PHYSICAL REVIEW B 84, 195323 (2011)

Functionalization of hydrogenated (111) silicon surface with hydrophobic polymer chains

F. Gala and G. Zollo*

Dipartimento di Scienze di Base e Applicate per l’Ingegneria (Sezione di Fisica), Universita di Roma “La Sapienza”,Via A. Scarpa 14–16, I-00161 Rome, Italy

(Received 20 June 2011; revised manuscript received 10 October 2011; published 28 November 2011)

The first stage functionalization of hydrogenated (111) Si surface with methyl-terminated monolayers to formhydrophobic coatings has been studied by accurate ab initio density functional total energy calculations. Thefirst stage adsorption events involving one or two deposited n-alkane and n-alkyl-silane molecules have beencharacterized from the geometrical and the energetic points of view; the ground-state adsorption configurationstogether with the geometrical and the energetic parameters relevant to self-assembling processes have beenobtained, such as the polymers tilt angles, the rotation energy barriers, the binding energies, and the electrostaticinteractions. The above-mentioned quantities have been related to the stability properties of self-assembledmonolayers and have been recognized to affect critically the stability and the uniformity of the hydrophobic filmelucidating the reasons why some commonly used polymers behave differently.

DOI: 10.1103/PhysRevB.84.195323 PACS number(s): 73.20.Hb, 71.15.Mb, 81.16.Dn

I. INTRODUCTION

The novel interest in fluid dynamics at the nanoscale haspointed out the need for a better understanding of transportproperties of liquids in contact with a solid surface. The subjectis of great interest in the fabrication of nanosized devices forthe analysis of biological species, such as proteins or DNAmolecules.1,2 Nowadays gel electrophoresis is still the standardmethod for separating proteins; however, the randomness ofthe gel’s structure makes it difficult to tune properly thesedevices in order to control protein selectivity. As an alternative,nanofluidic molecular sieving systems, implemented in theframework of the semiconductor nanotechnology, have beenproposed and applied successfully for biomolecules of varioussize.3,4 Such devices are made essentially by long channelsproduced on a silicon substrate by standard photolithographytechnique; if an external electric field is applied and the deviceis soaked in an electrolyte solution containing the biologicalmaterial to be separated, the sieving mechanism is obtained byalternating thick and thin regions in the canal through which thedifferent molecules are driven and from which they escape withdifferent time scales. These nanocanals may suffer of electro-osmotic effects due to charged walls: The ionic particles of theelectrolyte solution are forced by the electrostatic interactionsto rearrange themselves in the liquid in order to screen thecharge at the interface thus forming an electrical double layer(EDL) of adsorbed and semimobile particles. The couplingbetween the ions of the EDL and the diffusing biomolecules af-fects both the resolution and the fine tuning of the nanocanals.A standard method to avoid this problem is to depositon the surface a hydrophobic, self-assembled monolayer(SAM) with an ending methyl group, as chlorodimethyloctyl-silane5 (CH3(CH2)7Si(CH3)2Cl), octadecyltriethoxysilane6

(CH3(CH2)17Si(OC2H5)3), or octadecyltriclorosilane7 (CH3

(CH2)17SiCl3) (OTS); in particular, the latter one is agood choice for surface modifications and functionalizationapplications8 mainly because of the high quality of the SAMproduced (i.e., a great stability and a certain facility of forminguniform and complete self-assembled monolayers).

The study and characterization of SAMs obtained by depo-sition of alkyl silanes or alkyl chains on Si or SiO2 surfaces

has been undertaken mainly from the experimental point ofview by using several techniques to evaluate both the filmquality (coverage, surface roughness, temperature stability)and its structure (self-assembling properties, thickness, chainorientation, hydrophobic termination groups). Several exper-imental data from, for instance, ellipsometry, infrared spec-troscopy, x-ray photoelectron spectroscopy (XPS), reflectivityand absorption fine structure (NEXAFS),9–12 can be foundconcerning the structural properties of the deposited films.

It must be emphasized that the chemical composition ofthe SAM film depends dramatically on the deposition methodand on the chemical environment used to deposit it, whichcould result, usually, in different structural characteristics forfilms obtained from OTS, alkylmetyldiclorosilanes (whereone Cl atom is replaced by a metyl group), 1-octadecene(CH3(CH2)15CHCH2), fluorinated OTS, etc. Due to such awide number of case studies, much attention is required ifone wants to infer general trends concerning SAM propertieson hydrogenated (111) Si substrate. Indeed, the physicalproperties of SAM on Si substrate could be quite differentdepending on the way the SAM is deposited on the surface,which turns out to depend on the chemical environmentand on the precursor used during the deposition process.As mentioned before, from a careful examination of theexperimental literature on SAM functionalized Si, someindication concerning the atomistic description of the adhesioncan be inferred such as the tilt angle θtilt formed by thecarbon chain axis and the Si surface normal axis;10,12,13 morespecifically, the tilt angle on the (111) Si substrate has beenmeasured in the range θtilt ∈ [0◦,10◦] for OTS and θtilt ∼ 35◦

for n-alkyl monolayers,9 respectively. The cited experimentaldata, however, may be affected by inaccuracies related tothe experimental techniques (such as the ellipsometry case)and thus reliable atomistic models of the investigated filmsand adhesion configurations are highly desirable also asguidelines to interpret the experimental data. Following a fewpreliminary results published elsewhere,14 in this article wereport on accurate ab initio atomistic models of adhesionpatterns of n-alkane and n-alkyne silane as building blocksof hydrophobic SAM on a hydrogenated (111) Si surface

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F. GALA AND G. ZOLLO PHYSICAL REVIEW B 84, 195323 (2011)

focusing on the first-stage processes involving one or twoadhesion events.

