On the Origin of the Energy Gain in Epitaxial Growth of Molecular Films

Letter pubs.acs.org/JPCL

On the Origin of the Energy Gain in Epitaxial Growth of Molecular Films Christian Wagner,*,† Roman Forker,§ and Torsten Fritz§ †

Peter Grünberg Institut (PGI-3) and JARA-Fundamentals of Future Information Technology, Forschungszentrum Jülich, 52425 Jülich, Germany § Institut für Festkörperphysik, Friedrich Schiller Universität Jena, 07743 Jena, Germany ABSTRACT: The material properties of organic thin films depend strongly on their order. The different types of epitaxy may complicate the exploration of the large variety of ordered systems and its exploitation in potential electronic devices. In this Letter, we develop a coherent description of the driving force that creates epitaxial systems. We focus on flat-lying organic adsorbates and explain the energy gain in commensurate, point-online, and line-on-line epitaxy. We use potential energy maps to visualize our concept and to derive a relation that allows anticipating epitaxial growth from low-energy electron diffraction (LEED) data. A unified description facilitates the identification and interpretation of experimentally observed adsorbate structures, whereas the rationalized expectation from LEED means a considerable speed gain if suitable candidates for organic−organic epitaxy are searched for in a combinatory approach. SECTION: Surfaces, Interfaces, Catalysis

A

one molecule. The case of organic heteroepitaxy is illustrated using the example of quaterrylene (QT) molecules on a hexaperi-hexabenzocoronene (HBC) ML.21 To accentuate the specific properties of organic substrates and adsorbates, we use the case of single atoms of an arbitrary kind on a Au(111) surface for comparison. For the sake of simplicity, we will always refer to the adsorbed species as “molecule”. Because they are used for illustrative purpose only, the discussed adsorbate lattices do not correspond to the experimental results in ref 21. The driving force for the occurrence of epitaxial molecular films is a gain in the total PE which is the sum of both, the molecule−substrate potential EMol‑Sub and the intermolecular potential EMol‑Mol (if not stated otherwise, all energies discussed are per molecule). We want to study the properties that arise from distinct relations between substrate and adsorbate lattice (i.e., type of epitaxy and EMol‑Sub), whereas EMol‑Mol, which solely depends on the adsorbate structure (lattice and azimuthal orientation of the adsorbed molecules), is treated in a very schematic way. Let us assume an undisturbed adsorbate structure (i.e., a structural equivalent to a free-standing film consisting of flat-lying molecules) with lattice vectors b1̃ and b2̃ that would form on a hypothetical substrate without any corrugation where Ẽ Mol−Sub = V0 (V0 < 0). The tilde above symbols refers to this hypothetical case of an undisturbed adsorbate structure on an uncorrugated substrate. This structure features the lowest possible intermolecular potential

tomic epitaxy is among today’s standard techniques for the manufacturing of electronic devices and functionalized surfaces.1−3 Epitaxy involving organic molecules is, by comparison, a rather young development.4−7 Organic films can possess new, desired material properties, depending on its order or growth mode (smooth surfaces, high charge carrier mobility, highly ordered multilayer systems, etc.). This holds for monolayers (MLs)8 as well as for thicker crystalline layers.9,10 The growth mode of the latter is often preassigned by the structure of the former,11,12 which explains the strong interest in epitaxial MLs. Unfortunately, epitaxy is a rather intricate concept as soon as it goes beyond commensurism. In particular, in the case of organic adsorbates epitaxial relations of lower degree, that is, point-on-line (POL) or line-on-line (LOL), are frequently observed.4,13−21 The complex, anisotropic inner structure of the molecules and the weak intermolecular interactions (per atom, if compared with inorganic species) often result in different metastable phases and interface structures. The complex structure also has its benefits as even completely different molecular species can be epitaxially grown on each other.17−21 Usually, the attempts to quantify the energy gain in epitaxial systems are either specifically tailored for the substrate−adsorbate system under study22 or are universal but quite simple.4 Here we introduce a unified scheme to describe and quantify the energy gain in epitaxial systems (i.e., specific combinations of substrate and adsorbate) by using potential energy (PE) calculations for realistic examples. The discussion is limited to 2D lattices containing one flat-lying molecule per unit cell. The term “molecule” always refers to the basis of the lattice. Our considerations remain valid even if the basis contains more than © 2012 American Chemical Society

