Dielectric Properties of Self-Assembled Monolayer Coatings on a (111

Article pubs.acs.org/JPCC

Dielectric Properties of Self-Assembled Monolayer Coatings on a (111) Silicon Surface Fabrizio Gala* and Giuseppe Zollo Dipartimento di Scienze di Base e Applicate per l’Ingegneria (Sezione di Fisica), Universitá di Roma “La Sapienza”, Via A. Scarpa 14−16, 00161 Rome, Italy ABSTRACT: Novel nanomaterial systems as possible candidates for gate dielectric insulators play a key role in the fabrication of next-generation transistor devices in both metal-oxide-semiconductor (MOSFET) and organic thin-film transistors (OTFTs). We focus on one of these new alternative gate dielectric nanostructured materials: selfassembled monolayers (SAMs) of hydroxylated octadecyltrichlorosilane (OTS) chains deposited on a (111) Si substrate. Starting from the evaluation of the surface partial dipole of the SAM coating on the Si surface, we report a quantitative ab initio study of the static dielectric constant of the OTS thin-film coating at different coverage values of the hydrogenated (111) Si surface ranging from partial to full coverage. The main physical features of the OTS SAM films at different coverages have been studied with respect to their influence on the static dielectric constant, and a two-layer model is established. A linear dependence of the static dielectric constant versus the coverage is shown to hold, resulting from depolarization phenomena of the main contributors.

1. INTRODUCTION Molecular electronics is expected to play a crucial role in nanoelectronics, which is a strategic field in modern technology. As the transistor size is reduced to nanometric dimensions, only a few atoms would work as a transistor; thus, organic molecules, thanks to their reduced size, are well-suited for the fabrication of molecular devices.1 Among them, self-assembled monolayers (SAMs) have been recently studied and reviewed in detail2−5 because of their possible use in low-cost devices for applications in many fields. Among all the possible choices of the organic molecules employed in the formation of SAM films, alkyl-silanes exhibit appealing properties that make them good candidates for gate insulators; moreover, alkyl-silane coatings have been already employed to functionalize a Si surface to obtain low mechanical friction4 or high-level hydrophobic6,7 coatings. Hence such systems are already well-suited for the Si technology. In particular, octadecyltrichlorosilane films (CH3(CH2)17SiCl3, OTS) deposited on Si or SiO2 have been considered as excellent candidates for gate dielectrics in lowvoltage OTFTs thanks to their insulating properties mainly related to their highly ordered aliphatic chain. The actual performance of such SAMs obviously depends on overall properties of the film; hence, provided that a good control of the film quality can be achieved,8−10 a system made of OTS SAM coatings on the Si surface is potentially appealing for the fabrication of novel organic thin-film transistors (OTFTs) at the nanoscale where the usage of silicon dioxide (SiO2) is prevented by the occurrence of high leakage currents. Generally speaking, an organic monolayer formed through self-assembly should be a close-packed and a highly ordered structure. However, defects or incomplete domain boundaries may occur during the SAM formation;11,12 hence, SAM © XXXX American Chemical Society

coatings are quite often nonuniform, being characterized by neighboring, small-sized, ordered domains11 with different orientations and disordered domain boundaries. In a field emitting transistor (FET), this would be catastrophic, as impurities may penetrate the SAM film, reducing the effective dielectric thickness and creating low-resistance current paths across the coating; thus, a key challenge for realizing an efficient and low-voltage OTFT lies in developing gate dielectrics with low leakage current, low interface trap density, and high capacitance. At a first stage, the study and characterization of SAMs obtained by deposition of alkylsilanes on Si-based surfaces were undertaken mainly from the experimental point of view by ellipsometry, infrared spectroscopy, X-ray photoelectron spectroscopy (XPS), reflectivity, and absorption fine structure (NEXAFS) spectroscopy13−15 and have concerned the coarsegrained properties of the film structure and quality such as the surface roughness, temperature stability, self-assembling properties, etc. Quite recently, theoretical modeling of such systems has been performed, and many aspects of these systems, such as the adhesion geometry and energetics, were clarified at the atomistic scale by ab initio calculations.16,17 In that context, the role played in the self-assembling mechanism by H-bonds formed between hydroxyl groups of neighboring OTS molecules was evidenced showing also that a possible source of irregularities of the SAM film might reside in the multiple covalent attachments per molecule; moreover, the work function, which is a key quantity in FET technology, was Received: January 8, 2015 Revised: March 12, 2015

A

DOI: 10.1021/acs.jpcc.5b00193 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

polarization P(E), additional optimization runs of the systems considered have been performed in the presence of a static external electric field of amplitude 0.002 au. The method adopted is valid only if a linear regime is assumed to hold. For this reason we have tested our calculation schemes for different values of the external field to check if the linear regime holds, and it was shown that the static electric field of 0.002 au we have used is well within the linear regime region. The knowledge of the z component of the partial dipole moments17 with respect the vacuum region is calculated through the formula

calculated (by extrapolation at full coverage using a simple superposition model17), indicating that such coatings increase the hole isolation of the Si−H surface.17 In this article, we focus on the insulating properties of hydroxylated OTS-SAM coatings deposited on a (111) hydrogenated Si surface at different partial coverages with particular reference to the static dielectric constant. Generally speaking, such a quantity can be calculated exactly in the context of the many-body perturbation theory, but the system under consideration is not eligible for such heavy calculations. Therefore, we adopt a total ground-state approach on the atomistic models obtained with and without a static electric field; in this way, the static dielectric constant is calculated at various coverage ratios, and then it is extrapolated at full coverage using a superposition model similar to the one already used to calculate the work function.17

d(E)(z) =

∫z

c

(z′ − z)ρ(E)(z′) dz′

(1)

where c is the supercell size along z and ρ(E)(z) is the xy average of the total charge density in the presence of a static external electric field (Eext), which allows the calculation of the macroscopic electrostatic potential as a function of z (the socalled “Z-potential”) and the average internal electric field inside the slab. Notice that eq 1 reduces to the standard definition of partial c polarization d(z) = ∫z z′ ρ(z′) dz′ only for those z values where