II. THEORETICAL METHOD

In the present work, the properties of SAMs on the (111)Si surface have been studied by first-principles calculationsbased on density functional theory (DFT). A generalizedgradient approximation (GGA), using the Perdew-Burke-Ernzerhof formula15 (PBE) for the electron exchange andcorrelation energy have been employed, and norm-conservingpseudopotentials have been constructed with the Troullier-Martins scheme16 in the framework of a plane-wave basisset expansion. All the first-principles calculations have beenperformed using the QUANTUM-ESPRESSO package,17 with aplane-wave energy cutoff of 150 Ry for the wave functions.

The silicon surface has been modeled as a three-layer slabof 96 atoms with 32 Si atoms per layer, the vacuum regionshave been chosen to be equal to 18 Si atomic layers (∼43 A),and all the dangling bonds of the Si slab have been passivatedwith H atoms. Periodic boundary conditions (PBCs) havebeen employed together with a dipole correction rectifyingthe artificial electric field across the slab induced by PBC.18

The (111) surface has been chosen to lay in the xy plane.Due to the computational workload entailed, the 0K

ground-state configurations of the studied structures wereachieved by means of a two-stage optimization procedure: wefirst performed a constrained optimization by varying staticallysome geometrical parameters, such as the angles formed bythe polymer carbon chain and the surface normal axis or thesurface unit vectors and keeping fixed some internal anglesand bond distances; then, the minimum energy configurationobtained statically was fully relaxed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method19 together with theHellmann-Feynman forces acting on the ions. Both calcula-tions were performed using a (2×2×1) Mokhorst-Pack k-pointgrid20 for the Brillouin zone sampling that has been proven toguarantee the total energy convergence as confirmed by severalaccurate tests performed on the Si surface concerning the totalenergy convergence with the energy cutoff and the k-pointmesh (see Fig. 1). The ionic minimization was done until theconvergence threshold of 0.001 a.u. of the total force wasachieved.

The precursors used in the present study for the surfacefunctionalization were chosen looking at the experimentalliterature: Indeed, both the octadecane and the OTS areamong the most commonly used polymers for hydrophobiccoatings of Si. In the OTS case, however, we consider thehydroxylated molecule because in water solution the Clatoms are replaced by the −(OH) groups via the reactionCH3(CH2)17SiCl3 + 3H2O ⇀↽ CH3(CH2)17Si(OH)3 + 3HCl.

The molecule adsorption occurs following one of the tworeactions:

CH3(CH2)17Si(OH)3(CH3)2(CH2)16

}+ H:Si ⇀↽ A/H:Si + B(g), (1)

where H:Si indicates the silicon surface passivated withhydrogen atoms, A/H:Si is the molecule (OTS or 18-alkyl)adsorbed on such a surface, and B(g) is in general a gaseous

FIG. 1. Total energy of the supercell containing the hydrogen-terminated Si(111) slab as a function of the energy cutoff for differentMonkhorst-Pack k-point grids.

hydrogenated molecule containing an H atom coming fromthe adsorption site of the surface.

The adsorption energies of reactions in Eq. (1) are definedas

Eads = E(A/H:Si)+ E(B)

−{

E(CH3(CH2)17Si(OH)3)E((CH3)2(CH2)16)

}− E(H:Si). (2)

The adhesion bond between the molecule and the surfacehas been analyzed with the aid of maximally localized Wannierfunctions21 (MLWFs) wn(r − R) centered on it, and associatedwith band n in cell R, given in terms of Bloch states |ψnk〉 as

wn(r − R) = 〈r|Rn〉 = �

(2π )3

∫BZ

e−ik·R〈r|ψnk〉d3k, (3)

where � is the total volume of the supercell; MLWFs havebeen evaluated through the WANNIER90 package.22

Using the ground-state electron charge density ρel(r) of thedifferent configurations studied, we have calculated the totalelectrostatic potential by solving the Poisson equation in thereciprocal space18,23 with the Fourier transform of the totalcharge density ρ(r) = ρion(r) + ρel(r) as a source function.The ionic part of such density is modeled as a superpositionof delta functions in the real space:

ρion(r) =∑

j

Zvalj δ(3)(r − Rj ), (4)

where Zvalj and Rj are the valence charge and the position of

the j th ion in the supercell, respectively. From the obtainedpotential field maps, the force field of short-range strongdipolar interactions, such as hydrogen bonding, will beevidenced and studied while qualitative indications will bededuced concerning the weaker long-range Van der Waalsdipolar interactions; it is known, indeed, that state-of-the-arttime-independent DFT calculations, in both the LDA and GGAapproximations, are affected by inaccuracies concerning the

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long-range Van der Waals interactions due to the formulation ofthe exchange-correlation electron many-body energy term,24

even though a general qualitative scenario can still be inferredat this level of theory. However, wherever required by thesystem examined, such as in the case of the two 18-alkylpolymers adsorbed at adjacent sites (see Sec. III B 1), we haveused a semiempirical correction to evaluate more precisely thelong-range dispersion forces and their contribution to the totalenergy.25

III. RESULTS AND DISCUSSION

In this section we report on the properties of isolatedhydrophobic polymers adsorbed on the hydrogenated (111)Si surface and of the system made of two interacting polymersadsorbed at adjacent sites of the surface to form the nucleationseed of a SAM; the cases of isolated and interacting polymersare discussed separately.

