Structural Characterization of Alkylsilane and Fluoroalkylsilane Self

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Structural Characterization of Alkylsilane and Fluoroalkylsilane SelfAssembled Monolayers on SiO by Molecular Dynamics Simulations 2

Otello Maria Roscioni, Luca Muccioli, Alexander Mityashin, Jerome Cornil, and Claudio Zannoni J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b03226 • Publication Date (Web): 21 Jun 2016 Downloaded from http://pubs.acs.org on June 25, 2016

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The Journal of Physical Chemistry

Structural Characterization of Alkylsilane and Fluoroalkylsilane Self-Assembled Monolayers on SiO2 by Molecular Dynamics Simulations Otello Maria Roscioni,∗,† Luca Muccioli,∗,†,‡,¶ Alexander Mityashin,§ Jérôme Cornil,k and Claudio Zannoni† † Dipartimento di Chimica Industriale “Toso Montanari”, Universit` a di Bologna, 40136 Bologna, Italy, ‡ Laboratoire de Chimie des Polymères Organiques, UMR 5629, Université de Bordeaux, 33607 Pessac (France), ¶ Institut des Sciences Molécularies, UMR 5255, Université de Bordeaux, 33405 Talence (France), § IMEC, 3001 Leuven, Belgium, and k Laboratory for Chemistry of Novel Materials, Université de Mons, 7000 Mons, Belgium E-mail: [email protected]; [email protected] Phone: +39-051-2093387; +33-5-40006320

∗

To whom correspondence should be addressed † Dipartimento di Chimica Industriale “Toso Montanari”, Università di Bologna, 40136 Bologna, Italy ‡ ‡ Laboratoire de Chimie des Polymères Organiques, UMR 5629, Université de Bordeaux, 33607 Pessac (France) ¶ ¶ Institut des Sciences Molécularies, UMR 5255, Université de Bordeaux, 33405 Talence (France) § § IMEC, 3001 Leuven, Belgium k k Laboratory for Chemistry of Novel Materials, Université de Mons, 7000 Mons, Belgium †

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Abstract We present molecular dynamics simulations of self-assembled monolayers (SAMs) chemisorbed on an atomically flat amorphous silicon dioxide substrate. We model two prototypical SAM-forming alkylsilanes, octadecyl trichlorosilane (OTS) and 1H,1H,2H,2Hperfluorodecyl trichlorosilane (FDTS), that find widespread use in organic electronic applications.

Crucially, our model does not rely on an explicit bonding between

the alkylsilane and the substrate, thus allowing for the spontaneous organization of molecules into regular structures, that we studied as a function of coverage. By comparing the calculated tilt angle, film thickness, and lattice parameters with experiments, we conclude that the simulated morphologies are quantitatively consistent with the experimental evidences, demonstrating the accuracy of the simulation methodology. We take advantage of the atomistic resolution of the calculations for carrying out a detailed one-to-one comparison between the structure and the electronic properties of the two SAMs. In particular we find that OTS molecules show a coverage-dependent tilt, while FDTS molecules are always vertically oriented, regardless of the coverage. More importantly for organic electronic applications, we observe that OTS SAMs do not alter the electrostatic potential of silica, while FDTS SAMs induce a negative voltage shift which increases with coverage and saturates at about -2 volts.

Introduction Trichlorosilane 1,2 and phosphonic acid 3 derivatives can be grafted onto hydroxylated silicon oxide surfaces yielding chemically bound semicrystalline two-dimensional films which are in their essence self-assembled monolayers (SAMs). The resulting surfaces have controlled chemical and physical properties of interest for organic electronics applications, such as low gate leakage currents, good chemical/thermal stability, minimized interface trap state densities, increased compatibility with both p- and n- type organic semiconductors, increased capacitance, and efficient fabrication via solution-phase processing methods. 4 These are ob-