2. THEORETICAL METHOD OTS SAMs on the (111) Si surface have been modeled by ab initio density functional theory (DFT) with a generalized gradient approximation (GGA), using the Perdew−Burke− Ernzerhof formula18 (PBE) for the electron exchange and correlation energy. Norm-conserving pseudopotentials, constructed using the Troullier−Martins scheme,19 and a plane wave basis set expansion scheme have been employed with an energy cutoff of 150 Ry for the wave functions. All the firstprinciples calculations have been performed using the QUANTUM-ESPRESSO package.20 The large cutoff used is needed because partial dipoles used in the following are quite sensitive to convergence errors. The Si(111) surface in the xy plane has been modeled with a slab geometry made of six bilayers and a vacuum region ∼45 Å thick in the z direction; all the dangling bonds at the surface have been passivated with H atoms. The supercell size in the xy plane has been varied according to the coverage ratio we were interested in for 1/4, 1/2, and 3/ 4 partial coverage ratios (i.e., the OTS molecules occupy one, two, or three in four surface adsorption sites, respectively); an orthorhombic supercell containing the Si slab has been designed with 48 Si atoms (8 atoms per bilayer). In this case, a (4 × 4 × 1) Mokhorst−Pack k-point grid21 has been used for the Brillouin zone (BZ) sampling; for a partial coverage of 1/3, the slab has been constructed with 72 atoms (12 Si atoms per bilayer) and the same k-point sampling scheme as before was adopted. Finally, calculations on a full coverage configuration template have been treated in a hexagonal supercell with 12 Si atoms where a (12 × 12 × 1) k-point grid has been employed. All the above calculation schemes have been checked for convergence. In particular, we have considered the slab thickness as a possible source of errors; as a consequence, the slab thickness has been chosen so that the dielectric constant of bulk silicon could be recovered. Moreover, the model used has been checked for convergence also regarding to the Brillouin zone sampling and the energy cutoff employed. Periodic boundary conditions (PBCs) have been employed together with a dipole correction rectifying the artificial electric field across the slab induced by the PBCs.22 The ground-state configurations have been fully relaxed using the Broyden− Fletcher−Goldfarb−Shanno (BFGS) method23 with the Hellmann−Feynman forces acting on the ions, together with empirical long-range corrections.24 Optimizations have been performed until the convergence threshold of 0.001 au of the total force was reached. To calculate the macroscopic

c

d′(z) = 0 (being such condition satisfied where ∫z ρ(z′) dz′ = 0, i.e., where the supercell is split into two neutral subunits25); hence, it is well-defined only at these points. Using eq 1, it is possible to write the Z-potential in the presence of an external static electric field Eext (of magnitude Eext) oriented along the z-axis as V (E)(z) = − =

1 2ε0A

∫0

c

|z − z′|ρ(E)(z′) dz′ − zEext

⎞ 1 ⎛ d(E)(0) ⎜⎜ − d(E)(z)⎟⎟ − zEext ε0A ⎝ 2 ⎠

(2)

where A is the xy surface area. Differentiation of eq 2 leads to the total electric field ⎛ 1 d (E) ⎞ ⃗ (E) E(E) d (z) + Eext⎟k̂ tot = −∇V (z) = ⎜ ⎝ ε0A dz ⎠ = E(E) int + Eext

(3)

where k̂ is the unit vector along the z-direction. As we are interested in the macroscopic dielectric function, the internal field has to be averaged between two reference points (say z1 and z2 with z2 ≥ z1) to eliminate local field effects, giving 1 z 2 − z1 1 = ε0A(z 2 − z1)

∫z

⟨E(E) int ⟩ =

z2

E(E) int (z) dz

1

∫z

z2

1

d (E) (d (z)) dz k̂ dz

(E)

=

(E) 1 d (z 2) − d (z1) ̂ k ε0A z 2 − z1

(4)

On the other hand, for a polarized dielectric linear slab in the presence of an external electric field, the macroscopic polarization P(E) between two reference points z1 and z2 can be obtained as B


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Figure 1. Partial dipole, d(z), for a single OTS molecule adsorbed on the Si surface with and without the external field (red and orange lines, respectively). The partial dipole of the H:Si slab (black line) without the external electric field is also reported as a reference. Partial dipoles of the subunits specified in the text are evidenced, together with the special points splitting the structure into two neutral subunits where partial dipoles evaluated through eq 1 agree with the usual definition.

P(E) = =

1 1 A z 2 − z1

z2

∫z

on a surface, the z2 value in eq 4 must be chosen with some care, as it falls in the vacuum region, resulting in ⟨E⟩(E) int ∝ −d(E)(z1) /(z2−z1). Referring to the single OTS molecule adsorbed on a Si surface reported in Figure 1, it is clear that each z2 chosen in the vacuum region beyond 95.0 a0 satisfies the neutrality condition, but the larger the z2 value, the smaller the average internal electric field (calculated through eq 4). Thus, in order to calculate the true SAM property, z2 has been chosen as the closest point outside the thin-film coating that satisfies both the conditions |ρ (0)(z2)| ≤ 10−6e and |ρ(E)(z2)| ≤ 10−6e; z1 has been chosen immediately below the Si surface (zs in Figure 1, corresponding to the midplane of the topmost Si− Si bond), where also the surface dipole d(zs) is measured; the criterion employed in the choice of z2 implies that also a small part of vacuum (of the order of ∼2−4 Å) is included in the evaluation of the macroscopic dielectric constant of the thin film coating the surface; therefore, the dielectric constants here calculated are expected to be slightly underestimated. With the above choices, the internal electrostatic field variation cast into

z′ρ(E)(z′) dz′k̂

1

1 1 ( A z 2 − z1

∫z

c

z′ρ(E)(z′) dz′ −

1

∫z

c

z′ρ(E)(z′) dz′)k̂

2

1 1 = (d(E)(z1) − d(E)(z 2))k̂ = − ε0⟨E(intE)⟩ A z 2 − z1 (5)

provided that both z1 and z2 satisfy the neutrality condition d′(zi) = 0 ∀ i = {1,2}. Notice that eq 5 is a restatement of the Lorentz local field inside a one-dimensional dielectric material,26 permitting us to evaluate the static linear susceptibility (χ) as the polarization response of the system to the total electric field: δ P = ε0χδ⟨E(E) tot ⟩