A. Isolated hydrophobic polymers on (111) Si:H

Hydrophobic SAM films on hydrogenated (111) Si surfaceshave been often realized through the deposition of n-alkylchains or OTS in different chemical environments; thus in thissubsection we report on the properties of isolated 18-alkyl andOTS polymers on the hydrogenated (111) Si surface and thetwo cases are treated separately.

1. The 18-alkyl case

The adhesion of an octadecane molecule on the (111) Si:Hsurface occurs through the formation of a Si-C bond. First of allwe have found the equilibrium Si-C bond length keeping fixedthe tetrahedral coordinations of the C atoms. The equilibriumlength of the adhesion bond is found to be dSiC ≈ 1.88A,that is, quite close to the values reported in the literaturefor tetrahedrally coordinated SiC politypes;26 then we haveperformed a sequence of preliminary static calculations toexplore the possible adhesion configurations of the polymer onthe Si surface. More specifically we have changed the directionof the polymer axis with respect to the normal axis n alignedalong the [111] direction and two reference in-plane axes onthe (111) Si surface, e1 and e2 [see Fig. 2(a)]. Therefore wehave used two configuration angles ϕ1, ϕ2 between the Si-Cbond direction and the unit vectors e1 and e2, respectively, inthe (n, e1) and in the (n, e2) planes and one rotation angle θ

of the Si-C bond direction around the [111] direction, namelythe angle formed between the projection of the polymer axison the (111) Si surface and the reference in-plane direction e1

[see Fig. 2(b)].The results collected by varying the ϕ1 and ϕ2 angles

are shown in Fig. 3(a) where it clearly emerges that theminimum energy configuration obtained is the one withthe Si-C bond aligned along the [111] direction (i.e., theone preserving the tetrahedral coordination of Si); there-fore the tilt angle θtilt ∼ 35◦ formed between the directionof the polymer chain and the [111] direction is constrainedby the tetrahedral coordination of the Si and the C atomsinvolved in the adhesion configuration. The static calculationsperformed by varying θ with φ1 = φ2 = π/2 are reported inFig. 3(b) evidencing that the minimum energy configuration

FIG. 2. (Color online) Adsorption configuration of the alkyl chainon the (111) Si:H surface. The adhesion geometry is described interms of the ϕ1 and ϕ2 angles, formed by the Si-C bond direction withrespect to the surface unit vectors e1 and e2, and the θ angle betweenthe polymer chain projection on the surface and the e1 unit vector(see the text). The configuration angles are changed statically duringthe constrained first optimization stage.

is the one with θ = 0◦ or, equivalently, θ = n π/3 (n =0,1 . . . 5), which guarantees the weakest interaction betweenthe next lowermost hydrogens of the polymer and the hy-drogenated Si surface; this result is in qualitative agreementwith previous experimental measurements9 and evidences, as

.

FIG. 3. (Color online) Total energies for different CH3

(CH2)17/H : Si configurations obtained during the constrained firstoptimization stage (see the caption of Fig. 2 for the details) byvarying either ϕ1/ϕ2 (with θ ≡ θmin = 0) (a) or θ (with ϕ1 =ϕ2 = π/2) (b). All the energies are referred to the most stableconfiguration. Both the static calculations have been performedwith the fixed Si-C adhesion bond of ∼1.88 A as discussed in thetext.

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expected, that the most stable configuration is simply drivenby the sp3 coordination constraints of the C and Si atoms andby the steric hindrance between the hydrogen atoms of thealkyl chain and the ones on the hydrogenated surface.

The energy barrier for rotations around the equilibrium Si-Cbond direction (i.e., around the [111] axis) is only 38 meV,which, using simple transition state theory considerations,27

leads to the estimate of the rotation frequency of ν ∼ 1012 s−1

at room temperature (RT). Hence, high coverage values aremost probably prevented because the available Si surfaceadsorption sites, which are neighbors of a 18-alkyl function-alized surface site, are hindered by the thermal rotation of thepolymer; this circumstance, together with the observation thatstrain effects at high coverage values may result in instabilitiesof the alkyl monolayer,28 may limit coverage of the (111) Sisurface with alkyl chains, even for long reaction times, inagreement with the experimental finding of partial coverageof the hydrogenated (111) Si surface [about 50% monolayer(ML)] with fragmented island-shaped MLs.29 It should also bekept in mind that the alkyl chain may be in various differentisomeric configurations that are about 86 meV higher inenergy for each eclipsed geometry involving neighboring CH2

monomers and also this circumstance may affect the coveragelimit30 at a higher temperature than RT.

