Hydrocarbon Molecules Deposited onto Silicon Surfaces: A DFT Study of Adsorption and Conductance

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1 J Clust Sci (2007) 18: DOI /s ORIGINAL PAPER Hydrocarbon Molecules Deposited onto Silicon Surfaces: A DFT Study of Adsorption and Conductance A. M. Mazzone Æ R. Rizzoli Received: 22 March 2007 / Published online: 28 November 2007 Ó Springer Science+Business Media, LLC 2007 Abstract The purpose of this study is a systematic description of the properties of small deposited clusters in dependence of the cluster geometry and composition and of the shape of the adsorbing surface. Therefore hydrocarbon molecules deposited onto the dimerized Si(100) surface and onto monolayer steps of this surface, are considered and the properties of these systems are determined using the Density Functional and scattering theories. It has been found that, though the step is a weaker sink than the flat surface, the molecules are bonded to the step and the adsorption geometries reproduce the ones of the flat surface. The transmission function depends on the type of molecule and of the substrate and on the transport channels available to the deposited system. However the contact potential has a paramount importance and deep resonances are produced by a proper tuning of this quantity. Keywords Hydrocarbon molecules Silicon steps DFT Scattering theories Introduction The adsorption of hydrocarbon molecules onto the Si(100) surface is the focus of many current researches. These systems have in fact four aspects which deserve attention. First, from a basic point of view, they touch upon the important problem of the interaction of a small cluster with a surface. Second, in studies on the functionalization of Si(100) [1 3] molecular adsorption is regarded as a relevant step towards the formation of films of monolayer thickness with the wanted pattern of deposition. Third, in the field of molecular electronics (see, for instance, [4, 5] and references therein) a small molecule is considered as an electronic device which allows charge transport along its populated energy levels so that the transport A. M. Mazzone (&) R. Rizzoli C.N.R-IMM- Sezione di Bologna, Via Gobetti 101, Bologna 40129, Italy mazzone@bo.imm.cnr.it

2 870 A. M. Mazzone, R. Rizzoli properties depend on the electronic structure of the molecule. Fourth, vicinal surfaces are considered an important template for the production of 1D or 2D structures and highly vicinal silicon surfaces are currently used for the production of single-atom chains formed by covalent and metallic elements [6 13]. All these aspects are dealt with in the present study, though not all of them with the same accuracy. The study further develops a similar study [14] whose focus was on the computational side and on large systems with a complex geometry treated by using simple semi-empirical Hamiltonians. Here the accuracy of the representation is improved by the use of the Density Functional theory though, as in [14], the evaluation of the transport properties is based on the simplest formulation of the transport theory available in the current chemico-physical literature. The calculations illustrate the electronic properties and the conductance of a system formed by hydrocarbon molecules deposited onto the flat Si(100) and onto a monolayer step on this surface and attempt to state a clear link between these two types of properties. The Computational Methods From the standpoint of functionality, important properties of the silicon surfaces are a high reactivity and the many shapes that can be accessed by varying the sample orientation and the processing temperature [2]. This surface, in fact, reconstructs, even at room temperature, by the formation of dimer rows (a silicon dimer is a pair of atoms lying on the silicon surface with a bondlength equal to 2.4 Å, which is slightly relaxed with respect to the bulk value of 2.32 Å). The structure of the surface, when cut with a very low angle with respect to the (100) axis, is formed by steps of a monolayer height. In the steps the dimerization axis rotates 90 on passing from the upper to the lower terrace and, according to the current nomenclature, the step is SA or SB, depending on the orientation of the dimers in the upper terrace being parallel or perpendicular to the step-edge. Of the two steps, SA is the one with the lowest formation energy [15, 16] and for this reason has been considered in the following calculations. The structure of the step and of the flat Si(100) is illustrated in Fig. 1 (this plot and the one in Fig. 3 have been also presented in [17] and are repeated here for commodity of the reader). In the following calculations the exposed surface, either Si(100) or SA, is described using a cluster model, which has been previously applied to the study of deposition of atoms, chains and small molecules [17 19]. As reported below, adsorption of hydrocarbons involves several adsorption geometries. Their study requires a large computational workload and this justifies the small size of the clusters used in the present series of calculations. However the evaluation of characteristic energies, using clusters of a different size, showed changes limited to a few percents. The cluster is formed by four to five atomic layers of crystalline silicon with compensating hydrogen atoms applied to the bottom layer and with the exposed surface free. A semi-infinite solid is simulated by the use of 2D periodic boundary conditions parallel to the surface. For SA, accordingly to the model adopted in [15], each terrace has a pattern (for testing purposes also 6 9 2