(6)

where δP = P − P is the difference between the macroscopic polarization with and without external electric field. Then the static dielectric constant can be easily obtained in connection with eqs 4 and 5 as (E)

εr = 1 + χ = 1 +

(0)

−1 ⎛ δ⟨E int⟩ ⎞ 1 δP ⎜⎜1 + ⎟⎟ = (E) ε0 δ⟨Etot δEext ⎠ ⟩ ⎝

δ⟨E int⟩ = −

1 Δds , ε0A z 2 − zs

Δds = d(E)(zs) − d(0)(zs) (8)

where d(z2) ∼ 0 with and without the external electrostatic field. The knowledge of Δds thus permits the indirect evaluation of the macroscopic dielectric constant of the OTS SAM at various coverage ratios depending on the quality and the uniformity of the coatings. Following the above-described scheme, we have calculated both the high-frequency dielectric constant, εOTS ∞ , and the static dielectric constant, εOTS ; the former was calculated from selfr consistent calculations with and without the external electric field on the system optimized without the electric filed, the latter taking into account both the optimized configurations

(7)

where δEint is the difference between the average internal electric field with and without a static external field Eext. The macroscopic dielectric constant evaluated through eq 7 has been checked for the bulk diamond phase of Si; the calculation performed using our slab geometry in a supercell containing nine bilayers of bulk Si, in fact, results in εSir ≃ 11.8 for the Si bulk region, in excellent agreement with the experimental value of εSir ≃ 11.9.27 Because we are interested in applying the above-described method to the case of a thin film made of molecules adsorbed C


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The Journal of Physical Chemistry C obtained with and without the external electric field. Indeed, we assume that the dielectric constant at high frequency depends only on the polarization due to the electron charge rearrangement induced by the external field, while the atomic rearrangement is excluded because the rapid variation of the electric field cannot be followed by the ions.

molecules at adjacent sites so that one of the two free hydroxyl groups binds the adjacent adsorbed molecule through a planar H-bond; the corresponding ground-state structure obtained after optimization is reported in Figure 2a, in which a zigzag pattern of hydrogen bonds between molecules is evidenced; taking into account PBCs, this configuration corresponds to a partial coverage of 1/3.

3. RESULTS We start our discussion on the dielectric properties of a partial SAM coating of the (111) Si surface by considering the simplest possible case: an isolated molecule adsorbed on the surface. The fully relaxed ground-state configuration (obtained without the external electric field) of the isolated OTS molecule adsorbed on the surface is shown in the upper panel of Figure 1. Taking into account that PBC are adopted, the coating here modeled corresponds to a nominal partial coverage of 1/4 and consists of a defective uniform OTS coating where no selfassembling occurs because each deposited molecule is surrounded by empty adsorption sites. Basically, the coating here modeled is the one with the largest coverage if selfassembling phenomena are excluded. The main geometrical parameters are reported in Table 1 for both the relaxed configurations; as foreseen, in the relaxed

Figure 2. Top view (a) and lateral view (b) of the fully relaxed configurations of two OTS molecules adsorbed on adjacent sites on the hydrogenated (111) Si surface. The hydrogen bonds between the hydroxyl groups, together with the supercell edges, are reported as dotted black lines.

Table 1. Tilt Angles and Relative Orientation of the OH Bonds with Respect to the z-Axis of the Optimized Configurations Obtained with and without the External Electric Field at Various Coverage Ratios coverage ratio

Eext (a.u.)

1/4

0.000 0.002 0.000 0.002 0.000 0.002 0.000

1/3 1/2 3/4

0.002 1

0.000 0.002

θtilt 10.3° 10.6° (2.5°, 2.9°) (2.5°, 2.9°) (2.5°, 2.6°) (2.5°, 2.7°) (1.0°, 2.2°, 2.4°) (1.0°, 2.2°, 2.4°) 0.0° 0.0°

θup OH 44.2° 37.7° (85.0°, (85.4°, (83.6°, (83.5°, − − 122.1° 121.9°

88.3°) 85.9°) 96.4°) 95.6°)

θdown OH

The relaxation pattern results in the slight torsion of both the alkyl chains; such torsional deformation occurs for steric reasons as the H-bond, formed between OH groups, keeps the two polymers quite close to each other; indeed, the torsional deformation relaxes part of the elastic interaction between the polymers and thus contributes to set the binding energy at negative values.16 Moreover, the ground-state configuration obtained with Eext = 0.002 au is quite similar to the one without the external field (see the main geometrical parameters reported in Table 1, such as the tilt angles of the polymer chains and the OH groups orientation with respect the z-axis that are nearly the same). Hindrance effects result in two notable results: the first one is that the polymer chains are nearly aligned along the z-axis (both having θtilt ≤ 3°), while the second one is the relative torsion of the CH2 trimers. On the other hand, the adhesion chemistry almost agrees with the previous case in which only one OTS molecule was adsorbed onto the Si surface (PC 1/4). The surface dipole difference, zs, for this partial coverage is Δds/A ∼ 0.036 D/Å2, which implies a macroscopic dielectric constant εOTS ∼ 1.71 (having included approximately 4.0 Å of r vacuum from the upper H atom of the OTS terminating methyl group). Again, the obtained value is slightly larger than the corresponding high-frequency dielectric constant for which we have obtained the value εOTS ∞ = 1.66. Starting from the relaxed structures obtained in the previous section, we have reduced the leading lateral dimension of the (111) Si surface to mimic a partial coverage of 1/2; ionic relaxation in a smaller supercell results in minor changes of the atomic structure, leaving the general situation depicted in Figure 2 almost unchanged. The obtained surface dipole variation of Δds/A ≃ 0.044 D/Å2 implies a static dielectric constant at half coverage of εOTS = 2.02 (to be compared to the r