Received: November 25, 2011 Accepted: January 18, 2012 Published: January 20, 2012 419

dx.doi.org/10.1021/jz2015605 | J. Phys. Chem. Lett. 2012, 3, 419−424

The Journal of Physical Chemistry Letters

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Ẽ Mol−Mol. In contrast, on a real surface with a corrugation, a lattice with EMol‑Sub < V0 might form yielding an energy gain Egain = EMol − Sub − V0 (Egain < 0)

parameters23 were used for the atom−atom pair potential calculation with the software PowerGrid.14,18,24 For the calculation, the QT molecule was placed coplanar onto the HBC ML with an azimuthal angle of 16° (cf. bottom-right corner of Figure 1). The Esingle map for this angle is highly structured, which helps us to visualize our concept. Keep in mind that Esingle will change if the azimuthal angle changes. The force-field calculations should produce realistic results for physisorbed species. Because we discuss rather site-specific energy differences than absolute energies, the accuracy of the calculation is assumed to be sufficient. For the same reason, no absolute energy scale is given in Figure 1. Whereas we first discuss the PE of a single molecule or atom, Esingle, we subsequently derive the relevant expressions for the (average) PE of a molecule in a ML, EMol‑Sub. For the following discussion of the different types of epitaxy, the strict periodicity of the PE maps in Figure 1 is of high relevance. Commensurate epitaxy is the most intuitive type of epitaxy with all adsorbate molecules occupying equivalent positions on the substrate. Obviously, these are the positions of minimal PE like the hollow sites of the (111) surface in Figure 1a. Hence, the molecule−substrate energy is

(1)

This structure most likely deviates from the undisturbed structure discussed above (b1 ≠ b1̃ ,b2 ≠ b2̃ ). Consequently, an energy penalty ̃ − Mol (Ep > 0) Ep = EMol − Mol − EMol

(2)

for the intermolecular interaction has to be paid that increases with increasing deviation. For a given system of substrate and adsorbate, V0 and Ẽ Mol−Mol do not depend on the structure of the adsorbate. Real adsorbate structures will then represent a minimum in the sum Esum = Egain + Ep. We will now elucidate the relation between the structure and Egain, followed by a brief discussion of Ep. We favor a description of the structure in reciprocal space over a description via the epitaxial matrix. The former is beneficial as many POL and LOL structures belong to one and the same Egain value. The PE maps for the two exemplary systems mentioned above are shown in Figure 1. They represent the positiondependent PE of a single adsorbed molecule Esingle(r). The maps are calculated by a force-field approach. OPLS nonbonding

EMol − Sub = min(Esingle(r))

(3)

In-higher-order commensurate epitaxy means that there is a commensurate super cell and that all molecules in the basis of the super cell have identical orientations but occupy nonequivalent positions on the substrate (Figure 1b). Hence, there exists a primitive but noncommensurate lattice with only one molecule per unit cell. The average molecule−substrate energy per molecule with s molecules in the commensurate super cell is given by EMol − Sub =

1 s

s

∑ Esingle(r0 + rl) l=1

(4)

The rl denote the relative positions of each molecule in the super cell. The optimal adsorption sites are found by searching for the minimum in EMol‑Sub while varying r0 within one substrate unit cell. Now, the on-line types of epitaxy, namely, POL and LOL, shall be discussed. Both types bear strong similarities and are of high importance for the growth of organic layers.4,18 Because the position-dependent potential Esingle(r) is periodic, it can be expanded into a Fourier series.1,22 Esingle(r) = V0 +

∑ VG exp[i(Gr + ϕG)] G≠0

(5)

The sum is over all reciprocal substrate lattice vectors G. VG and ϕG are the amplitude and the phase of each standing PE plane wave. The location-independent (attractive) potential V0 denotes the incommensurate energy. Unlike noncommensurism, incommensurism is the absence of any epitaxial relation. Using eq 5, the molecule−substrate potential per molecule becomes (with n molecules in the domain)

Figure 1. PE maps of a single atom on Au(111) in panels a and c and a single QT molecule on a HBC layer in panels b and d. Dark colors mean a low PE value. Four exemplary adsorbate lattices are shown. The substrate unit cell is drawn in yellow; the adsorbate unit cell is drawn in red. The structures exhibit the following epitaxial relations and properties of the epitaxial matrix C: (a) Commensurate: C contains integers only. (b) Commensurate in higher order: C contains only rational numbers. (c) POL: C contains a column of integers. (d) LOL: elements of C are irrational numbers. The commensurate supercell in panel b as well as the coincident lattice lines in panels c and d are depicted as dashed blue lines.

