Electrostatic Field Driven Alignment of Organic Oligomers on ZnO Surfaces
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J a n Electrostatic Field Driven Alignment of Organic Oligomers on ZnO Surfaces
F. Della Sala
National Nanotechnology Laboratory, Istituto Nanoscienze-CNR, Via per Arnesano, I-73100 Lecce, ItalyCentre for Biomolecular Nanotechnologies, IIT, Arnesano, Italy andIRIS Adlershof, Humboldt-Universit¨at zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany
S. Blumstengel and F. Henneberger
Institut f¨ur Physik, Humboldt-Universit¨at zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany (Dated: November 11, 2018)We study the physisorption of organic oligomers on the ZnO(10¯10) surface using first-principlesdensity-functional theory and non-empirical embedding methods. We find that both in-plane loca-tion and orientation of the molecules are completely determined by the coupling of their quadrupolemoments to the periodic dipolar electric field present at the semiconductor surface. The adsorptionis associated with the formation of a molecular dipole moment perpendicular to the surface, whichbears an unexpected linear relation to the molecule-substrate interaction energy. Long oligomerssuch as sexiphenyl become well-aligned with stabilization energies of several 100 meV along rows ofpositive electric field, in full agreement with recent experiments. These findings define a new routetowards the realization of highly-ordered self-assembled arrays of oligomers/polymers on ZnO(10¯10)and similar surfaces.
PACS numbers: Valid PACS appear here
Hybrid structures made of conjugated organicmolecules and inorganic semiconductors exhibit an enor-mous application potential as they combine the favorablefeatures of both components in a single new material [1].However, interfacing of organic molecules with the typ-ically highly reactive semiconductor is a complex issue.Rupture and fragmentation are frequently observed lead-ing to ill-defined interfaces [2]. On the other hand, theelectronic structure of the semiconductor surface mightbe exploited for developing novel strategies of molecularaggregation. In this Letter, we demonstrate that the elec-trostatic interaction between the semiconductor and the π -electron system gives indeed rise to the self-assemblageof stable and highly ordered monolayers for a wide classof conjugated organic molecules.The specific surface under consideration is the non-polar (10¯10) crystal plane of ZnO. The chemistry of ZnOsurfaces, see e.g. Ref. 3, has been largely investigatedin the context of catalysis [4] and, more recently, muchattention is paid to the linkage with organic dyes andpolymers, driven, e.g., by photovoltaic applications [5, 6].In particular, it has been found experimentally that p-sexiphenyl (6P) absorbs flat on the ZnO(10¯10) surfacewith the long axis of the molecule perpendicular to thepolar [0001] direction [7]. In this study, the hybrid in-terface has been formed entirely under ultra-high vac-uum conditions suggesting that intrinsic features of thesemiconductor-molecule system are behind that type ofaggregation. The theoretical analysis presented belownot only confirms this conjecture but reveals systematictendencies common to all oligomers that can be used toengineer the growth of inorganic/organic structures.In order to establish a proper and efficient methodicalframework, we start with biphenyl (2P) as a short model oligomer. Fig. 1a and b depict the configuration ex-amined. The origin of the reference coordinate system islocated at the center of a surface Zn-O bond, the z - and y -axis point along the surface normal and the polar [0001]direction, respectively. The position of the molecule isdenoted by the coordinates of its center of mass. We con-sider a clean, non reconstructed surface optimized usingdensity functional theory (DFT) as described in Ref. 8.Our goal is the construction of the ground-state potentialenergy surface (PES) of the molecule-semiconductor sys-tem. In a first step, we set the center of the molecule ontop of the Zn-O bond ( x = y =0) with its long axis alignedin x -direction and the molecular plane parallel to the sur-face. The interaction energy of this arrangement keepingboth the molecular and ZnO(10¯10) surface configurationfrozen is plotted versus distance from surface ( z ) in Fig.1c. The curves are computed at the PBE level [9] andwith dispersion correction (PBE+D) [10], using two dif-ferent computational methods: a periodic pseudopoten-tial plane-wave (PW) approach[11] and the periodic elec-trostatic embedded cluster method (PEECM) [11, 12], asimplemented in the TURBOMOLE [13] program.Figure 1c shows that the PEECM results agree verywell with the PW ones. The practical advantage ofPEECM lies in the fact that it considers only a singlemolecule in interaction with the surface. Unlike the PWmethod, where a whole periodic organic monolayer (ofhypothetical structure) has to be treated, PEECM de-fines thus a cost effective way to tackle the initial ad-sorption step of the molecule. As expected from previ-ous studies, see e.g. Ref. 14, the PBE functional leads toweak binding, while the dispersion correction increasesthe binding energy and reduces the molecule-substratedistance. In order to verify the accuracy of PBE+D for y x zy z [A] -1.0-0.8-0.6-0.4-0.20.00.20.4 I n t e r ac ti on E n e r gy [ e V ] PBE(PEECM)PBE(PW)PBE+D(PEECM)PBE+D(PW)HF(PEECM)MP2(PEECM) a)b) c)
Zno
FIG. 1: a) Top and b) side view of 2P on theZnO(10¯10) surface (dotted rectangle: surface unit cell). c)Molecule-substrate interaction energy for 2P verus verticaldistance z ( x = y =0), as computed by different theoreticalmethods (see text). ZnO surfaces, we performed reference MP2 calculationswithin the PEECM scheme[11]. Figure 1c exposes thatPBE+D is quite far from MP2 and thus cannot be safelyused for ZnO surfaces. The MP2 predicts an interactionenergy of 370 meV with an equilibrium distance z ≈ y [A] -0.10-0.050.000.050.10 I n t . E n e r gy [ e V ] PBE(PW)PBE(QM/PPC)PBE+D(PW) y [A] -0.4-0.200.20.4 D i po l e [ D ] µ z µ y a)b) FzFy c)d)
FIG. 2: a) Molecule-substrate interaction energy versus y -position measured relative to y = 0 ( x = 0 , z = z ), by differ-ent theoretical methods. The length of the ZnO(10¯10) surfaceunit cell in this direction is 5 .
