayer. The following parameters were determined for the symmetric and asymmetric CH2 stretching vibrations: F1x(2919 cm-1) ) 40000 cm-2; F1z(2919 cm-1) ) 5000 cm-2; Γ1 ) 17 cm-1; F2x(2851 cm-1) ) 67500 cm-2; F2z(2851 cm-1) ) 6500 cm-2; Γ2 ) 16 cm-1. With substitution of these values in eq 7, a molecular tilt angle of 19° was calculated from (6). Assuming about 10% uncertainty in the determined oscillator strengths (when correlated to the noise level in the s- polarized reflectance spectra), the uncertainty for the calculated tilt angle remains within (2°. The uncertainty might be higher since the anisotropy of the highfrequency refractive indices is not known and because of the effects of inhomogeneity. The determined values for F1 ) 85000 cm-2 and F2 ) 141500 cm-2 (from Fi ) Fix + Fiy + Fiz) are similar to the parameter of oscillator strengths as used for the calculations of polycrystalline polyethylene in ref 26 (Fi ) 3Fiiso): F1 ) 61000 cm-2; Γ1 ) 17.4 cm-1; F2 ) 151000 cm-2; Γ2 ) 15 cm-1. The oscillator parameters of the weaker CH3 bands
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Figure 4. (a) Measured tan Ψ spectra of octanedithiol monolayer on GaAs (bottom) and HDT monolayer on GaAs (top). The baseline was corrected for convenience. The incidence angle was 65°. (b) Spectra for tilt angles of 12°, 18°, 24°, 30°, 36°, and 42° simulated based on the optical constants used for HDT on GaAs.
cannot be determined with sufficient accuracy and were therefore not included in the simulations. The determined tilt angle for HDT on GaAs is slightly higher than but consistent with the previously reported values.8,10 The slight deviation (about 4°) from the documented values in refs 8 and 10 can be ascribed to the already discussed uncertainties as well as to the various measurement conditions applied in the different experiments. Molecular Orientations in HDT and Octanedithiol Monolayers on GaAs. The comparison between the experimental tan Ψ spectra of octanedithiol and HDT on GaAs is shown in Figure 4a. Figure 4b presents the simulated monolayer spectra of HDT based on the optical constants already used in the previous section. The appearance of the weak CH3 stretching band at 2966 cm-1 in the measured spectra of the octanedithiol film on GaAs might be indicative of sample contamination (most likely octanethiol), which precludes a quantitative interpretation of the tan Ψ spectra of octanedithiol on GaAs. The comparison of the experimental spectra (Figure 4a) with the simulations made for several tilt angles in Figure 4b implies that the weak negative bands for octanedithiol on GaAs could be qualitatively interpreted by larger tilt angles compared with those of HDT. Such characteristic band shapes are well-known for differently oriented molecular films.17 Another feature which is observed in the tan Ψ spectra of octanedithiol in Figure 4a is that the positions of CH2 stretching vibrations are shifted to higher frequencies. Some wavenumber shift is observed in the simulated spectra for which one and the same oscillator frequencies have been used for the calculations at different tilt angles. This indicates that part of this wavenumber shift is a pure optical effect, which occurs when the tilt angle becomes larger than about 30°. This behavior is well-illustrated in Figure 4b. The band shape upon change from positive to negative passes through a derivative-like band shape at about 30° tilt. Hence, the comparison of the experimental and the calculated amplitudes and band shapes in Figure 4 suggests a monolayer coverage with an average tilt angle larger than 30°. Molecular Orientation in HDT Monolayer on Au. The comparison between the experimental and simulated tan Ψ spectra of HDT on Au is shown in Figure 5. The same oscillator parameters which were determined for HDT on GaAs were used as input for the calculations. For the fit of the spectra shown in Figure 5a only the z-values for the parameters of the oscillator strength were adjusted: F1z(2919 cm-1) ) 6100 cm-2, F2z(2851 cm-1) ) 9600 cm-2. From these values the tilt angle of 22° and the twist angle of 45° are calculated. This tilt angle is consistent
Figure 5. (a) Simulated (black) and measured (gray) tan Ψ spectra of a HDT monolayer on gold. The incidence angle was set to 65°. (b) Simulations for tilt angles from 12° to 42°.
with published values determined from RAIRS.6,22,32 The similar results found for the HDT film on GaAs and Au imply a similar organizational structure of the HDT film on both substrates. Owing to the so-called surface selection rule the bands in tan Ψ spectra of thin organic films on metallic substrates look like typical IR bands in transmission spectra. Ellipsometric Maps. To study the homogeneity of the organic layer in more detail, the samples were mapped using the FT-IR ellipsometer at BESSY II.25 2D maps for two different samples are shown in Figure 6. The 2D maps show some large-scale inhomogeneity of the molecular layers, which can be deduced from the variation of the band amplitude at 2922 cm-1. For the film on Au, the change of the band amplitude could be assigned to a thickness variation of about (0.4 nm. It is important to note that in the laboratory measurements a sample area of at least 24 mm2 or larger is probed. These data provide information about the average values for tilt angle and thickness of the probed area. In the infrared optical simulations, the roughness of the substrates (typically 0.5 nm for GaAs and 2 nm for Au) is not taken into account in the idealized layer models. Due to the long wavelengths in the IR spectral range, the influence of roughness on phase shift and depolarization is much smaller than that in the VIS spectral range. However, the microscopic roughness may lead to a variation of the molecular orientation on a microscopic scale. In summary, the interpretation of IR spectra can give only average values for tilt angles and thicknesses for the probed area, which in our case in the laboratory experiments typically is between 24 and 50 mm2 and between 0.3 and 1 mm2 in the synchrotron experiments. (32) Porter, M. D.; Bright, T. B.; Allara, D. L.; Chidsey, C. E. D. J. Am. Chem. Soc. 1987, 109, 3559.
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Figure 6. Interpolated 2D map of the CH2 band amplitude at 2922 cm-1, which was taken from tan Ψ spectra: (a) HDT on Au; (b) HDT on GaAs. The step width was 1 mm.
Conclusions In this article, quantitative evaluations of polarizationdependent IR spectra of alkanethiol and alkanedithiol films on GaAs and gold substrates were presented. Tilt and twist angles of molecules in octanedithiol and HDT films were calculated from IRSE spectra. For HDT film on GaAs, an ordered self-assembled monolayer with molecules mainly in an all-trans conformation and a tilt angle of 19° was identified. These film characteristics resemble closely those observed for the same monolayer on Au. The monolayer formed by octanedithiol molecules on GaAs are more disordered with an average tilt angle larger than 30°. Overall, the spectra of monolayers on GaAs showed characteristic band shapes correlating with the molecular orientations. Synchrotron
mapping ellipsometry results allowed the investigation of the homogeneity of the monolayers. Acknowledgment. The authors thank I. Fischer for technical support and D. Aulich for his help in the synchrotron measurements. The financial support by the Deutsche Forschungsgemeinschaft (DFG 436 BUL 113/127), the Senatsverwaltung fu¨r Wissenschaft, Forschung and Kultur des Landes Berlin, and the Bundesministerium fu¨r Bildung and Forschung is gratefully acknowledged. This work was also performed in part at the U.S. Department of Energy, Center for Integrated Nanotechnologies, at Los Alamos National Laboratory (Contract DE-AC52-06NA25396) and Sandia National Laboratories (Contract DE-AC04-94AL85000). LA8026557