EMol − Sub = V0 +

1 n

n

∑ ∑ VG exp[i(Grj + ϕG)] G≠0 j=1

(6)

For small, noncommensurate domains, there is no simplification to eq 6. If n is, however, sufficiently large (typically, n ≈ 1000),24 the limit of an inf initely extended 420



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Figure 2. Reciprocal space plots of the lattices in Figure 1. The coincident reciprocal substrate lattice vectors G1, G2, and Gc are marked by purple arrows. (a,b) Reciprocal substrate (black, filled) and adsorbate lattice (red, empty) of the commensurate and in-higher-order commensurate real space lattices shown in Figure 1a,b. In panel a, the coincident vectors are of first order, and in panel b they are of higher order. (c) Reciprocal adsorbate lattice of the POL structure in Figure 1c superimposed on the FFT of the PE map in Figure 1c. The spot positions in the FFT resemble the reciprocal substrate lattice (cf. panel a). One of the first-order vectors is coincident. (d) Reciprocal adsorbate lattice of the LOL structure in Figure 1d superimposed on the FFT of the PE map in Figure 1d. Spot positions are identical to black dots in panel b. One higher-order vector is coincident.

domain is applicable. Then, for each vector G, one of two cases applies to the inner sum of eq 6: (1) There is no coherence between the specific PE plane wave (specified by the reciprocal substrate lattice vector G) and the adsorbate lattice. In this case the inner sum in eq 6 is zero (but the individual addends are not). Or (2) there is such a coherence, which means a coincidence between G and one reciprocal lattice vector of the adsorbate. In this Letter, the term coincidence always means identity with a reciprocal substrate lattice vector. In this case, the product Grj always yields a multiple of 2π. Hence, the inner sum of eq 6 can be anything between −nVG and +nVG, depending on the phase ϕG. How many of such coherences can exist? There can only be a coincidence of k = 1 or 2 linear independent reciprocal lattice vectors of substrate and adsorbate. The case of k = 0 characterizes incommensurate epitaxy. There, the inner sum of eq 6 is equal to zero for all values of G, and hence the average molecule−substrate potential is the incommensurate energy EMol‑Sub = V0. The case of k = 2 describes the commensurate group of epitaxial relations. For commensurate epitaxy, the two coincident vectors G1 and G2 are of first order, whereas at least one is of higher order in the case of higher order commensurism. This is shown in Figure 2a,b. The case that describes the on-line types of epitaxy is characterized by k = 1. Here the average molecule−substrate energy is EMol − Sub = V0 + VGc exp(i ϕG ) c

where Gc is the one coincident reciprocal substrate lattice vector. The phase ϕGc is defined by the relative shift of substrate and adsorbate lattice parallel to Gc. Real structures are characterized by ϕGc = π as this yields a minimum in EMol‑Sub = V0 − VGc. The relative shift is observable in the experiment and can be used to verify the results of PE calculations.21 A comparison with eq 1 yields Egain = −VGc for the on-line types of epitaxy. The picture drawn above is still somewhat oversimplified as a coincident reciprocal substrate lattice vector Gc implies also a coincidence of all multiples of Gc. Hence, eq 7 should, in fact, read ∞

EMol − Sub = V0 +

∑ VjG exp(i ϕjG ) c

j=1

c

(8)

On inorganic surfaces, the coefficients VjGc decrease rapidly with j, and thus eq 7 is usually applicable, whereas on organic substrates the contributions for j > 1 can be significant. The two types of on-line epitaxy are distinguished as follows: POL epitaxy means that the coincident reciprocal substrate lattice vector Gc is of f irst order, that is, a primitive one. This puts restrictions on the adsorbate lattice that are less strong compared with commensurate epitaxy but stronger than for the LOL type. LOL epitaxy occurs if any (nonprimitive) reciprocal substrate lattice vector is coincident.18 Theoretically, this requirement can always be fulfilled if Gc is of sufficiently high order. Although the resulting adsorbate lattice would then be

(7) 421



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Figure 3. Comparison between LEED patterns of a HBC ML on Au(111) taken at 52.7 eV (off center) in panel a and at 23.3 eV in panel c to the VG values for a single C atom on a HBC ML in panel b. The area of the filled circles corresponds to the magnitude of VG. The circles which are filled red mark experimentally found POL/LOL epitaxy on a HBC ML substrate along the respective lattice lines. A strong correspondence between the LEED spot intensities and the energetic gain is found. The (0,0) spot and the (1,0) spot of the Au(111) substrate are indicated in panel a.