128.2° 126.1° (122.5°, 135.8°) (122.2°, 135.2°) (112.7°, 120.4°) (110.1°, 119.8°) (119.4°, 122.7°, 125.7°, 132.7°) (119.1°, 122.6°, 125.1°, 132.2°) 127.9° 127.8°

configuration with Eext ≠ 0, the angles between the z-axis of the OH bonds have been varied according to the relative orientation of its dipole moment dOH (pointing from the O atom to the H atom), while the OH bond lengths have not changed, suggesting that orientation polarization would be the principal polarization mechanism for the polar OH groups; the corresponding surface dipoles measured in zs (see Figure 1) determines a surface dipole difference of Δds/A ∼ 0.031 D/Å2 per unit area and a macroscopic dielectric constant of εOTS ≃ r 1.60 (having included approximately 1.5 Å of vacuum from the upper H atom of the OTS terminating methyl group). The obtained value is slightly larger than the corresponding highfrequency value (εOTS ∞ ≃ 1.55); as expected, the ionic relaxation in the presence of an external electric field favors the formation of a depolarizing field inside the thin-film coating. As the coverage increases, one has to consider that selfassembling phenomena arise. In previous papers we have shown that such phenomena involve H-bonds. Therefore, hydrogen bond formation between OTS molecules adsorbed on the (111) Si surface has been modeled by placing two D


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Figure 3. Top view of two different OTS configurations at PC 1/2 (a, b). Even if the two configurations are almost energetically equivalent, the relative orientation of the OTS molecules is different; however, in both cases there is not enough space to place another OTS molecule on the Si surface, as evidenced by black and blue circles.

Figure 4. Top view (a) and lateral view (b) of the fully relaxed configurations of three OTS molecules adsorbed on adjacent sites on the hydrogenated (111) Si surface. The hydrogen bonds between the hydroxyl groups, together with the supercell edges, are reported as dotted black lines.

high-frequency value of εOTS ∞ = 1.93); this is the highest ordered partial coverage that can be obtained with only H-bonds linking OTS molecules at adjacent sites. PBCs, in fact, do not allow a further increase of the coverage ratio to obtain denser OTS SAM coatings in which the self-assembling proceeds only via H-bonds between hydroxyl groups; any attempt to increase the coverage failed because of hindrance effects (see Figure 3 in which two energetically equivalent configurations at PC 1/2 are shown). Looking at the configuration reported in Figure 2, one can appreciate that the average space needed to place an adsorbed OTS molecule at a given adsorption site is roughly a circle with a diameter of 4 Å (see the black circles in Figure 3a,b), while the free space available around an adsorption site is a circular area of only 2 Å in diameter (see the blue circles in

Figure 3a,b). This circumstance makes clear that for larger coverage values a more complicated self-assembling scenario should be considered rather than the simple one involving just H-bonds. The latter should be considered valid just for low coverage up to 1/2. Hence, the only way to increase further the coverage is to consider OTS silanization28 involving the hydroxyl groups and resulting in the release of a water molecule; this implies a lateral Si−O−Si covalent bonding between OTS molecules that, at least in principle, can favor the uniformity of the SAM coating. Having such considerations in mind, we have modeled a configuration with three OTS, thus simulating a 3/4 partial coverage of the Si surface; the ground-state configuration obtained after full optimization is depicted in Figure 4. There E


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of the CH2 trimers, and dCH3 = d(zc) − d(c) is the methyl group contribution. In eq 9, therefore, d* + dOH + dSA Si−O−Si accounts for all the other contributions to the surface dipole change of a perfect hydrogenated Si surface induced by the adhesion of the OTS, except for the ones from the alkyl chains already considered. Hence, dSA Si−O−Si is the contribution to the surface dipole eventually coming from the covalent Si−O−Si lateral bonds between adjacent OTS molecules resulting from silanization (which must be taken into account explicitly in the case of 3/4 partial coverage); dOH accounts for the hydroxyl groups contributions (included the ones involved in H-bonds); and d* accounts for three effects: the removal of H atoms from the perfect hydrogenated surface at the OTS adhesion sites, the contribution to the surface dipole coming from the adhesion groups, the contribution of two CH2 trimers that are closest to it, and finally also the contribution from the relaxation and the charge rearrangement of the first Si layer. A rigorous proof of eq 9 is detailed in Appendix A. While the evaluation of d(CH2)n = d(z*) − d(zc) and dCH3 = d(zc) − d(c) are straightforwardly obtained from partial dipoles, dOH contributions for the various configurations considered, either with or without the external field applied, are obtained as follows: the supercell total dipole of the configuration considered, either with or without the external field, is first calculated; then the total dipole of an identical system except for one OH group that, instead of being oriented downward, is rotated and constrained to relax in the xy plane is calculated. Hence, the two structures differ only in the relative orientation of one of the two OH groups, and the total dipole difference can be assumed to be the partial dipole of the OH group that is oriented downward. Lastly, by dividing it by the relevant cosine, one obtains the module of the OH contribution to the partial dipole. A similar strategy has been employed for the evaluation of the dSA Si−O−Si term, having compared the relaxed structure previously discussed for PC 3/4 with a configuration differing only in the plane where the Si−O−Si lateral bond lies; if α indicates the angle between the z-axis and the normal to the plane where the Si−O−Si lateral structure lies, then this angle has been changed from αSi−O−Si ≃ 128° to αSi−O−Si ≃ 180° (where the Si−O−Si contribution to the z component is expected to be negligible). The difference of the total dipole is taken as a measure of dSA Si−O−Si. Next, by a straightforward comparison with the relaxed structures of the bulk H:Si surface, the d* contribution has been extracted (see Appendix A) by calculating