3 Hydrocarbon Molecules Deposited onto Silicon Surfaces 871 Fig. 1 Lateral view along (110) of the SA step (top) and of the flat dimerized Si(100) surface (bottom) and structures have been analyzed) and on Si(100) the number of dimers is equal to the ones on a terrace onto SA. The molecules are deposited at an height h along the z axis perpendicular to the surface and the stable shape of the deposited system is obtained from the minimization of the total energy. In most works up-date the evaluation of transport properties is based on the Landauer Bůttiker theory [20]. In this formulation the current voltage characteristic I V at zero temperature is given by I(V) = 2e/h$N(E,V)dE where N(E,V) is the transmission function. Its value is determined by the three contributions of the active region and of the left and right absorber, indicated as L and R, respectively, according to NðE; VÞ ¼ TrðC L ðvþgðe; VÞC R (V) G ðe; VÞÞ: ð1þ In this equation G(E,V) is the Green function of the electronic charge and C L and C R are the matrix representation of the self-energies coupling the active device with the absorbers. The evaluation of these energies is complex and is generally dealt with solving the DFT Hamiltonian for the three regions and using iterative techniques to correct for their interactions. However in [21, 22] the assumption is made that the C s are the representation of the contacts potential in some chosen basis. Furthermore a simple power law, i.e. C = AR b l, where R l is an atomic location and A,b define the potential type, is adopted for these potentials. Under this assumption the Green s function in the equation above becomes G(E,V) = 1/(ES- (H-i/2(C L + C R ))), where S and H are the overlap and the Hamiltonian matrix in the active region and the C s are the contact potentials defined above (in the following we are concerned only with the intrinsic properties of the conductance and therefore the dependence on V is dropped from N). It is underlined that this evaluation has to be regarded as a semi-empirical estimate of the contacts self-energies. In the same spirit, other approaches in the

4 872 A. M. Mazzone, R. Rizzoli field of molecular electronics have used an equilibrium first-principle Hamiltonian for the nanostructure and the electrodes are described by using semi-empirical energies for the outermost atoms [23 25]. However for systems of the complexity, such as the ones considered in the present study, the specification of the contact geometry remains a complex task, due the large dimensions of the simulation cell, to its irregular shape and to the fact that several contact shapes are possible. In fact, the external leads can be directly connected to the molecule, being either suspended or deposited onto the surface. For Si(100) the deposited contacts can be directed parallel or perpendicular to the dimer rows and for SA there is the additional choice of a direction parallel or perpendicular to the step edge. In [18] it was shown that, instead of a rigorous evaluation of N accounting for the details of the contact geometry, the use of a parametrized form leads to simple, yet insightful, results. This formulation has been adopted also in the present study and the values of C L,R are chosen so as to reproduce the ones of H. The assumption underlying this modeling is that the allowed energies in the contacts and in the active region have a similar structure and the main difference between them consists in a rigid shift. A convenient presentation of these results is obtained using a value normalized to H o = Tr[H]. This presentation, in fact, offers three distinct advantages. First, it gives a direct hint on the relationship between the electronic structure in the active device and in the contacts. Second, it offers a simple understanding of the formation of resonances. In fact, using constants values S o and H o for S and H, the expression of the Green function G is G = 1/(ES o - H o (1 - i )). Poles of this function, located at the energies ES o = H o, may lead to resonant effects (i.e. enhancement of N). Third, it will be shown below that this assumption allows to state a clear functional relationship between the transmission function, on one side, and the characteristic energies and the type of the deposited molecule, on the other side. A disadvantage of the formulation is that it leaves the contact shape unspecified, which is of scarce relevance in the context of this work. The SIESTA software soler has been applied to the energy minimization and to the evaluation of the matrices required by N. The inputs for these calculations are: a spin-polarized Hamiltonian, a mesh cutoff 80.0 Ry, the Troullier Martins nonlocal pseudopotentials in the Kleinman Bylander form and the Ceperley Alder correlation functional. The electronic configuration of Si, C and H is 3s 2 3p 2,2s 2 2p 2 and 1s 1. The basis sets are formed by Slater-type Pseudo-Atomic Orbitals with either single or double-f quality plus polarization. The parameters of the electronic configuration of the deposited systems, reported below, are the binding energy and the Density of States, i.e. E b and DOS. E b is the total energy of the deposited system measured with respect to an ensemble of free atoms of the same composition. The DOS refers to the surface atoms (for this reason is indicated below as Local Density of States) and its evaluation is based on an internal utility of SIESTA by grouping the allowed energy levels with an approximately equal E and broadening E of a factor around 0.4 ev. For the molecules in the gas phase (Table 1) the HOMO level and the ionization potential I p are also reported. It is known that a rigorous estimate of I p requires techniques beyond DFT [26]. Here I p is simply calculated from the difference between the