commensurate structures are usually “further away” from the ideal unit cell, while there is always a LOL structure close by, the following relation usually holds

technically of the LOL type, the associated gain in energy VGc would be negligible. Therefore, in practice, one should speak of LOL epitaxy only if Gc is sufficiently small. In real space, POL and LOL epitaxy mean that certain lattice lines of adsorbate and substrate are parallel and identically spaced.18 Note that the energy gain for the commensurate types of epitaxy cannot be derived from just two of the coefficients VG. This may seem counterintuitive because there are the two coincident vectors G1 and G2, but only the knowledge of all values VG and ϕG allows deducing the minimum of Esingle(r). Obviously, for the on-line types of epitaxy, the coefficients VG play an important role. It is possible to examine them directly by looking at the Fourier transform of the respective PE maps. In Figure 2c,d, the reciprocal adsorbate lattice is superimposed on the FFT of the PE maps. Apart from artifacts resulting from the finite PE map size, the FFTs show the reciprocal substrate lattice. The intensity of the spots is a direct measure for the value of the coefficients VG. It shows the (relative) energy gain achievable in the case of an epitaxial alignment along the respective real-space lattice lines. The fundamental difference between inorganic and organic substrates (Figures 1 and 2c,d) is whether mainly first-order coefficients VG contribute to the potential as in panel c or whether there are also sizable contributions from higher order coefficients as in panel d. The PE map in panel c is close to a pure cosine potential. This has an important consequence for complex molecular adsorbates. Within the limit of atom−atom pair potentials, the PE map for such an adsorbate is just the sum of the maps of all of its individual atoms. All of these maps are cosine potentials of identical periodicity. As the sum over two cosine functions is another cosine function, the PE map for any adsorbate on Au(111) is (within the limits mentioned above) similar to Figure 1c. We can further conclude that for substrates with a single atom in the unit cell the higher order coefficients VG are small compared with the first-order VG values. Consequently, POL epitaxy is rewarding on these surfaces, whereas LOL epitaxy means only very little energetic gain. In contrast, for an organic substrate, some of the higherorder coefficients VG have values similar to the first-order values (Figure 2d). This is in complete agreement with the experimental finding that organic molecules frequently grow in POL mode on noble-metal single crystals,4,13−16 whereas the growth on organic substrates is dominated by LOL epitaxy.18−21 To quantify the occurrence of POL, LOL, and commensurate epitaxy in different scenarios, we compare the energy penalty Ep to Egain. Ep increases with the deformation of the unit cell away from its ideal shape. Because the few existing

Epcomm > EpPOL > EpLOL

(9)

The energy gain for the different types of epitaxy follows the opposite trend (cf. FFT in Figure 2c,d and Figure 3b). comm POL LOL Egain < Egain < Egain

(10)

The sum Esum = Egain + Ep is minimized in all real structures and will always be negative or zero. The “worst case” is the incommensurate epitaxy of the undisturbed lattice with Ep = 0 and Egain = 0. Relations 9 and 10 reveal why none of the types of epitaxy is generally prevalent and why even different types can be observed for one and the same system.8,25 A small distortion of the unit cell and a small epitaxial energy gain is as feasible as a large distortion and a large gain. As Ep also increases with increasing substrate unit cell size, LOL epitaxy occurs, especially on organic substrates (with a rather large unit cell), where Epcomm and EpPOL are often just too large. In contrast, commensurism is prevalent in atomic epitaxy where Egain is large due to the covalent bond type, and thus moderate lattice mismatches are acceptable. The conclusions drawn above will be valid in most cases. There are exceptions beyond the scope of this contribution like the LOL epitaxy of sexithiophene on Au(111).26 We now introduce a method to estimate the coefficients VG for flat organic substrates directly from LEED experiments. Our example is a 2D lattice of atoms adsorbed on a HBC ML substrate. Exemplarily, carbon atoms were chosen. Using atoms in the calculation eliminates the need to consider inner degrees of freedom for the adsorbate. Instead of showing the PE map and its FFT, we directly display the calculated values VG in Figure 3b. We show only the eight highest VG values to get a clearer figure. The plot in Figure 3b makes use of the six-fold substrate symmetry and resembles the reciprocal substrate lattice. Despite its simplicity, the model of just atoms as adsorbate has close relations to experiments done with complex molecular adsorbates: The red circles in Figure 3b mark experimentally found POL and LOL structures of QT and 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) on HBC.18,21,27 They are all among the eight highest VG values of the model system. The plot in Figure 3b is compared with two LEED patterns of a HBC ML on Au(111) taken at two different energies. The remarkable similarity between relative LEED spot intensities and VG values can be interpreted using kinematic LEED theory. 422