are two major differences with respect to the previous configurations at lower coverage: the H-bonds do not lay anymore in the xy plane but they are formed between hydroxyl groups and the O atoms belonging to the Si−O−Si adhesion group (which links the alkyl chain to the Si surface) and a Si− O−Si silanization bonding between adjacent SAM molecules is formed. The last characteristic contributes to the selfassembling scenario by adding this strong covalent bond to the pre-existing H-bond network. The binding energy of such a configuration, compared to the case of three isolated OTS molecules (see 1/4 partial coverage) is still negative: E b = E(3OTS/H:Si) + 2E(H:Si) + E(H 2O) − 3E(1OTS/H:Si) = − 1.0 eV

showing that this, more complicated, self-assembling scenario is, in principle, stable. However, the binding energy of a third OTS molecule added to two pre-existing ones (already assembled through H-bonds) and calculated as E b = E(3OTS/H:Si) + E(H:Si) + E(H 2O) − E(2OTS/H:Si) − E(1OTS/H:Si) = 0.96 eV

is positive; this implies that such coverage can proceed from 1/ 2 partial coverage only upon energy addition to the whole system. In the presence of the external electric field, the optimized geometry does not vary significantly as indicated by the small variation of the angle between the z direction and the OH groups (see Table 1). Hence, the calculated high-frequency OTS and static dielectric constants are nearly equal (εOTS = ∞ ≃ εr 2.41 with a surface dipole per unit area of Δds/A ≃ 0.051 D/ Å2). Before considering the full coverage of the (111) Si surface with an OTS coating, it is highly instructive to decompose the surface partial dipoles (at different partial coverages) in meaningful contributions to evidence the atomic groups (i.e., the adhesion group, alkyl chain, methyl group, etc.) that contribute the most to the integral defining the surface partial dipole difference (see eq 1). This task will be accomplished in the next section, with the aid of a simple model exploiting the linearity of eq 1. 3.1. Partial Dipole Decomposition. The linear dependence of the average internal field variation on the surface dipole change allows the decomposition of the dielectric constant into smaller blocks corresponding to the partial dipoles of meaningful atomic groups.17 The decomposition employed in the following sections is schematically shown in Figure 1 where zc is the z-coordinate of the C−C midbond linking the terminal methyl group to the rest of the OTS molecule, z* is the zcoordinate of the C−C midbond that links the alkyl chain to the adhesion group (in practice, z* defines the adhesion group on the alkyl chain side) and zs is the z-coordinate of the midbond of the topmost Si−Si bond (in practice, zs indicates the position where the surface dipole is calculated). Formally, the integral defining d(zs) ≡ dOTS(zs) is decomposed as

d = [d OTS(zs) − d OTS(z )] − [d H:Si(zs) − d H:Si(z )] * * * i − |dOH| ∑ cos(θOH ) − dSiSA− O − Si i

(10)

On the basis of the above decomposition, it is possible to study the individual contributions to the surface total partial dipole variation (and hence the static dielectric constant) for each partial coverage studied where eq 8 is such that Δds = d(E)(zs) − d(0)(zs) = ΔdH:Si(zs) + Δd* + ΔdOH + ΔdSA Si−O−Si + Δd(CH2)n + ΔdCH3. 3.2. Dielectric Constant and Partial Dipole Decomposition of Partial and Full Coverage OTS SAM. Following the previous section, let us first examine the behavior of Δd(CH2)n and ΔdCH3 obtained from the data reported in Table 2 concerning coverage ratios ranging from 1/3 to 3/4. It is

d OTS(zs) = d H:Si(zs) + d + dOH + dSiSA− O − Si + d(CH2)n + dCH3 * (9)

where dH:Si(zs) is the surface dipole of the hydrogenated (111) Si slab (i.e., the surface dipole of the hydrogenated surface with no adsorbed molecule), d(CH2)n = d(z*)−d(zc) the contribution F


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on the surface where no self-assembling phenomenon takes place and is far from the experimental evidence. After having evidenced the importance of depolarization phenomena in the systems considered, we apply the partial dipole decomposition described in the previous section to find all the other contributions to the dielectric constant. Such decomposition shows that there are two major contributions to the surface partial dipole: the first one, Δd(CH2)n, is the largest for all the configurations studied (0.85, 0.82, 0.69, and 0.56 D for 1/4, 1/3, 1/2, and 3/4 partial coverage ratios, respectively). This contribute is larger than ΔdCH3 values (0.13, 0.07, 0.07, and 0.05 D for 1/4, 1/3, 1/2, and 3/4 partial coverage, respectively) and much larger (by 2 orders of magnitude) than the contribution of the hydroxyl groups ΔdOH that are de facto negligible (0.0095, 0.0036, 0.001, and 0.00038 D for 1/4, 1/3, 1/2, and 3/4 partial coverage, respectively), as well as the Si− O−Si lateral bonding between OTS molecules in the PC 3/4 configuration (Δd SA Si−O−Si ≃ 0.0015 D). The other important contribution to the surface partial dipole, dOTS(zs), is given by the adhesion group Δd* measured following the prescription of the previous section, giving 0.28, 0.29, 0.21, and 0.17 D for 1/4, 1/3, 1/2, and 3/4 partial coverage ratios, respectively. It is thus evident that because the most important contributions to the surface dipole (and hence to the internal electric field induced by charge rearrangements) are related to the alkyl chain and to the adhesion group on the surface, the contributions of the atomic groups that are involved in the selfassembling mechanisms, namely the −OH group for coverage ratio up to 1/2 and the −OH and the Si−O−Si lateral bonding groups for larger coverage ratios, can be neglected, being 2 orders of magnitude lower than the major contributions. For this reason, a full coverage model can be built in such a way that one OTS molecule is adsorbed at each adsorption site of the hydrogenated Si surface irrespective of the selfassembling pattern or even in absence of any self-assembling phenomenon. Therefore, the full coverage model of the OTS adsorption has been considered using a small hexagonal supercell