Subsequently, starting from the previous minimum energyconfiguration, the system has been fully relaxed as detailedin the previous section; the ground-state configuration ofthe 18-alkyl adhesion on (111) H:Si, reported in Fig. 4(a),differs slightly from the one discussed previously because,despite θ being unchanged, the φ1 and φ2 values are equallymodified by a small quantity ϕ ∼ 5◦ while the tilt angle value

FIG. 4. (Color online) Fully relaxed configuration of the 18-alkylchain (a) and the hydroxylated OTS molecule (b) adsorbed on thehydrogenated (111) Si surface. In the insets the (111) plane view isreported for both the configurations.

is θtilt ∼ 33◦, in excellent agreement with the experimentalmeasurements,9 indicating that the adhesion geometry is stillled by the tetrahedral coordination of Si and C [see the insetof Fig. 2(a)]. In order to check this circumstance we havecompared the Si-C adhesion bond length and the Si-C-Cadhesion angle of the fully relaxed 18-alkyl adhesion geometrywith the same quantities in a fully relaxed hydroxylatedOTS molecule that may also be used as a precursor for theformation of a monolayer of pure alkyl chains as pointed outexperimentally;31,32 we found that these values are larger byabout +0.5 A and +0.6◦ with respect to the OTS values thatare, respectively, dSiC =1.86 A and αSiCC = 115.2◦; moreoverthe Lowdin population analysis shows a small variation q ∼−0.15 e− of the charge on the C atom involved in the bridgebond compared to the CH3(CH2)17Si(OH)3 case.

The nature of the chemical bonding between the moleculeand the Si surface has been investigated looking at the electroncharge density profile in the plane containing the adhesionbond and at the Wannier function centered on it. The resultsreported in Fig. 5 show that this bond has a clear σ characterbetween two sp3 hybrid valence orbitals belonging to Si andC; the MLWF center is shifted toward the C atom by about17% with respect to the bond midpoint as expected due to thelarger electronegativity of the C atom.

We have explored two possible reaction pathways for thedeposition of an 18-alkyl on a (111) Si:H surface involvingeither a hydroxylated OTS or a 18-alkane as precursors:

CH3(CH2)17Si(OH)3(CH3)2(CH2)16

}+ H:Si

⇀↽

{CH3(CH2)17/H:Si + HSi(OH)3(g)CH3(CH2)17/H:Si + H2(g).

(5)

The calculated reaction energy values, reported in Table I,show that the reaction is endothermic using OTS as precursors(Eads = 0.16 eV in parentheses in Table I), needing additionalthermal energy mainly to separate the −Si(OH)3 radical from

FIG. 5. (Color online) Charge density map (in e− units) in the(010) plane containing the Si-C adhesion bond (a). Contour plot inthe (010) plane of the maximally localized Wannier function centeredon the Si-C adhesion bond of the alkyl molecule and the (111) Sisurface (b). The MLWFs (in units of a

−3/20 ) observed along the Si-C

bond direction reveal the σ bonding features between two sp3 hybridsbelonging to Si and C.

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TABLE I. Adsorption energy for the various configurationsconsidered in the present work.

Configuration Eads (eV)

CH3(CH2)17/H:Si −2.38 (+0.16)2xCH3(CH2)17/H:Si −4.63 (+0.45)CH3(CH2)17Si(OH)2O/H:Si −0.642xCH3(CH2)17Si(OH)2O/H:Si −1.47

the OTS molecule before proceeding to the adhesion on thesurface; on the contrary the reaction is highly exothermicfor the n-alkane case (Eads= −2.38 eV), in agreement withprevious experimental results.31,32

2. The OTS case

The simplest chemical path that may be used to deposit OTSmonolayers on a hydrogenated (111) Si surface must involvethe octadecyltrihydroxysilane as a precursor obtained in watersolution from OTS.

In this way, the surface functionalization proceeds via thefollowing reaction:

CH3(CH2)17Si(OH)3 + H:Si⇀↽ CH3(CH2)17Si(OH)2O/H:Si + H2(g), (6)

where the polymer is expected to be bonded to the siliconsurface through an oxygen atom forming two Si-O bonds, onewith the Si atom belonging to the OTS molecule and the otherwith an Si atom on the (111) surface.

As for the alkyl case, for computational reasons we haveinitially studied the energetics and the configurations ofthe deposited molecule by total energy calculations withoutstructural relaxation; the different configurations have beenexplored by varying the direction of the Si-O bond at thetopmost Si layer with the silane group constrained at itsoriginal tetrahedral geometry. Thus, similarly to the 18-alkylcase, the static calculations have been performed by changingthe rotation angle ϑ around the [111] axis (see Fig. 6) and thetwo angles ϕ1, ϕ2 between the Si-O bond at the topmost Si layerand the e1, e2 unit vectors thus setting the chain orientation,respectively, in the planes (e1,n) and (e2,n). Moreover, we havealso explored other configurations that differ by the orientationof the hydroxyl groups in the silane structure because thesegroups interact with the hydrogens at the Si surface. The energyvalues of the various configurations obtained by varying ϕ1,ϕ2, and θ are shown in Figs. 7(a) and 7(b), respectively.The minimum energy configuration obtained by varying ϕ isreported in Fig. 6(a) and shows a slight distortion of the bondangle orientation with respect to the surface normal vector(∼ 6◦). The energy variation with θ exhibits the expectedquasiperiodic behavior with clear energy minima and maximareflecting the interaction between the two hydroxyl groups inthe silane structure and the hydrogen atoms on the Si topmostlayer; indeed, the most stable configuration is the one with thelargest distance between the hydrogen atoms of the hydroxylgroups and the ones at the topmost Si layer. The lone pairsof the oxygen atoms, instead, are unlikely to interact with thehydrogens on the Si surface that are too far away. The energybarrier measured between the highest energy configuration and