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viously desired qualities in particular for manufacturing gate dielectrics in organic field-effect transistors (OFET), for which the deposition of an organic semiconductor directly onto the untreated standard SiO2 substrate leads to ill reproducible results in terms of threshold/onset voltage and charge carrier mobilities due to the presence of defects. 5,6 The effect of SAM functionalization on OFET performances is often remarkable since it leads to controllable shifts of the threshold voltage (which depends on the chemical nature of the SAM itself), it allows to modulate the charge carrier mobility of the overlying organic semiconductor, 7–15 and even to control the band gap opening in highly conductive materials such as graphene. 16 The microscopic origin of the modulating effect of SAM on OFET performances is a matter of intense theoretical studies. On the one hand, two main intertwined physical origins have been identified: i) the SAM, even if supposed globally neutral, can modify the surface electrostatic potential of the bare oxide, 4,17–19 and consequently induce charge accumulation or depletion in the interfacial region of the organic semiconductor, 14,20 an effect often described as due to the presence of an interfacial or surface dipole; 13,21–23 ii) the roughness of the SAM surface is normally lower than that of untreated surfaces 24 so that the SAM reduces the number of surface defects which may give rise to the formation of deep traps, and in turn increases the charge carrier mobility in the semiconductor. 6 On the other hand, much less attention has been paid to the non-ideality of the SAM-semiconductor interface (coverage, composition, roughness, defects), and to the relationship between the local structure of the SAM and the electrostatic potential at the surface. This is because the non-ideality of the SAM-semiconductor interface cannot be captured entirely by quantum-chemistry calculations based on small-sized periodic cells; it is also difficult to be probed experimentally since it requires an array of different complementary techniques. 25 To account for thermal and structural disorder from a computational point of view, in particular for quantitatively predicting the change in surface potential induced by the SAM, it is necessary to resort to classical models that allow simulating sufficiently large structures

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(composed at the very minimum by hundreds of molecules). 26,27 By employing the atomistic molecular dynamics technique, we investigate and compare the microscopic structure of two popular SAMs with different polarity, formed by either n-octadecyltrichlorosilane (OTS) or perfluorodecyltrichlorosilane (FDTS) (Figure 1). The recent simulation literature on octadecyl SAMs on metal surfaces is quite abundant, in particular with many studies by Saha and coworkers describing the SAM stability and its dynamics at different partial coverages on gold substrates. 27–31 Turning to SiO2 surfaces, alkoxysilane-coated SiO2 nanoparticles have been simulated both in vacuum 32 and in alkane solvents; 26 Ewers and Batteas also studied functionalized silica interfaces, focusing on the modification of friction and attractive forces introduced by OTS coatings. 33,34 Regarding flat SiO2 surfaces, Castillo et al. studied OTS and the shorter dodecyl-TS on cristobalite at different coverages; 35 Black et al. performed a very similar investigation by employing a reactive force field which allows bond breaking and forming, to mimic the SAM formation process, 36 but obtaining tilt angles quite far from experimental estimates. Contrary to OTS, fluorinated SAMs were less studied, with a main focus on wetting and friction properties, 37–40 and their structure on SiO2 was never investigated in detail. The interest in the molecular arrangement at the interface is however rising because of many possible applications beyond microelectronic devices, 41 ranging from corrosion prevention to self-cleaning anti-fouling treatment. 42 To fill this gap, we present in the following detailed structural models of self-assembled monolayers arising from substituted alkyl-silanes grafted on amorphous silicon oxide surfaces, extending our previous study on the electrostatic effects of these SAMs on transistor characteristics. 20

Computational details The bulk structure of amorphous silica and the surface silanol groups were described with the Clay force field, 43 which was shown to reproduce accurately the structure of water/quartz