5 Hydrocarbon Molecules Deposited onto Silicon Surfaces 873 Table 1 Properties of hydrocarbon molecules Molecule E b (ev/atom) HOMO (ev) I p (ev) R b (Å) Si (-1.60) (7.50) 2.28 (2.26) CH (CH)(1.111) C 2 H (-4.42) (CC), 1.13 (CH)(1.203, 1.061) C 2 H (-3.06) (CC), 1.17 (CH)(1.339, 1.085) C 6 H (-4.97) (10) 1.41 (CC), 1.14(CH)(1.399, 1.089) E b, HOMO, I p and R b indicate the binding energy, the HOMO level, the ionization potential and the length of the CC or CH bond. The values in brackets are taken from [26 29] HOMO and the Fermi energy and therefore only an indicative meaning has to be attributed to these values. The Structural and Electronic Properties of the Deposited Systems Four hydrocarbon molecules, i.e. CH 2 (methylene), C 2 H 2 (acetylene), C 2 H 4 (ethylene) and C 6 H 6 (benzene), have been considered. This choice is intended to give a systematic view of an increasing number of CC bonds. However acetylene and ethylene have also a practical interest for the growth of carbon films and benzene is commonly considered in the field of sensor devices. The main properties of the four molecules in the gas phase are presented in Table 1. The comparison of the hydrocarbons with the Si 2 molecule shows the reduced length of the CC bonds, their strength and the deep-lying energy levels of the hydrocarbons. The first two properties are suggestive that the molecules can be easily hosted in the silicon skeleton and strongly bonded to it. The third one indicates that energy channels at variance with respect to the ones of the silicon substrate are made available by the hybridization of the C Si charges. In addition the comparison with experiment (in brackets in the Table) shows that, in agreement with literature data, the LDA Hamiltonian correctly describes the bondlenghts while overestimates E b (a further main divergence with respect to experiment is observed for I p. The crude character of this estimate has been pointed out above). However the dependence of E b on the molecule type is in agreement with the experimental trend. The views in Fig. 2 show the structure of the four molecules (top) and also some molecules deposited onto SA (bottom). This presentation indicates that the adsorption sites on a dimerized surface can be distinguished into two main groups, i.e. on the dimer top (as shown by benzene and methylene on the upper and lower SA terrace) or between dimers (acetylene on the lower SA terrace). Furthermore the molecule may be adsorbed parallel to the surface or perpendicular to it. A careful theoretical and experimental investigation of the possible adsorption sites has been performed for acetylene and, to a less extent, for ethylene deposited onto Si(100) (references are given in [17, 30 32]. These studies indicate the existence of four main adsorption geometries. These are di-r, either bridging between dimer atoms or

6 874 A. M. Mazzone, R. Rizzoli Fig. 2 The molecules used in this study. From top to bottom clockwise: methylene, acetylene, ethylene and benzene. The view at the bottom shows deposition directly on dimer top or in the trench between dimers. The figure shows also the single and double CC bonds and is color coded (on-line). Carbon, hydrogen and silicon atoms are marked green, pink and blue cross two dimer rows, and tetra-r, both in a pedestal location or along the dimer rows (these locations are reported in Fig. 3 in the order a, b, c, d). All the four configurations are bonding and a main difference is in the number of dimer atoms with which the molecule makes bonds: two in di-r and four in tetra-r configurations. In [31] a careful review of recent, and less recent, studies is presented and an analysis is made of the evaluation of the binding strength of those adsorption sites. It is concluded that both experiment and theory favor the di-r locations, though some divergences exist in the theories and are thought to arise from the technicalities of the calculations. No direct simulation is available for methylene and benzene. However the concept of cycloaddition, which is adopted in the chemical literature to account for hydrocarbons adsorption onto Si(100), suggests that the adsorption sites for these two molecules are equal to the ones of acetylene and ethylene. In the context of this study the difference between the flat and the stepped surface represents an important issue. However the adsorption sites on Si(100) and on the terraces of SA are likely equal. Subtle differences between the two cases are expected only if the site is near the step-edge. In such case the molecule-surface interaction is modified, with respect to the flat surface, by the different height of the dimers in the two terraces and by the slightly relaxed bonds of the step-edge atoms [33, 34]. To elicit these differences the calculations were performed placing the molecules in the four configurations above onto Si(100) and onto SA and in this last