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(7) Tautz, F. S. Structure and Bonding of Large Aromatic Molecules on Noble Metal Surfaces: The Example of PTCDA. Prog. Surf. Sci. 2007, 82, 479−520. (8) Dienel, T.; Loppacher, C.; Mannsfeld, S. C. B.; Forker, R.; Fritz, T. Growth-Mode-Induced Narrowing of Optical Spectra of an Organic Adlayer. Adv. Mater. 2008, 20, 959−963. (9) Dimitrakopoulos, C.; Malenfant, P. Organic Thin Film Transistors for Large Area Electronics. Adv. Mater. 2002, 14, 99−117. (10) Ueno, N.; Kera, S. Electron Spectroscopy of Fundamental Organic Thin Films: Deep Insights into Valence Electronic Structure in Relation to Charge Transport Property. Prog. Surf. Sci. 2008, 83, 490−557. (11) Koller, G.; Berkebile, S.; Krenn, J. R.; Netzer, F. P.; Oehzelt, M.; Haber, T.; Resel, R.; Ramsey, M. G. Heteroepitaxy of Organic-Organic Nanostructures. Nano Lett. 2006, 6, 1207−1212. (12) Forker, R.; Kasemann, D.; Dienel, T.; Wagner, C.; Franke, R.; Müllen, K.; Fritz, T. Electronic Decoupling of Aromatic Molecules from a Metal by an Atomically Thin Organic Spacer. Adv. Mater. 2008, 20, 4450−4454. (13) Mannsfeld, S.; Toerker, M.; Schmitz-Hübsch, T.; Sellam, F.; Fritz, T.; Leo, K. Combined LEED and STM Study of PTCDA Growth on Reconstructed Au(111) and Au(100) Single Crystals. Org. Electron. 2001, 2, 121−134. (14) Mannsfeld, S. C. B.; Fritz, T. Understanding Organic−Inorganic Heteroepitaxial Growth of Molecules on Crystalline Substrates: Experiment and Theory. Phys. Rev. B 2005, 71, 235405. (15) Franke, R.; Franke, S.; Wagner, C.; Dienel, T.; Fritz, T.; Mannsfeld, S. C. B. Epitaxial Nanolayers of Quaterrylene: Influence of the Substrate on the Growth of the First and Second Monolayers. Appl. Phys. Lett. 2006, 88, 161907. (16) Wagner, C.; Franke, R.; Dienel, T.; Forker, R.; Jacob, R.; Fritz, T. Degradation and Segregation: Thermal Stability and Highly Ordered Epitaxial Thin Films of Large Aromatic Molecules. Appl. Phys. Lett. 2007, 91, 113111. (17) Staub, R.; Toerker, M.; Fritz, T.; Schmitz-Hübsch, T.; Sellam, F.; Leo, K. Scanning Tunneling Microscope Investigations of Organic Heterostructures Prepared by a Combination of Self-Assembly and Molecular Beam Epitaxy. Surf. Sci. 2000, 445, 368−379. (18) Mannsfeld, S. C. B.; Leo, K.; Fritz, T. Line-on-Line Coincidence: A New Type of Epitaxy Found in Organic-Organic Heterolayers. Phys. Rev. Lett. 2005, 94, 056104. (19) Campione, M. Rubrene Heteroepitaxial Nanostructures With Unique Orientation. J. Phys. Chem. C 2008, 112, 16178−16181. (20) Campione, M.; Raimondo, L.; Moret, M.; Campiglio, P.; Fumagalli, E.; Sassella, A. Organic-Organic Heteroepitaxy of Semiconductor Crystals: α-Quaterthiophene on Rubrene. Chem. Mater. 2009, 21, 4859−4867. (21) Kasemann, D.; Wagner, C.; Forker, R.; Dienel, T.; Müllen, K.; Fritz, T. Line-on-Line Organic-Organic Heteroepitaxy of Quaterrylene on Hexa-peri-hexabenzocoronene on Au(111). Langmuir 2009, 25, 12569−12573. (22) Smilgies, D.-M.; Kintzel, J. E. J. Epitaxial Orientations of ParaSexiphenyl Platelets Grown on Alkali Halide (001) Surfaces. Phys. Rev. B 2009, 79, 235413. (23) Damm, W.; Frontera, A.; Tirado-Rives, J.; Jorgensen, W. L. OPLS All-Atom Force Field for Carbohydrates. J. Comput. Chem. 1997, 18, 1955−1970. (24) Mannsfeld, S. C. B.; Fritz, T. Advanced Modelling of Epitaxial Ordering of Organic Layers on Crystalline Surfaces. Mod. Phys. Lett. B 2006, 20, 585−605. (25) Stadler, C.; Hansen, S.; Kröger, I.; Kumpf, C.; Umbach, E. Tuning Intermolecular Interaction in Longrange-Ordered Submonolayer Organic Films. Nature Phys. 2009, 5, 153−158. (26) Kiel, M.; Duncker, K.; Hagendorf, C.; Widdra, W. Molecular Structure and Chiral Separation in α-Sexithiophene Ultrathin Films on Au(111): Low-Energy Electron Diffraction and Scanning Tunneling Microscopy. Phys. Rev. B 2007, 75, 195439.