FIG. 6. (Color online) Adsorption configuration of the alkyl chainon the (111) Si:H surface. The adhesion geometry is described interms of the ϕ1 and ϕ2 angles, respectively, formed by the Si-O bonddirection (d) and the surface unit vectors e1 and e2, and the θ anglebetween the polymer chain projection on the surface and the e1 unitvector (see the text). The configuration angles are changed staticallyduring the constrained first optimization stage.

FIG. 7. (Color online) Total energies for different adsorptionconfigurations of a hydroxylated OTS molecule on the (111) Si:Hsurface obtained during the constrained first optimization stage(see the caption of Fig. 6 for the details) by varying ϕ1 (ϕ2)with θ ≡ θmin = 0) (a) and ϕ2 = π/2 (ϕ1 = π/2) (a) or θ (withϕ2 = π/2 and ϕ1 = ϕ2 + π/30) (b). All the energies are referred tothe most stable configuration. Both the static calculations have beenperformed with Si-O adhesion bond length constrained at its equi-librium value dSiO ∼ 1.65 A in a fully relaxed CH3(CH2)17Si(OH3)molecule.

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the most stable one is E ≈ 0.1 eV and is large enough toprevent any rotation around the [111] axis at RT.

Then a full structural optimization has been performedstarting from this initial configuration and following theprescriptions discussed in Sec. II; the resulting minimumenergy configuration is shown in Fig. 4(b); it is worth notingthat the equilibrium final positions of the two hydroxyl groupshave been somehow constrained by the repulsive interactionwith the hydrogen atoms bonded on the surface. The tiltangle between the main direction of the polymer chain andthe [111] surface normal is θtilt ∼ 10.9◦, in good agreementwith the experimental measurements.10,13 Generally speaking,the equilibrium configuration of the OTS adhesion obtainedafter the full relaxation is quite similar to the fully relaxedconfiguration of the isolated hydroxylated OTS moleculewith no significant geometrical difference even in the sylanegroup; moreover the bond distance between the Si atom ofthe surface and the O atom of the molecule has been foundto be dSiO = 1.65 A (i.e., almost the same Si-O distancein the isolated molecule). The hydroxylated OTS polymeris the natural precursor for deposition on the hydrogenated(111) Si surface and the calculation of the adsorption energy,reported in Table I, gives Eads = −0.64 eV revealing thatthe adsorption reaction is exothermic. It must be emphasized,however, that the adsorption energy in this case is about fourtimes lower than the adsorption energy of one 18-alkyl withthe 18-alkane as precursor and, as a consequence, it is expectedthat, at least in principle, this last reaction should be largelyfavored.

The electron charge density map of the ground-stateconfiguration, reported in Fig. 8(a), reveals that a significantcharge transfer occurs with respect to the isolated hydroxylatedmolecule involving, in particular, the O atom connecting the

FIG. 8. (Color online) Charge density map (in e− units) in the(010) plane containing the Si-O adhesion bond (a). Contour plot inthe (010) plane of the MLWFs centered on the Si-O adhesion bondbetween the hydroxylated OTS molecule and the (111) Si surface(b). The MLWFs (in units of a

−3/20 ) observed along the Si-O bond

direction evidences a slight distortion of the σ bond between Siand O.

Si surface and the silane group. Indeed the Lowdin populationanalysis shows that the electron charge on the oxygen atomis reduced by q = 0.3 e− with respect to its charge in theOH group of the isolated OTS case (q = 6.45 e− for O andq = 0.55 e− for H); this surprising charge depletion of the Oatom is accompanied by a slight increase of the negative chargebelonging to the first C atom of the polymer chain.

The other O atoms belonging to the OH groups not involvedin the bond with the surface, on the contrary, do not show anycharge transfer with respect to the isolated OTS molecule. Inthis case the valence electron charge belonging to an oxygenatom that contains the contributions from the two lone pairs isalso increased by half an electron transferred from the bondedH atoms, thus resulting in a negative charge density excessthat might be involved in long-range interactions between twoor more OTS molecules adsorbed at adjacent sites of a siliconsurface.

B. Interaction of hydrophobic polymers on (111) Si:H surface

Besides the adhesion stability, other important structuralproperties of SAM films deposited on the (111) Si surfaceare uniformity and coverage that depend on the interaction be-tween adjacent adsorbed molecules; hence we have studied theproperties of the ground-state configuration of two polymers,either 18-alkyl or hydroxylated OTS, adsorbed at adjacent siteson the hydrogenated (111) Si surface.