7 Hydrocarbon Molecules Deposited onto Silicon Surfaces tetra c d 16 y[a] di a b Fig. 3 Known adsorption sites for acetylene and ethylene deposited onto Si(100).The plots show only the CC axis of the molecule and the arrows indicate the SiC bonds. a, b, c, d indicate the two di-r and the two tetra-r, adsorption geometries x[a] case the locations were near the step-edge. Only in the case of benzene, owing the many configurations accessible to this large molecule, the adsorption sites were limited to a di-r locationl, with the molecule oriented parallel or perpendicular to the surface. In addition, a small chain of n molecules was simulated by using n replicas of one molecule deposited in one of the sites mentioned above. A detailed description of these adsorbed systems is being presented elsewhere [35] and only the essence of these calculations is reported here. The adsorption sinks and the progression of their adsorbing strength were equal on Si(100) and on SA, the main difference between the two cases lying in the strength of adsorption and on the fluctuations arising from different sites. These effects have two sources, i.e. structural differences, such as the ones arising from the adsorption sites located on the upper or lower part of the step edge, and the different modes of relaxation of the two surfaces. A qualitative presentation of these effects is given by the calculations in Fig. 4. It is further added that, while the results for C 2 H 2 and C 2 H 4, in agreement with literature, favor the di-r, locations, for CH 2 the locations in the trench between dimers are stronger sinks owing to the larger number of atoms with which the molecule makes bonds. For the same reason for C 6 H 6 adsorption with the molecule parallel to the surface is preferred to the one with the molecule oriented perpendicular to the surface. The properties of the electronic charge of the deposited systems are illustrated in Figs. 4 and 5, which show the binding energy E b and the LDOS, respectively, for the four molecules deposited onto Si(100) and onto SA. For a deposited system the values of E b are determined by the contributions of the intrinsic binding energy of the exposed surface and of the deposited molecule and from the adsorption energy

8 876 A. M. Mazzone, R. Rizzoli A E b [ev/atom ] B E b [ev/atom ] Si(100) SA SA optimized molecule type SA,n=1 SA,n=2 clean methylene acethylene ethylene benzene Fig. 4 (A) The binding energy of the deposited system as a function of the molecule type. Deposition template: Si(100) and SA. (B) The effect of the increase of the number n of the deposited molecules. In this figure and in Fig. 7 the lines are drawn as a visual guidance A 0.2 LDOS Si(100) clean SA clean B SA+CH 2 SA+C 6 H 6 LDOS E(eV) Fig. 5 The LDOS for the conditions shown of the deposited molecule. This sum is obviously complicated by the structural relaxation occurring upon adsorption and by the accompanying effects of charge exchange and hybridization. With the aim of illustrating these effects, in Fig. 4 two series of calculations are reported for SA. In one case the molecules were deposited

9 Hydrocarbon Molecules Deposited onto Silicon Surfaces 877 at an height h which was optimize maintaining a rigid lattice. In the second case (indicated as optimized) the entire system was relaxed to an energy minimum (the data for Si(100) refer to this second procedure). In agreement with the general features outlined above, the calculations in Fig. 4 show that the values of E b are responsive either to the type of the surface or to the deposited molecule. For Si(100) the dependence of E b on the molecule type almost parallels the binding strength of the molecules in the gas phase, as reported in Table 1. Therefore a modest alteration of the geometry and of the electronic configuration of the molecule is produced by the bonds formed upon adsorption by the dangling orbitals of the molecule with the silicon atoms underneath and for acetylene and ethylene this is also a literature result. In fact, a change of the bond lengths in the range of a few percent is generally reported for the adsorption of these molecules on Si(100) [14]. The comparison of Si(100) and SA indicates that adsorption on SA reproduces the features of the flat surface, a part from the increase of the binding energy. The comparison of the E b of the two surfaces without the deposited molecule suggests that this property arises from the inherent weakness of SA and is due to the relaxed bonds of the step-edge atoms. The modest decrease of E b, observed in the relaxed step, is in line with the limited structural changes occurring upon adsorption. A detailed account of the structure of the deposited surface, either Si(100) or SA, and of the structure of the molecule upon adsorption is presented in [35]. Here we mention only that in the figure the scattering of the SA data-points arises from the differences in the adsorption sites on the upper or lower side of the step-edge. As shown by the figure, these effects are perceivable only in the rigid lattice and lead to E b changes in the range of a few percents. A more substantial increase of E b, in the range of 0.2 ev/atom, was only found for benzene deposited perpendicular to the surface with respect to the parallel orientation. This result is in line with transport studies in molecular electronics [36], which underline the differences arising from the orientation of the deposited molecule. The dependence of E b on the number n of the deposited molecules (Fig. 4B) shows that in almost all cases E b decreases with the increase of n. However exceptions also exist and a slight increase of E b is observed in a small chain of acetylene deposited in the tetra-r locations. From the physical point of view these features indicate that the formation of attractive, and bonding, or, repulsive, and anti-bonding, interactions has a complex dependence on the type of the adsorbed molecule and on its adsorption site. The practical implication of this result is that the growth of linear chains aligned along the step-edges is a selective process determined by two key factors, namely, the type of incident molecules and the allowed adsorption sites. Further properties of the electronic structure are reported in Fig. 5, where a comparison is made between the LDOS of the clean structures (Fig. 5A) and of the SA steps with the deposited molecules (Fig. 5B). In the clean structures the energies around the Fermi level (the zero of the energy scale) are due to the 3p states of the silicon atoms whereas the deeper bands arise from the 3s states and from the hybridization of these states with 3p ones. The bandwidth distribution appears responsive to the structural details and is different on Si(100) and on SA. Upon adsorption these bands are altered by a further hybridization with the 2p states of the