There, the scattering potential is the inverse Fourier transform of the scattering amplitudes f G. γ(r) =

∑ fG exp(iGr) G

(11)

By comparing eqs 5 and 11 (neglecting the phase ϕG), we find that the scattering cross section |f G|2 and the amplitudes of the PE plane waves VG are related if the scattering potential γ(r) is related to Esingle. For physisorbed species, the latter quantities bear indeed clear similarities. The PE landscape of a physisorbed adsorbate is mainly determined by Pauli repulsion and van der Waals attraction. Both quantities are related to the local substrate electron density. Because the scattering of lowenergy electrons is determined by the local electron density as well, γ(r) and Esingle(r) should have a similar dependency on r, explaining the observed similarities between |f G|2 and VG. The recipe to identify prospectively stable organic−organic heterosystems with a well-fitting epitaxial relation is summarized now: Each candidate (substrate or adsorbate) should be grown alone as ML on a weakly interacting substrate, and LEED patterns of each sample should be recorded at identical energies. If there are prominent LEED spots in pairs of these patterns that have (nearly) the same distance from the (00) spot, then the two respective materials are promising candidates for a POL or LOL epitaxy when combined as substrate and adsorbate. This recipe saves time and experimental effort, especially if many substances are under consideration. In summary, we have illustrated how PE gain emerges in epitaxial systems. Qualitative statements on the energy gain in different epitaxial growth modes were derived from FFTs of simulated PE maps. The importance of individual Fourier components for the POL and LOL epitaxy was shown, and a novel method to estimate their value from LEED experiments was introduced. We anticipate that this method will have a substantial impact on the field of organic electronics as it allows a systematic search for suitable material combinations that offer highly ordered stable interfaces.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

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ACKNOWLEDGMENTS Financial support by the Deutsche Forschungsgemeinschaft (DFG) Grant No. FR875/11-1 is gratefully acknowledged. We thank SCB Mannsfeld for valuable discussions that helped us considerably in improving the manuscript.

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REFERENCES

(1) Matthews, J. W. Epitaxial Growth; Academic Press: New York, 1975. (2) Chambers, S. A. Epitaxial Growth and Properties of Thin Film Oxides. Surf. Sci. Rep. 2000, 39, 105−180. (3) Herman, M. A.; Richter, W.; Sitter, H. Epitaxy: Physical Principles and Technical Implementation; Springer: New York, 2004. (4) Hooks, D. E.; Fritz, T.; Ward, M. D. Epitaxy and Molecular Organization on Solid Substrates. Adv. Mater. 2001, 13, 227−241. (5) Rosei, F.; Schunack, M.; Naitoh, Y.; Jiang, P.; Gourdon, A.; Laegsgaard, E.; Stensgaard, I.; Joachim, C.; Besenbacher, F. Properties of Large Organic Molecules on Metal Surfaces. Prog. Surf. Sci. 2003, 71, 95−146. (6) Schreiber, F. Structure and Growth of Self-Assembling Monolayers. Prog. Surf. Sci. 2000, 65, 151−256. 423



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(27) Wagner, C. Potential Energy Minimization as the Driving Force for Order and Disorder in Organic Layers, Ph.D. Thesis, Technische Universität Dresden, 2009.

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On the Origin of the Energy Gain in Epitaxial Growth of Molecular Films

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