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NVT conditions, until energy equilibrium was reached. After this step the surface is characterized by an irregular distribution of silanol groups, similarly to real amorphous silica surfaces. Note that this model is different from those relying on crystalline silica structures (as for instance in reference 35 ) since it takes into account surface roughness and local chemical inhomogeneities. Indeed, recently some of us have shown that thin films of the nematic liquid crystal 5CB align differently at the interface with crystalline (cristobalite) versus amorphous silica surfaces. 50 This finding shows that even tiny differences in the morphology of chemically identical substrates produce dramatic effects on an overlying molecular film, and consequently that cristobalite could not be an appropriate model for amorphous silica. The hydroxylated substrate of amorphous silica was used to construct five samples of OTS and four of FDTS SAMs by simulating the grafting of individual molecules to silanol (Si−OH) groups on the surface. We had in mind the experimental process of the monodentate, noncrosslinked SAM formation 51 beginning with the reaction between a trichlorosilane derivative and the hydroxylated surface of amorphous silica, followed by hydroxylation of the remaining chlorine atoms. 52–55 As a result, the alkyl silane groups are fully hydroxylated and bonded to the silica surface by single Sisurf −OSi(OH)2 R bonds, with R being the alkyl chain. In our approach, every silanol group SiOH selected for reaction with the SAM was replaced by a Si atom and a OSi(OH)2 R residue. The SAM was therefore composed of molecular ions, each with the formal charge of the replaced − OH group (-.525 e in the Clay FF, which we distributed evenly over the three oxygens), so as to maintain the charge neutrality of the whole slab. No covalent bond was specified between the Si atom and the oxygen of the OSi(OH)2 R residue. However, the electrostatic and Lennard-Jones interactions between the SAM oxygen atoms and the Si atoms of the silica surface are sufficiently strong (similar to those between Si and O silica atoms) to keep the molecules adsorbed, while leaving them with enough mobility to reach a convenient docking site during the MD simulations, hence to self-assemble. Actually, at the coverage and surface area we simulated, no empty space

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on the surface appears, and the lateral movement of SAM molecules after equilibration is limited to fluctuations of a few tenths of ˚ A. The coverage of the resulting SAMs ranged from 2.5 to 4.5 molecules/nm2 . The samples with the highest surface density, that is 4.5 molecules/nm2 for OTS and 3.8 molecules/nm2 for FDTS, correspond to a defect-free, closely packed system. Only for these two samples, the initial structure was built by replicating a SAM crystal cell (inferred from the simulations at lower coverage) on the amorphous silica slab. The range of coverages considered is consistent with the experimental one of 3.1–5.3 molecules/nm2 reported for a SAM at full coverage. 6,56,57 MD simulations of OTS/SiO2 and FDTS/SiO2 samples were carried out in the NVT ensemble. The SAM and the upper layer (∼ 15 ˚ A) of the SiO2 slab were subject to thermal motions while silicon and oxygen atoms in the bottom part of the slab were kept frozen to save computing time. First, the systems were annealed at 400 K for about 200 ns; subsequently they were cooled to 300 K and, once thermal equilibrium was reached (in about 100 ns), a production trajectory of 60 ns was produced for each sample. Molecular Dynamics simulations of SAM/SiO2 were carried out using the program NAMD. 58

Results and discussion Overall structure of the self-assembled monolayers In order to introduce some of the aspects discussed in the remainder of the paper, we start by inspecting a few typical top- and side-view snapshots of OTS and FDTS SAMs shown in Figure 2 as a function of the surface coverage. Without going into details, it is apparent that i) OTS and FDTS have in some degree a different structure ii) OTS appears to be tilted; iii) coverage does play a role in determining the film roughness and morphology; and iv) some crystalline hexagonal positional order is always present, at least in a fraction of the sample. For achieving a more quantitative information on the SAM structure, we show in Figure 3 7



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OTS: 2.5 molecules/nm2





FDTS: 2.5 molecules/nm2




Figure 2: Lateral and top views of OTS and FDTS SAMs on silica at different surface coverages. Atoms are represented as spheres and coloured according to the element: red/oxygen, yellow/silicon, grey/carbon, white/hydrogen, green/fluorine. (top panels) the linear density profile across the films, from which it becomes apparent how alkylated chains exhibit a much lower density with respect to fluorinated ones, not 8