Table 2. Values of the Partial Dipole Changes Due to the Addition of the Static Electric Field (See the Text)a coverage ratio

ΔdOTS /A (D/Å2) s

Δd(CH2)n (D)

ΔdCH3 (D)

Δd* (D)

1/4 1/3 1/2 3/4 1

0.031 0.036 0.044 0.051 0.053

0.85 0.82 0.69 0.56 0.50

0.13 0.07 0.07 0.05 0.05

0.28 0.29 0.21 0.17 0.10

The values are calculated per unit molecule. The data in the first column are per unit molecule and per unit area. a

immediately seen that these contributions decrease as the coverage increases. This behavior is clearly due to the depolarization effect that arises when the alkyl chains are close to each other. The depolarization behavior of both these contributions has been analyzed with the help of a simple model, as detailed in Appendix B. The depolarization curves for both the contributions, obtained from a template system of alkanes, are reported in Figure 5. As clearly evidenced, the measured values of Δd(CH2)n and ΔdCH3 (the blue square dots reported in Figure 5) for the various coverage are in very good agreement (except for the 1/4 coverage case) with the simple phenomenological depolarization model represented in the same figure as a solid curve. The reason why the values measured in the 1/4 coverage case diverge from the depolarization curves (see Table 2) is mainly related to the different relaxation pattern obtained in this case with respect to all the others because the 1/4 coverage case does not involve any self-assembly; as a consequence, the tilt angle of this configuration (θtilt ≃ 10°) is different from that of the template array of CH3(CH2)16CH3 molecules used to obtain the depolarization curve (see Appendix B). Indeed, these, are aligned along the z-axis (with θtilt ≃ 0°) similarly to the partial coverage cases involving self-assembling. In any case, this circumstance does not affect our results because, as we have already stated and deeply discussed in previous papers,16,17 this case basically consists of isolated OTS

Figure 5. Partial dipole variations (black dots) for the d(CH2)n (a) and dCH3 (b) terms in configuration made of a partial coverage of a CH3(CH2)16CH3 thin-film coating when an external electric field is applied. The values, obtained without ionic relaxation, can be fitted (red curve) with a simple three-parameter formula (see eq 17) with high accuracy (with χ2 = 1 × 10−5). The data measured for well-relaxed OTS-SAM film coatings onto the Si surface (blue square dots) are in good agreement with the depolarization curve. G


Article

The Journal of Physical Chemistry C containing just one adsorption site, i.e., considering the (111) Si surface hexagonal unit cell where an OTS molecule is adsorbed. The full coverage is a consequence of the PBCs. It is worth noting that this model is valid only for the calculation of the dielectric constant and should not be considered as a reliable atomistic model of the SAM structure that, as previously specified, involves self-assembling through both hydrogen bonds and silanization covalent bonds. The fully relaxed configuration is shown in Figure 6; as discussed, the simulated structure does not contain important

Figure 7. Static dielectric constant (black circles dots, red straight line) for OTS coatings on the (111) Si surface at different partial coverage (θ) compared to that of an infinite perfect alkyl chain matrix (black square dots, blue straight line).

constant can be decomposed into the two contributions from 2)n−CH3 the two layers. By defining ε*r and ε(CH such that (ε*r − r (CH 2 ) n −CH 3 1)/εr* = Δd*/l* and (εr − 1) /εr(CH2)n−CH3 = Δd(CH2)n − CH3/l(CH2) − CH3, respectively, the measured value of the dielectric constant casts into

Figure 6. Top view (a) and lateral view (b) of the fully relaxed configuration made of a single OTS molecule adsorbed on the (111) Si surface at full coverage.

εr =

features of a real full coverage SAM coating onto the (111) Si surface such as correctly aligned H-bonds, covalent Si−O−Si resulting from silanization, or a reliable distortion of the polymer chain.16 Moreover, the negligible tilt angle measured for the alkyl chain in this case is due to the hindrance between the chains at such dense OTS packing. However, such configuration contains the key features needed to evaluate the static dielectric constant at full coverage, such as depolarization effects for the Δd(CH2)n and the ΔdCH3 terms (the blue square dots reported in Figure 5) that are still in very good agreement with the simple phenomenological depolarization model perviously discussed and the depolarization of the adhesion group resulting in Δd* ≃ 0.10 D, lower than the corresponding Δd* value for the partial coverages discussed above. The obtained SAM coverage behaves as a good dielectric thin film, showing a surface dipole difference of Δds/A = 0.053 D/Å full full and resulting in εOTS ∼ εOTS ≃ 3.1 (having included ≃4 Å r ∞ of vacuum from the H atom of the methyl group), a value 2 smaller than the corresponding one for SiO2 (εSiO ≃ 3.9). This r value is also in very good agreement with the corresponding 2)n high-frequency value ε(CH ≃ 3.2, calculated for an infinite ∞ alkyl chain placed at the same packing density of the full OTS coverage with density functional perturbation theory (DFPT).29 In Figure 7 we have reported the calculated values of the static dielectric constant versus the coverage ratio: the linear behavior is quite clear, and the linear fit values are reported in the inset. Because we have shown that the dielectric constant values basically depend on the partial dipole contributions from the alkyl chain and the adhesion group, a simple two-layer model accounts for the values measured, and the dielectric

(l + l(CH2)n − CH3)εr*εr(CH2)n − CH3 * (l εr(CH2)n − CH3 + l(CH2)n − CH3εr*) *

(11)

. On the basis of the above formula it is clear that the adhesion group markedly affects the measured value of the dielectric constant and the way it deviates from the alkyl chain one. Indeed, the value reported for a full coverage array of the perfect alkyl chain is slightly larger than that of the full coverage OTS SAM, indicating that the adhesion group degrades the dielectric constant. In Figure 7, we have also reported the measured value of the dielectric constant of a perfect alkyl chain as a function of the coverage ratio, and we have compared it to the same curve obtained here for the OTS SAM. As expected the two lines intersect so that for coverage values lower than a certain value Θ* (between 1/4 and 1/3), the OTS coverage has larger dielectric constant than a simple array of alkyl chains at the same coverage value, whereas for coverage values larger than Θ*, the opposite occurs. This indicates clearly that the depolarization of the adhesion group is the main reason why the isolation properties of the SAM coatings can be degraded with respect to those of the alkyl chain on top of it.