1. The 18-alkyl case

Multiple adsorption events may occur at different sites inde-pendently through the reaction nCH3(CH2)16CH3 + H:Si ⇀↽nCH3(CH2)17/H:Si + nH2(g), n � 2. However, if the adsorp-tions occur at nearest sites, the interactions between theadjacent polymers strongly depend on the dipolar field aroundthe polymers. The interaction is entirely due to long-rangeelectrostatic forces between chain tails and steric hindrancephenomena, with the related distortions of the two neighboringmolecules. Thus, first of all we have calculated the totalelectrostatic potential V (r) generated by the dipolar chargedensity of the 18-alkyl chain; the density map of V (r) in themidplane between the H atoms of the Si(111) surface and the Hatoms of the lowest −CH2 trimer of the alkyl chain, reportedin Fig. 9(a), evidences, as expected, a positive electrostaticpotential that implies necessarily a repulsive interaction (thusan energy increase) between adjacent polymeric chains ad-sorbed on the (111) Si surface. Subsequently we have studiedthe system involving two alkyl chains adsorbed on adjacentsites of the Si (111) surface; the starting configuration, withthe two alkyl chains initially parallel to each other, has beenfully relaxed following the prescription discussed in Sec. IIand the final ground-state configuration is reported in Fig. 10.It is worth evidencing that the finding of the ground-stateconfiguration required quite a long relaxation pattern becausean intermediate configuration, with similar but larger totalenergy, different from the one reported in Fig. 10, occurredfirst, which is characterized by the two alkyl chains repellingeach other almost rigidly through the distortion of the adhesionSi-C bond by θ = 12◦ thus allowing the two chains to stayalmost parallel with a negligible distortion of the tetrahedrallycoordinated monomers with a maximum spread of the internal

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FIG. 9. (Color online) Density maps of the electrostatic potential for the ground-state adsorption configurations in the 18-alkyl (a) and theOTS (b) cases. The density maps have been drawn on meaningful planes parallel to the (111) Si surface, respectively: (a) the midplane betweenthe topmost H atoms of the Si:H surface and the lowermost H atom of the alkyl chain (i.e., the one of the lowermost −CH2 trimer); (b) themidplane between the topmost H atoms of the H:Si surface and the lowermost H atom belonging to the OH groups. The distances from thesurface are 0.70 A in (a) and 0.73 A in (b).

angles of α ≈ 2◦. The ground-state configuration, therefore,has been obtained by using more stringent convergence criteriathat allowed the distinction between the intermediate and theground-state configurations.

The ground-state configuration obtained, on the contrary,keeps almost unchanged the tetrahedral coordination of thesurface Si atom for both the polymers, but one of the twomolecules undergoes a bending in the lower part of the chainthat allows the upper part of the polymers to stay almostparallel [see Fig. 10(a)]. Hence, at the end of the unconstrainedrelaxation run of this system, the two chains undergo a sub-stantial repulsion with the upper part of the chains being about5.83 A apart, that is, nearly 6% larger than the distance betweenthe chains measured for the intermediate configuration. Thusthe energy increase due to the bending distortion occurring inone of the two molecules is overcompensated by the energydecrease due to the mutual repulsion. The calculation of theadsorption energy in the present case gives Eads = −4.63 eVrevealing that, despite being highly exothermic, the adsorptionof two 18-alkyl molecules at adjacent sites is unstable againstthe adsorption of two isolated molecules that would involve anadsorption energy of Eads = −4.76 eV. The energy increasedue to the distortion induced by the interaction between theadjacent chains can be calculated simply as

Eb = E = E(2A/H:Si) + E(H:Si) − 2E(A/H:Si),

(7)

where E(2A/H:Si) is the total energy of the supercell contain-ing two adjacent alkyl chains adsorbed on the hydrogenatedSi slab, E(H:Si) is the total energy of the hydrogenated Sislab, and E(A/H:Si) is the total energy of the supercellcontaining one alkyl chain adsorbed on the hydrogenatedSi slab. The positive binding energy value obtained, Eb =56 meV, evidences that simple alkyl chains are definitely unfitas building blocks for dense and homogeneous hydrophobicfilms on the hydrogenated (111) Si surface because the alkyl

adsorption at distant sites is energetically favored with respectto the adsorption at adjacent sites.

FIG. 10. (Color online) Fully relaxed configurations of twopolymers adsorbed at adjacent sites on the hydrogenated (111)Si surface for the 18-alkyl (a) and the hydroxylated OTS(b) cases.

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The case under study can be potentially affected by theinaccuracies concerning the long-range interactions betweenpolymer chain tails arising from the used formulation ofthe exchange-correlation energy;25 as a consequence, in thepresent case we have corrected the total energy in order togive a better estimate of the long-range interactions by addinga semiempirical correction to the total energy of the varioussystems involved in the calculation of the binding energy fromEq. (7).25 In the case under study the contribution to the totalenergy of the system from the empirical dispersion term isEd = −1.59 Ry, that is, approximately 0.12% of the totalenergy. The inclusion of this attractive term forces the twomolecules to stay closer but does not change the sign of thebinding energy that remains positive (Eb = 12 meV) meaningthat isolated alkyl chains are energetically favored with respectto the case of the two molecules adsorbed on nearest sites,in agreement with the previous DFT calculations where thedispersion term was omitted.