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surprisingly considering the bulk densities of the corresponding alkanes and perfluoroalkanes (liquid octadecane has a density of about 0.78 g/cm3 at 25 ◦ C, and perfluorodecane of 1.77 g/cm3 ). However the local densities reached at high coverages by the SAMs appear to be higher than those of the corresponding liquids, suggesting the presence of dense solid-like packing. It is also worth noting how the monolayers become more uniform at increasing coverage, with the density reaching a plateau at z=15-20 ˚ A, in particular for the thickest OTS films. To better verify the uniformity of the SAMs, it is useful to also analyze the distributions of local thickness plotted in the middle panels of Figure 3, where the thickness is defined as the projection on the surface normal of the silicon to terminal-carbon distance for each grafted molecule. The thickness distributions become sharper at increasing coverage, and this is reflected as expected in a decrease of the (top) surface roughness, reported in Table 1. Roughness was calculated as the root mean square deviation of the SAM height, defined as the minimum vertical position accessible by a cubic tip with a lateral size 1.8 ˚ A. At any coverage, the root mean square roughness is very low, ranging from ≈ 4 ˚ A to ≈ 2 ˚ A, with OTS values very similar to those reported by Castillo et al. for MD simulations on cristobalite. 35 The average thicknesses of the SAMs are also reported in Table 1. The computed values represent the silicon to terminal-carbon distance discussed above, corrected by adding an estimated shift of 4 ˚ A to take into account the van der Waals diameter of the terminal atoms (the same correction is applied to the probability distributions, in Figure 3). Hence, the reported values can be compared directly to experimental data of thickness, typically coming from ellipsometry measurements, and are considered to bear an uncertainty of ± 2 ˚ A. 1 Experimental data for OTS are abundant but rather scattered, probably because the preparation of a uniform SAM with full coverage is difficult to achieve experimentally and requires special care. 51 At full coverage, typically assumed to be close to 5 molecules/nm2 , film thicknesses range from 21 to 27.6 ˚ A: 1,6,51,59,60 the computed OTS value of 24.6 ˚ A at 4.5 molecules/nm2 is in line with this range, and all values in Table 1

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2.5 OTS (coverage) 4.5 4.2 3.6 3.0 2.5

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0.4

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0

15

20

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25

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Figure 3: Top: Linear density profile for OTS (left panel) and FDTS (right panel) monolayers at different coverages. Middle: Distribution of the thickness for OTS and FDTS monolayers at different coverages. Bottom: Distribution of molecular lengths (silicon to terminal-carbon atoms) for OTS and FDTS monolayers at different coverages. Coverages are given in units of molecules/nm2 .

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˚), tilt angle θ (deg), Table 1: Surface coverage (molecules/nm2 ), thickness (A order parameter hP2 i, percentage of alkyl chains in all-trans and kink configuA) of OTS and FDTS computed from MD ration (%), RMS surface roughness (˚ simulations. coverage OTS 2.5 3.0 3.6 4.2 4.5 FDTS 2.5 3.2 3.5 3.8

thickness

θtilt

hP2 i

all-trans

kink

roughness

16.8(5.0) 19.6(4.5) 21.7(3.3) 23.6(2.1) 24.6(0.8)

48(16) 38(15) 32(12) 25(8) 23(5)

-0.17(1) 0.11(2) 0.57(2) 0.851(8) 0.965(2)

12.7 17.0 27.3 36.1 50.4

31.3 41.1 59.4 71.7 85.5

4.1 4.2 3.5 2.6 2.1

12.8(2.8) 14.2(2.1) 15.7(1.1) 16.1(1.0)

37(20) 26(16) 15(9) 11(7)

0.09(2) 0.42(2) 0.77(1) 0.858(7)