4. CONCLUSIONS Using first-principles calculations based on the density functional theory, we have studied the ground-state configurations and the corresponding dielectric properties of hydroxylated OTS polymer chains adsorbed on the (111) H:Si surface at different partial coverages. For this purpose, we have constructed the atomistic model of OTS SAM coatings on the hydrogenated Si surface at various coverage values showing that for low coverages the self-assembling proceeds through Hbonds, whereas for larger coverage values silanization processes H


Article

The Journal of Physical Chemistry C must be necessarily considered. The OTS SAM models at various partial coverage ratios have been studied focusing on the polarizability properties of OTS polymer thin film in the presence of an applied external electric field obtained through the evaluation of the Z-potential and partial dipoles. The obtained values of the dielectric constants have been examined on the basis of a decomposition in partial dipoles of the relevant atomic groups, showing that basically there are two major contributions to the overall polarizability properties: the alkyl chain and the adhesion group. In contrast, we have shown that the groups involved in the self-assembling phenomena such as H-bond formation or silanization (for large coverage) do not affect the polarizability of the film. The role of the various contributions has been studied also concerning the depolarization phenomena occurring as a result of the close interaction between the OTS molecules. On the basis of the study of partial coverage, we have constructed a full coverage template model valid concerning only the polarizability properties that has allowed us to obtain the dielectric constant at full coverage. Hence, by studying the way self-assembly proceeds at increasing coverage and the partial dipoles involved, we have put in evidence the linear behavior of the static dielectric constant versus the coverage. Such a behavior reflects the marked depolarization of both the adhesion group and the alkyl chains that degrade the isolation properties of the coatings. Moreover, the depolarization of the adhesion group causes the degradation of the dielectric constant at a larger extent than the one that occurs with an ideal alkyl chain coating. The studied systems have been indicated as good candidates for gate dielectrics in FET technology (especially in OTFTs technology) where, for instance, the tail of the OTS polymer chains could be modified to obtain selectivity of compatible organic/inorganic interactions, resulting in improved device performances. Moreover, such systems can exploit the selfassembling mechanism to obtain high-quality and densely packed thin-film gate dielectrics without impurities in the SAM film that could reduce the effective dielectric thickness or create low-resistance current paths through the SAM film. We have shown that such films may suffer from limitations of the dielectric constant that do not arise from a poor self-assembling or the low-quality ordering but are inherent in the film structure because of the adhesion groups of the OTS molecules. The reason why the full coverage OTS-SAM film has a dielectric constant that is lower than that of the SiO2 insulators but also lower than that of the alkyl chain that is on top of the film is related to the depolarization behavior of the adhesion group. The contribution of the adhesion group increases the dielectric constant of the film with respect to the alkyl chain one at low coverage ratios, while at large coverages its depolarization is more marked than the one of the alkyl chain, thus reducing the dielectric constant below that of the alkyl chain at the same coverage ratio. Hence, the limiting factor for such systems as gate dielectrics in FET technology is the adhesion group. It is therefore desirable to look for new adhesion chemistry in order to overcome this limitation. Presently, we can conclude that the static dielectric constant of such coatings at full coverage is 20% lower than the SiO2 value.

∫z

d(zs) = +

∫z

zc

c

∫z

(z′ − zs)ρ(z′) dz′ = s

*

(z′ − zs)ρ(z′) dz′

s

c

∫z

(z′ − zs)ρ(z′) dz′ +

z

(z′ − zs)ρ(z′) dz′

c

*

where zs, z*, and zc are special points satisfying the neutrality condition d′(z) = 0 and 0 < zs < z* < zc < c. The second term on the right hand side, however, can be written as

∫z

zc

(z′ − zs)ρ(z′) dz′ =

*

+ (z − zs) *

∫z

zc

∫z

zc *

(z′ − z )ρ(z′) dz′ *

ρ(z′) dz′ =

*

∫z

zc *

(z′ − z )ρ(z′) dz′ *

where

∫z

zc

ρ(z′)dz′ =

*

∫z

c

ρ(z′)dz′ −

∫z

c

ρ(z′)dz′ = 0

c

*

(12)

for the neutrality condition. Similarly, we can decompose the remaining terms as

∫z

zc *

(z′ − z )ρ(z′) dz′ = *

∫z

−

c

c *

(z′ − z )ρ(z′) dz′ *

(z′ − z )ρ(z′) dz′ = d(z ) − d(zc) * *

c

∫z

∫z

c

(z′ − zs)ρ(z′) dz′ =

c

+ (zc − zs)

∫z

∫z

c

(z′ − zc)ρ(z′) dz′

c

c

ρ(z′) dz′ = d(zc) − d(c)

c

If now we consider the total charge of a system made of a thin film of OTS molecules adsorbed on a perfect hydrogenated Si surface, we have d OT S(zs) =

∫z

z

*

(z′ − zs)ρOTS (z′) dz′

s

+ (d OTS(z ) − d OTS(zc)) + (d OTS(zc) − d OTS(c)) * and choosing zs, z*, and zc as in Figure 1, we can identify the following terms: dCH3 = d OTS(zc) − d OTS(c) d(CH2)n = d OTS(z ) − d OTS(zc) * d H:Si(zs) + (d + dOH + dSiSA− O − Si) = *