2. The OTS case

The interaction between two hydroxylated OTS polymersadsorbed at adjacent sites on the (111) Si surface dependson the dipolar potential field in the vicinity of the polymerchain that, unlike the 18-alkyl case, is strongly affected by thepresence of the hydroxyl polar groups. The total electrostaticpotential field V (r) generated by an isolated OTS moleculedeposited on the (111) Si surface has been calculated bysolving the Poisson equation with the ground-state chargedensity obtained in the case of the fully relaxed adsorptionconfiguration. In Fig. 9(a) it is shown the density map of thepotential field in the midplane (parallel to the Si surface)between the topmost H atoms of the Si surface and the

lowermost H atom of the OTS hydroxyl groups. The densitymap clearly evidences the negative potential area related to theO lone pairs that coexist with the positive potential regionsoriginating from the alkyl chain. Thus the OH groups favorthe interaction, via an H bond, of the OTS with the positivecharges of the unscreened hydrogens of a second hydroxylatedOTS molecule, eventually adsorbed at an adjacent site ofthe (111) surface. Since Pauling,33 the hydrogen bond hasbeen recognized to play a crucial role in understanding theshort-range order in polar liquids and between polar molecules;it has been shown, moreover, that the hydrogen bond is alsopartially covalent34 and thus it is expected that PBE-basedDFT calculations can describe it accurately within the accuracylimits required here.

Hence we have performed a full relaxation of the hy-drogenated Si slab with two hydroxylated OTS moleculesadsorbed at adjacent sites. The starting configuration waschosen with two exactly parallel OTS molecules on nearestsites of the (111) surface. The adsorption energy calculatedwith respect to the ground-state configuration of hydroxylatedOTS molecules is Eads = E(2A/H:Si) − 2(E(A) − E(H2)) =−1.47 eV (see Table I) that, compared to the adsorption energyof an isolated OTS molecule, indicates that the adsorption atadjacent sites is favored against the adsorption of the isolatedmolecules. During the relaxation process, one of the two OTSmolecules started rotating around its own axis until the H atom,belonging to one of the two OH groups, approached the O atombelonging to one of the hydroxyl groups of the other OTS, thusconfirming that the geometry optimization is determined by thedipolar interaction originating from the hydroxyl groups of theinteracting molecules (i.e., by the formation of one hydrogenbond). In the ground-state configuration that is reported inFig. 10(b) the measurement of the hydrogen bond length

FIG. 11. (Color online) Density maps of the electrostatic potential for the ground-state configurations of two polymers adsorbed at adjacentsites on the hydrogenated (111) Si surface. The density maps for the OTS (a) and the 18-alkyl (b) cases have been drawn on meaningful planesparallel to the (111) Si surface, namely the one that in the OTS case contains the (almost) linear H bond between the OH radicals of the twomolecules (a) and the middle plane between the topmost H atoms of the Si surface and the lowermost H atoms belonging to the alkyl chain(b) [almost the same as Fig. 9(b)].

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and angle are, respectively, dOH = 1.8 A and αOHO = 173◦suggesting the formation of an almost linear H bond. Unlikethe 18-alkyl case, the calculation of the binding energy inthe present case gives Eb = −0.19 eV evidencing that thesystem of two interacting molecules adsorbed at adjacent sitesis stable against the isolated adsorbed OTS molecules. Becausethe relaxation pattern results in the torsion of both the chains,we have evaluated the torsion energy by calculating the totalenergy of an isolated and distorted OTS deposited on the Sisurface that, referred to the energy of the ground-state OTSadsorption configuration, gives Etorsion= 0.085 eV. Using thisvalue, we can now evaluate the energy gain involved in thehydrogen bond as

EHbond =E(2A/H:Si)+E(H:Si)−2[E(A/H:Si)+ Etorsion]

=Eb−2Etorsion, (8)

resulting in EHbond = −0.36 eV. The values of the H-bonddistance and angle here obtained are close to the typicalfingerprints of the H bond measured by x-ray diffraction inice,34,35 respectively, dOH =1.75 A and αOHO = 180◦ whilethe H-bond energy value here obtained is slightly largerthan the consensus in ice (EHbond= −0.29 eV) revealing thatin this case the H bond has a noteworthy stabilizing valuethat is certainly the origin of the observed self-assemblingpatterns in the experiments. Moreover, it is worth noting thatthe computational scheme chosen, and particularly the PBEfunctional formula, is certainly suitable to handle accuratelythe physics and the chemistry of (111) Si surface hydrophobicfunctionalization with OTS SAMs. For the sake of clarityin Fig. 11(a) the potential in the system is drawn containingtwo interacting polymers for both the OTS and the 18-alkylcases. In the OTS case, the V (r) density map, drawn in theplane containing the O-H-O atoms, evidences the existenceof a significant potential energy region [V (r) ∼ 1.7 eV]connecting the two adjacent polymers that is the result of theH bond between the O lone pair (that is located below the planewhere the density map is considered) and the positive H [seeFig. 11(a)]. It is worth noting the torsional deformation of boththe hydroxylated OTS polymers occurring for steric reasonbecause the H bond keeps the two polymers quite close to eachother; the torsional deformation, indeed, relaxes part of theelastic interaction between the polymers and thus contributesto set the binding energy at negative values. This circumstanceis in striking contrast with the case of the two alkyl chains,where a stiffly separation has happened with no other apparentinteractions during the relaxation process, as evidenced alsoby the V (r) density map reported in Fig. 11(b) with negligiblepotential energy values in a region in between the twopolymers.