5.4 8.6 21.9 29.9

26.7 35.2 54.5 64.4

3.0 2.7 2.3 2.3

are consistent with coverage-dependent thicknesses reported by Whitesides’ group (at cover˚ 59 ). age 5.0 molecules/nm2 , 27.4 ˚ A; 3.65 molecules/nm2 , 19.8 ˚ A; 2.8 molecules/nm2 , 15.4 A Experimental measurements for FDTS are less abundant, but we register a good agreement with the thickness of 13.5-15 ˚ A measured with ellipsometry on silica, 7,61,62 and with the height of 16 ˚ A measured with atomic force microscopy for FDTS islands on diamond-like carbon. 63 The distribution of conformations of molecules in the monolayers cannot strictly be extracted from, but should be compatible with the distribution of molecular lengths, shown in the bottom panels of Figure 3. The molecular length is defined as the distance between the silicon and terminal-carbon atoms for each grafted molecule, analogously to the way thickness is defined. The distributions of molecular lengths confirm, as it was possible to guess from the snapshots in Figure 2, that there are always at least a few SAM molecules in extended conformation, even at low coverages. In fact, a sharp rightmost peak ascribable to all trans conformation is present at any coverage. These conformations become predominant at high coverages, where the SAM is expected to be fully crystalline. A second peak, broader and positioned at about 1 ˚ A apart, is likely due to alkyl chains containing one or more bonds in

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a gauche conformation, as we shall analyze in the following. The exact conformation of molecules in OTS and FTDS monolayers is obtained by computing the dihedral angles along the alkyl chains. The trans configuration is assigned to any angle between 120◦ and 240◦ . With this convention, we do not make distinction between the helical and trans configurations of FDTS. However, this observable is still valid to identify the most stable geometries of FDTS, as the trans configuration is just a torsional deformation of the helical one (and not a distinct minimum). 64 The results in Table 1 show that a fraction of molecules is always in the all-trans conformation, corresponding to an extended geometry, in agreement with the distribution of molecular lengths. In addition to the all-trans conformation, we define a kink geometry as one that includes two opposite gauche angles separated by a trans one, and consequently is still linear. Using this relaxed criterion, we find that already at a coverage of 3.5 molecules/nm2 the majority of molecules is in a straight configuration. The percentage of molecules in the all-trans conformation is larger than the relative area of the outermost peak in the distribution of molecular lengths (Figure 3), because the fully extended conformation is assigned to alkyl chains with dihedral angles distorted up to 60◦ with respect to the conventional 180◦ equilibrium angle. On the other hand, the fraction of molecules in a straight configuration corresponds roughly to the three rightmost peaks in the distribution of molecular lengths.

Orientational and positional order Another very important observable for monolayers is the tilt angle θ, i.e. the angle formed by the long molecular axis with respect to the normal to the surface, where the long axis is defined as the end-to-end distance vector. It is well known that alkylated SAMs form tilted monolayers on most substrates, 65,66 and that their tilt angle decreases with coverage. 35 Specifically for OTS on silica, reported tilt angles start from 27-30◦ at low coverage 51,67 and reach 16-21◦ at full coverage. 51,59 Despite its apparent simplicity, the exact tilt angle appears 12


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to be hard to reproduce by MD simulations, possibly because it is strictly related to the intimate nature of the chemical bonding at the surface. 65 For instance, using a reactive force field in principle superior to the non-reactive we use here, Black et al. 36 obtained too high tilt angles, ranging from 32 to 40 degrees at full coverage (4.9 molecules/nm2 ). Conversely Castillo et al. 35 obtained values unsatisfactorily lower than the experimental ones (less than 10◦ at full coverage), probably because they simulated SAMs on a perfectly crystalline SiO2 substrate rather than on an amorphous one. Our average values for OTS reported in Table 1 are found to be in better agreement with experiments. Turning to FDTS SAMS, in the literature there is a consensus on the fact that they are not tilted, 68–71 though the values obtained from the analysis of the dichroism of NEXAFS spectra point to angles of 8-10 degrees, 71,72 probably because of thermal fluctuations around the equilibrium values of 0 degrees. In fact, the experiment does not provide information about the uniformity of the tilt, as it actually measures the expectation value of cos2 θ averaged over all molecules of the sample. Our estimation of θ=11◦ at high coverage (calculated from the average of cos θ) is in a good agreement with the experimental works. 68–71 To better appreciate the differences between the two SAM orientations, it is informative to inspect the distribution of cos θ rather than discussing only the average tilt angle. Figure 4 shows striking differences in the distribution of tilt angles computed for OTS and FDTS: for OTS, the distribution peaks at values different from zero, with the position of the peak moving to lower values with increasing coverage. On the contrary, for FDTS, the distribution of cosθ always peaks at zero at any coverage. Hence, for FDTS, there are always vertical chains, with their number increasing at increasing coverage: even if a given experimental technique could measure hcos2 θi 6=0, this indicates the spread of angles rather than a real tilt. The orientation of the monolayers can be further characterized by computing the order parameter of the chains with respect to specific directions. We start with the main orientation axis (tilted for OTS and normal to the surface for FDTS). To obtain it, an order matrix