10 878 A. M. Mazzone, R. Rizzoli molecule (Fig. 5B) and it is also seen that this process is responsive to the molecule type. The Conductance It is useful to cast the following results in the perspective of the current literature, though the efforts directed at the study and systematization of the transport properties are intensive and not easily summarized. In broad terms the studies in the physical literature center on quantization effects and on the attainment of 1D and 2D limit. On the other side, in the chemical literature, the study of conduction in molecular systems [36] leads to the identification of three different regimes: coherent electron motion, quasi-particle formation and diffusion, ohmic and gated electron transfer. In the coherent regime the motions can be non-resonant or resonant and the most peculiar feature in this last case is that there is no dependence on the structural parameters, but only on the number of available modes. It will be shown below that many features of the deposited structures qualify their conductance as of the resonant type. The properties of the transmission function N are illustrated by the calculations in Figs. 6 and 7. The calculations in Fig. 6 show the effects of the allowed energy levels E and of the contact potential for deposition onto Si(100) (Fig. 6A) and onto SA (Fig. 6B). The values of N for the different molecules have been projected onto the same curve for a given. The relevant aspects of these calculations are two. First, N has primary dependence on E and on. It is in fact seen that the value of N increases monotonously with the decrease of the absolute value of E. The effect A transmission function N B transmission function N =10 =1 =10 = E(eV) Fig. 6 The transmission function as a function of the contact potential (A) Si(100) (B) SA

11 Hydrocarbon Molecules Deposited onto Silicon Surfaces 879 is obviously attributable to the reverse proportionality between G and E through G = 1/(ES o - H o (1 - i )). Second, the effect of on N is complex. When strongly deviates from H o (i.e., = 10,100), and N are proportional. When is approximately equal to H o, the formation of well-defined resonances is observed and the related energies correspond to the slightly populated states above the Fermi energy. Therefore the origin of these conductive channels has to be attributed to electrons promoted from the contacts above the Fermi see of the active device. In Fig. 7 the effects of the deposited molecules are observed on finer scale than in Fig. 6. The quantity plotted in this figure is the difference dn between the N values for the surface with and without the deposited molecule. The values refer to the energy values around the N maximum (i.e. E= 2.25 ev) though lower than the resonant ones. The conductance appears enhanced in the deposited structures and the explanation of these features is offered by the properties of the DOS (Fig. 5). In fact, the extra-states produced by the deposited molecules increase the number of the conductive channels and this, in turn, leads to the observed increase of N. To conclude this section we underline that the comparison of the results above with experiments or with higher-order calculations is impossible, due to the developing state of the art in this field. On the other side, a comparison of the scattering formulation adopted in this study with Hartree-Fock calculations has already been presented in [22]. Therefore the validation of the present results relies on two general facts, related to the current state of experiment and theory. First, the stability of linear deposited structures (Fig. 4) is in agreement with the current use of vicinal surfaces for the production of structures of this type. Second, the scarce effect of the structural parameters on the transmission function is reminiscent of the resonant mode in molecular transport and the participation to conduction of the energy levels above the Fermi see suggests that these energies have to be seen as A 0.04 DN =100 =10 = B DN clean =100 =10 =1 methylene acetylene molecule type ethylene benzene Fig. 7 The contribution to the transmission function due to the molecule type

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