C. Conclusions

Hydrophobic coatings on hydrogenated (111) Si surfacesare often obtained by deposition of methyl-terminated longalkyl chains. Using first-principles calculations based onthe density functional theory and the PBE formula for theexchange-correlation potential, we have studied the ground-state configurations and the energetics 18-alkyl and hydroxy-

lated OTS polymers adsorbed on the (111) H:Si surface and theinteraction between two polymeric chains adsorbed at adjacentsites. Our study has been focused on those aspects, such asconfigurational properties and dipolar interactions, playing acrucial role for the onset of self-assembling phenomena thatare beneficial for uniform and stable hydrophobic functional-ization of Si. Moreover, we have calculated some importantenergy values, such as the adhesion energy with respect tosome possible adsorption reactions, the binding energy, thetorsional energy, etc., that can be used to evaluate the stabilityof SAM against the precursors and the isolated polymersadsorbed on the Si surface. On the basis of the collected results,we can state that alkyl chains, despite the significant valuesof the adsorption energy for reaction involving 18-alkanes asprecursors (while using OTS precursors the reaction is stronglyendothermic), are definitely unfit for the fabrication of stableand uniform hydrophobic layers, mainly for two reasons: Thefirst one is related to the ground-state adsorption geometry ofan isolated 18-alkyl molecule, namely the CH3(CH2)17/H:Sistructure, that exhibits a significant tilt angle value (θtilt ∼ 33◦)hindering the other possible adsorption sites thus preventingfurther adsorption events. Moreover, the hindrance phenomenaat the surface is even worsened by the small energy barriervalue calculated for rotations around the [111] axis that impliesa large rotation frequency at RT resulting in an extendedhindered area around the adsorbed molecule. Other limitationsemerge if one considers the positive value of the binding energyof adjacent parallel 18-alkyl chains with respect to the isolatedones. This is mainly due to the repulsive interaction betweenthe polymers that results in a not-counterbalanced distortionof the chain tails from the ground-state configuration of thetwo isolated molecules; the absence of polar groups, indeed,prevents the possibility of energetic favored self-assembling.In the case of hydroxylated OTS molecules adsorbed on thehydrogenated (111) Si surface, on the contrary, despite thelower adsorption energy values with respect to the 18-alkylcase, the ground-state configuration of both the isolated andtwo adjacent polymers exhibit some favorable propertiesthat make OTS particularly suitable for Si functionalizationwith homogeneous, uniform, and stable hydrophobic self-assembled monolayers. Indeed, the ground-state adsorptiongeometry is almost orthogonal to the (111) surface, with alower value of the tilt angle (θtilt ∼ 10.9◦) that, contrarily to the18-alkyl case, prevents the steric hindrance of the neighboringsurface adsorption sites by the deposited molecule; thereforethe hindrance of adjacent adsorption sites is, in the presentcase, practically negligible despite the length of the polymericchain because, as in the alkyl case, we do not expect to haveeclipsed isomers at RT. Moreover, the polymer is much morestable at RT against the rotation around the [111] normal axiswith respect to the 18-alkyl case and is practically inhibitedbecause of an energy barrier of about 0.1 eV. The adsorption ofOTS at adjacent sites is, therefore, not only allowed but ener-getically favored because the interaction energy between twoadjacent molecules is driven by the H bond formed betweentwo hydroxyl groups belonging to the different molecules.In this case, indeed, the repulsive energy between the carbonchain is lower than the energy involved in the H bond that keepsthe OTS molecules tightly packed; as a consequence, the closeinteraction between the molecules induces the major part of

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the repulsive energy to be relaxed into a torsional deformationof the carbon chain and the polymers stay packed on thesurface. We can therefore conclude that both the adhesion bondchemistry of the adsorption configuration (i.e., the Si-O-Sibridge versus the Si-C bond) and the existence of tightinteraction phenomena driven by the formation of H bondsfavor the initial self-organizing processes that are a prerequisitefor the synthesis of self-assembling hydrophobic coatingson the (111) Si surface with methyl-terminating polymericchains.

ACKNOWLEDGMENTS

Computational resources have been provided by ConsorzioInteruniversitario per le Applicazioni di Supercalcolo perUniversita e Ricerca (CASPUR) under HPC Grant 2010 andby the Italian National Agency for New technologies, Energyand Sustainable Economic Development (ENEA) under theENEA-GRID CRESCO project. Isosurfaces in the figures havebeen plotted with XCRYSDEN code.36 The authors thank Dr.G. Giovannetti for many helpful discussion concerning thesubject treated in the present study.

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