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20 2.5 3 3.5 4 4.5 Coverage (molecules/nm2)

40 30 20

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10 2.5 3 3.5 4 Coverage (molecules/nm2)

0 0.4

0.6 0.8 Tilt Angle (cosθ)

1

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1

Figure 4: Distribution of the tilt angle of OTS and FDTS monolayers at different coverages. O is computed for each given configuration of a MD trajectory, O = hˆ u ⊗ uî, where uˆ is the long axis of the molecule (defined as the normalized distance vector from Si to terminal C atoms). The order matrix O is diagonalized, and the eigenvector n ˆ corresponding to the maximum eigenvalue λmax gives the molecular director, with the order parameter being hP2 i = 23 λmax −

1 2

= 32 hˆ n · uî − 21 . The corresponding order parameters are given in table

1. At low coverage, the SAM chains are most often lying flat on the SiO2 surface and with random planar orientation, as indicated by hP2 i values close to zero and consistently with the high tilt angles reported above. When coverage increases, SAM molecules get more closely packed and start to align parallel one to another, as confirmed by the high values of the orientational order parameter, typical of a smectic or crystalline system. OTS achieves a higher orientational order than FDTS: this is a consequence of the difference in the torsional potential along the alkyl chain. 20 While the full trans conformer for − CH2 −CH2 − corresponds to an equilibrium angle of 180 degrees, and hence to perfectly linear chains with all the C-C bonds lying in a plane, for − CF2 −CF2 − the minimum is at about 160 degrees, and consequently the shape of the chain is more irregular and the order parameter is lower. The peculiar differences of the orientation of Si-C and C-C bonds in FDTS and OTS are better highlighted by the order parameters of the carbon-carbon bonds along the chain, plotted in Figure 5, calculated with respect to the direction normal to the silica surface. For OTS

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we observe the typical alternation of the bond orientation for “odd” and “even” bonds, with increasing disorder moving towards the free surface. FDTS instead has a very peculiar trend due to the shift from H-substituted to F-substituted carbons (bonds 1,2,3); proceeding along the chain, the order parameter is low for the methylene carbons, then it suddenly increases for fluorinated carbons, and decreases smoothly getting close to the surface. The alternation behavior found for OTS is here absent, as expected from the − CF2 −CF2 − torsional potential. Despite the differences in the local order along the chain, we underline that for both SAMs we observe a strong effect of coverage on the bond order parameter, associated to the decrease in the tilt angle and the simultaneous increase of the overall orientational order at increasing coverage. The high orientational order parameters at high coverages 0.6 OTS (coverage) 4.5 4.2 3.6 3.0 2.5

0.5 0.4 〈P2〉z

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FDTS (coverage) 3.8 3.5 3.0 2.5

0.3 0.2 0.1 0 1

4

7

10 13 C−C bond

16 18

1

4

7 10 C−C bond

Figure 5: Order parameter hP2 i computed for the silicon-carbon (n=1) carbon-carbon bonds (n=2,. . . ) of the alkyl chain of OTS (left panel) and FDTS (right panel) monolayers at different coverages. and the snapshots in Figure 2 suggest the presence of positional order in the SAMs. For assessing it, we calculated the two dimensional radial distribution function in the x,y plane for the different samples, as shown in Figure 6. In practice this quantity is proportional to the probability of finding the center of mass of neighbouring molecule for a given position on the plane, while the reference molecule center of mass is fixed at the origin. Figure 6 clearly shows how hexagonal order is progressively growing at increasing coverage, for both SAMs, and that some local order is present also at low coverages. The positional order decreases 15



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rapidly with distance, hinting to a short translation correlation length as also reported by ˚ 59 ). Whitesides and coworkers (45 A The experimental hexagonal lattice parameter measured by grazing incidence X-ray diffrac-