∫z

z

*

(z′ − zs)ρOTS (z′)

s

dz′

where the last equality defines the quantity d* + dOH + dSA Si−O−Si in terms of partial dipole difference between the perfect hydrogenated surface and the one with an OTS-SAM on it d + dOH + dSiSA− O − Si * z * = (z′ − zs)ρOTS (z′) dz′ −

∫z

■

=

APPENDIX A In this section, eq 9 is formally obtained starting from the definition of the partial dipole moment given in eq 1. The surface partial dipole moment, in fact, can be decomposed as

∫z

s

z

*

∫z

c

(z′ − zs)ρH:Si (z′) dz′

s

(z′ − zs)[ρOTS (z′) − ρH:Si (z′)] dz′

s

= [d OTS(zs) − d OTS(z )] − [d H:Si(zs) − d H:Si(z )] * *

(13)

Collecting all the results, the decomposition dOTS(zs) = dH:Si(zs) + d* + dOH + dSA Si−O−Si + d(CH2)n + dCH3 is proven. I


Article


■

APPENDIX B At different surface partial coverages, depolarization effects due to xy charge rearrangements between SAM molecules have to be taken into account carefully in the computation of the variation of the surface dipole Δds; if we consider different coverage ratios, indicated in the following as θ, the effect of dipole fields in the plane containing the SAM molecules is expected to reduce the partial dipole values in the decomposition in eq 9 for θ approaching 1 (i.e. full coverage), thus affecting the internal electric field in the SAM coating. This effect is expected to be more marked in the presence of an external applied electric field; the total electric field in the SAM coating is the sum of the two. While these consideration fully apply for the d(CH2)n and dCH3, the d* term is expected to behave differently because of its most intricate definition, which involves the removal of a Si−H bond and the formation of a Si−O bond between the hydrogenated Si surface and the OTS molecule and the inclusion of the first Si monolayer, which is unaffected by dipolar modifications. A simple phenomenological model25,30 can be employed to explore the role of such effects. In the model, each part of the SAM molecule (the Si(OH)3(CH2)2 adhesion group, OH groups, CH2 trimers, and CH3 group, see above) is treated as a point dipole, and the SAM coverage of the Si surface is therefore modeled as a collection of planar ordered arrays of vertically oriented polarizable point dipoles. On the two-dimensional (111) Si surface the position of each adsorption site can be expressed as r = na + mb with n and m integers and a and b the hexagonal translation vectors of the (111) Si surface. A point dipole array creates a vertical electric field Edip Z at the dipolar plane that affects a SAM molecule at the origin (r = 0) Ezdip[θ ] =−

d =− 4πε0

+∞

A simple test for eq 5 has been carried out for a system mimicking different partial coverages of the Si surface of densely packed arrays of CH3(CH2)16CH3 molecules aligned along the z axis, resembling what we would have in a typical partial coverage of the H:Si slab, provided the PBCs are applied. The test has been carried out by studying the variation per unit molecule, at different partial coverages, of the (CH2)n and CH3 dipole moments when an external electric field is applied. From eq 5, the variation is expected to follow α Δd[θ ] = (d[θ ] − d(0)[θ ]) = Eext 1 + αk[θ ]/a3 a = (17) 1 + bθ c The fitting curves obtained are shown in Figure 5 (black dots) together with the fitted values for a, b, and c; the χ2 values of the fitting curves are rather small (being of the order of 10−5). As mentioned before, of the other contributions that we have considered in our decomposition, namely ΔdOH[θ], Δd SA Si−O−Si[θ] (where present), and Δd*[θ], the first two are two orders of magnitude smaller than the major contributions; therefore, the depolarization effects can be neglected for them. The Δd*[θ] term is not negligible; therefore, its depolarization affects markedly the dielectric constant. However, this term is quite intricate by definition because it includes the adhesion group, the removal of one Si−H bond from the surface, two CH2 groups, and the surface rearrangement due to the different optimization pattern one obtains with and without the external field. Moreover, because d* is typically one third of d(CH2)n, one could expect that also the alkyl chain depolarization affects the Δd*[θ], making rather more complicated its depolarization behavior. As a consequence, the depolarization curve of this term does not follow the simple depolarization model described above.

χm , n [θ ]

∑ m , n =−∞

[a 2n2 + b2m2 + 2mna ·b]3/2

k[θ ] d a3

■

(14)

*E-mail: [email protected].

where d is the point dipole along the z axis and χm,n is equal to 1 only when the adsorption site identified by m,n is occupied, otherwise is equal to 0. k[θ] is a function depending on both the geometry of the surface via the infinite summation, and it is a monotonic function of the θ parameter. Hence, a point dipole located at r = 0 is polarized by the electric field Edip z [θ] and the external applied electric field Eext, i.e. d ≡ d[θ ] = d0 + α(Ezdip[θ ] + Eext)

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Computational resources have been provided by the Italian National Agency for New Technology, Energy and the Environment (ENEA) under the ENEA-GRID CRESCO project. We warmly acknowledge these institutions for contributing to the present article.

(15)

■

where α is the polarizability and d0 is the z component of the intrinsic dipole moment of the isolated molecule adsorbed on the surface. The above equations give for the dipole, d, the value d[θ ] =

d0 1 + αk[θ ]/a

(0)

3

= d [θ ] + Eextf [θ ]

+ Eext

AUTHOR INFORMATION

Corresponding Author

REFERENCES

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α 1 + αk[θ ]/a3 (16)

The first term, d [θ], is the variation of the intrinsic point dipole moment due to the array of the other dipoles with no external electric field applied, while the second one is the additional contribution to the depolarization when an external electric field is applied. (0)

J


Article


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Dielectric Properties of Self-Assembled Monolayer Coatings on a (111

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