Figure 6: Two-dimensional molecule-molecule radial distribution functions (arbitrary units) of OTS and FDTS monolayers at different coverages. The inset shows the average value of the tilt angle as a function of the coverages; vertical error bars correspond to the standard deviation. tion for alkylsilanes is on the range of α =4.1-4.3 ˚ A, 25,73–75 corresponding to values of the in-plane scattering vectors q⊥ = 2π/α =1.46-1.53 ˚ A−1 and to an intermolecular in-plane √ distance of d = 2α/ 3 =4.7-5.0 ˚ A. Actually, there is a lot of debate over these apparently small variations in the hexagonal lattice parameter: Ulman proposed the spacing, and the tilt angle as well, to be dependent on the axial / equatorial position of the Si−OR bond. 65 Fontaine et al. 76 suggested that it is the formation of siloxane bonds (Si−O−Si) between the SAM molecules which is responsible for the reduction of d from ≈4.8 ˚ A to ≈4.3 ˚ A. Wang et al. 51 suggested that in the case of crosslinking, an even lower intermolecular distance of d =4.1 ˚ Ais achieved, together with an increase in the tilt of the SAM chains. On the simulation side, thioctadecanethiol on Au showed an average sulphur-sulphur distance of d=4.8 ˚ A for partial coverages, 29 decreasing down to d=4.5 ˚ A at full coverage. 30 16


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As our simulations refer to an ideal situation where inter-SAM siloxane covalent bonds are not formed, our calculated in-plane intermolecular distance of d =5.08 ˚ A (α=4.4 ˚ A), obtained from the analysis of the distance from the origin of the first neighbour peaks of in-plane radial distribution in Figure 6, matches well with the largest values reported in the literature. For FDTS we are not aware of experimental data on SiO2 , but the calculated value of d =5.62 ˚ A (α =4.87 ˚ A) is consistent with reported packing distances for partially fluorinated alkanethiols on GaAs and on Au(111)/mica (d =5.7 and 5.9 ˚ A, respectively 70,77 ).

Charge density Aside morphological changes, the introduction of a SAM on top of an insulating oxide also modifies the charge density at the interface, with important effects on the performance of SAM-based devices, as discussed in the introduction. Here we start by analyzing the electron charge density, which can be accessed experimentally by complex analysis of X-ray reflectivity measurements, but that is very simple to calculate from MD simulations trajectories, as it is given by the sum over space of the atomic numbers minus the partial atomic charges. Actually, the measurement of the electron density is often exploited for assessing the quality of the film and for providing an estimation of the layer thickness, rather than for being correlated with device performances. Experimental SAM electron densities invariably appear to present a monotonic decreasing profile which possibly depends on the fitting model. We see from Figure 7 that this is not always the case: at high coverages and in particular for A3 , there exists a neat peak associated FDTS, after the SiO2 plateau at density equal to 0.7 e/˚ to the well-formed crystalline monolayers. Apart this peculiar feature, the calculated electron density profiles are very similar to experimental ones available in the literature. 59,60,75,78 It is worth noting that MD has a better resolution than X-ray reflectometry measurements, suggesting that the synergistic combination of the two techniques could advance the state of the art of electron density measurements in thin films.

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0.8 Electron density (e/Å3)

OTS (coverage) Exp. 4.5 4.2 3.6 3.0 2.5

0.6

0.4

FDTS (coverage) Exp. 3.8 3.5 3.0 2.5

0.2

0 −10

0

10

20

30

40 −10

0

10

z (Å)

20

30

40

z (Å)

Figure 7: Electron density profile for OTS (left) and FDTS (right) at different coverages. Blue dots and green squares correspond to experimental data from references 60 and. 78

0 OTS FDTS

−1

−1

−2

µz (D)

0 Potential (V)

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−2 2.5

3

3.5

4

4.5 2

Coverage (molecules/nm )

Figure 8: Electrostatic potential shift (filled symbols) and surface dipole (empty symbols) generated by OTS and FDTS SAMs with respect to the bare silica support.

To complete our discussion, we calculated the total charge density as the histogram of atomic partial charges averaged in vertical slabs parallel to the silica surface. From this quantity, the potential (or the electric field E(z)) can be accessed by applying the one-dimensional Poisson equation and numerically integrating twice (once) the total charge density along the z direction, with boundary conditions V (0) = 0, E(0) = 0, and by taking

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ǫ0 = 1 as customary in molecular dynamics simulations: ∂ 2 V (z) −ρ(z) = ∂ 2z ǫǫ0 Z z 1 ∂V (z) ρ(z ′ )dz ′ = −E(z) = − ∂z ǫǫ0 0 Z z E(z ′ )dz ′ . V (z) = −

(1) (2) (3)

0

In practice, the simulated sample is treated as an infinitely extended bi-dimensional layer of point charges, an assumption that is valid only at short distances from the surface, 79 e.g. the distances experienced in a thin film of semiconducting molecules deposited on top of the SAM. In the case of the infinite 2D layer, the potential is expected to fluctuate inside the layer, and to reach a constant value on the two sides, as nicely discussed by Heimel and coworkers. 79 The shift ∆V in electrostatic potential produced by the SAM is then calculated as the difference between the plateau value of the potential on top of the SAM and the same quantity obtained for the bare SiO2 surface (see SI for details). The estimates given by this methodology are approximate because polarization effects are neglected, 80 as the atomic point charges of the force field are fixed in time; however, the results shown in Figure 8 are consistent with the fact that OTS has an almost zero vertical component of the molecular dipole, while that of FTDS points towards the silica surface. Calculations carried out at the wB97XD/aug-cc-pVTZ level for RSi(OH)3 give a longitudinal dipole of 3.8 D for FDTS and a lateral one of 1.3 D for OTS. In order to measure the effective interface dipole, we took advantage of Helmholtz equation 79 and computed it as µz = ∆V ǫ0 /C where C is the coverage. These dipoles, plotted in figure 8 as a function of the coverage, are almost negligible for OTS and range from -0.8 to -1.5 D for FDTS. It can be then concluded that the differences in electrostatic potential originate both from the different intrinsic dipole moment of the two SAMs and from the absence of tilt for FDTS that allows for the molecular dipole to be normal to the surface. From Figure 8 it can be noticed that, as indicated by the corresponding surface dipoles, these effects translate in an 19



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almost null and coverage-independent potential shift for OTS SAMs, and in a negative and coverage-dependent voltage for FDTS, reaching about -2 V at dense coverage. A similar difference between OTS and FDTS (2.5 V) was measured by Kelvin probe force microscopy on Al2 O3 . 81 It should be however kept in mind that, as nicely illustrated experimentally by Aghamohammadi et al. 81 and theoretically by Mityashin et al., 20 the shift in surface potential that we are discussing here, and the SAM-induced threshold voltage shift measured in transistors are quantities that are correlated, but not necessarily coinciding, with the roughness of the potential energy surface and the thickness of the dielectric also playing an important role in determining the final value of the threshold voltage.

Conclusions In this study we presented the application of an atomistic model for self-assembled monolayers which does not require an explicit bonding term between the substituted alkyl-silane derivatives and the amorphous silica support. This model allows for the self-organization of molecules while retaining the correct bond distance at the SAM/support interface. We applied it to the prediction of the morphology of octadecylsilane and perfluorooctylethylsilane SAMs as a function of surface coverage. For both SAMs, standard physical observables such as density of packing, thickness of the monolayer, tilt angle of molecules, crystal structure are in excellent agreement with the large set of experimental data available in the literature. The computed profiles of electron density are also consistent with those obtained from X-ray reflectometry measurements, with the notable difference of having a higher resolution than experiments; we hope that this information will stimulate the use of more complicated functions for the modelling of experimental electron density profiles. Regarding the SAM structure, we found that the orientational order of the molecules within the monolayer is strongly dependent on surface coverage, with the presence of a disordered

20


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phase at low coverage (

Structural Characterization of Alkylsilane and Fluoroalkylsilane Self

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