19 ˚A. b) Induced moleculardipole moment, components µ y and µ z ( µ x = 0) computedin QM/PPC. The electrostatic field of the ZnO(10¯10) surface,from PW/PBE calculations, is illustrated (color online) inc) ( z -component) and d) ( y -component). The colormap cov-ers the range from -5V/nm (intense blue) to 5V/nm (intensered). Also shown is the molecule position at minimum µ y ( y = 2 . As a next step, we now consider the change of themolecule-substrate interaction energy (∆ E ) when themolecule is translated along y -direction. As displayed inFig. 2a, the computations performed again in differentapproximations commonly reveal a distinct minimum for y ≈ point-charges with values+ q and − q at the lattice positions of the Zn and O atoms,respectively. We call this method QM/PPC (quantummechanics/periodic point-charges), because the moleculeis treated quantum mechanically at PBE level, while theZnO surface is classically described. Hence, only the elec-trostatic interaction between the molecule and the sub-strate is considered in this approach. For q =1.2, excellentagreement with the PBE(PW) result is indeed achieved.This value q is very close to what is found in the Mullikenpopulation analysis of the ZnO(10¯10) surface [8]. There-fore, we conclude that exchange-correlation forces deter-mine the absolute energy (see Fig. 1c), but the energyvariation when moving the molecule within the surfaceplane is completely dominated by the electrostatic cou-pling. Exchange-correlation effects vary on the atomiclength scale, but are averaged out as the molecule islarger than the ZnO(10¯10) unit cell.The alternating point charges which characterize theZnO(10¯10) surface create a periodic dipolar electric field ~F . An important consequence of this field is that it gen-erates in turn an induced dipole moment ~µ in the 2Pmolecule. For symmetry reasons, F x is negligible, while F y and F z reach values of several V/nm. The resultant µ y and µ z are plotted versus y -position in Fig. 2b. Overthe length a of the unit cell, they change sign with a rel-ative of shift of a/
4. This behavior reflects the dipolarcharacter of ~F , as illustrated in Fig. 2c,d. The electricfield is largely inhomogeneous, but sufficiently far fromthe surface where the molecule is located, it has oscillat-ing character. When y ≈ . µ y reaches its negativemaximum. At this position, as schematized in Fig. 2d,the molecule experiences a negative electric field over al-most its whole size, whereas the average of F z is almostzero and thus µ z ≈ x -direction and rotation around the z -axis. TheQM/PPC approach makes it possible to scan a set of1500 different molecular configurations. The results arecondensed in Fig. 3. The QM/PPC interaction energy(relative to the isolated molecule) is represented in Fig.3a as a function of the rotation angle θ for the whole setof x - and y -positions sampled over the ZnO(10¯10) surfaceunit cell. θ [degree]-0.20-0.15-0.10-0.050.000.050.10 I n t e r ac ti on E n e r gy [ e V ] -0.5 0 0.5 µ y [D] -0.2 0 0.2 µ z [D] a) b) c) θ=90 FIG. 3: Adsorption scenario of 2P on the ZnO(10¯10) surfaceas computed by the QM/PPC method. a) Molecule-substrateinteraction energy versus rotation angle θ for all x - and y -positions counted. θ = 0: long molecular axis along x -direction (see Fig 1a). In b) and c), the interaction energyis plotted versus the z - and y -component, respectively, of theinduced dipole moment The absolute minimum is found at θ = 90 ◦ (long 2Paxis k y ). However, there is also a second minimum at θ = 0, which corresponds to the one in Fig. 2a. Theenergy difference between the two minima is only 20meV and hence within the numerical error range. Weconclude that the 2P molecule can be arranged on theZnO(10¯10) surface in two different cross-aligned orienta-tions which makes the formation of a well ordered mono-layer rather questionable.The central question to be answered is about the mech-anism controlling the alignment of the molecule. Theinterplay between the surface electrostatic field, the in-duced dipole moment, and the interaction energy be-comes evident from Fig. 3b and c. There is a distinctlinear relation between the ∆ E and µ z . The energy ismimimized if and only if the dipole moment along z ismaximized . On the other hand, as seen in Fig. 3c, itholds µ y ≈ µ z .The above findings become more transparent in ananalytical model gathering the leading features of themolecule-substrate electrostatics. The energy of amolecule with zero static dipole but finite quadrupolemoment M ij in a weak but non-uniform electric field( F x ≈
0) is [16]∆ E ≈ − X i = y,z (cid:18) M ii d F i d r i + α ii F i (cid:19) , (1)where α ij is the molecule’s polarizability tensor. Thisexpression is derived from perturbation theory: the firstterm represents the electrostatic interaction between theexternal non-uniform perturbing field and the unper-turbed molecule, the second one the induction energy [16] accounting for the molecular polarization created by thefield. Eq. (1) is valid for a large class of planar, sym-metric oligomers characterized by vanishing off-diagonalelements of M ij and α ij . The ZnO(10¯10) surface peri-odic dipolar electric field seen by the molecule can beapproximated by (see Fig 2c,d and Ref. 11) F y ( y, z ) ≈ A e − kz cos( ky ) , F z ( y, z ) ≈ − A e − kz sin( ky )with k = 2 π/a so that its norm ( F ≈ A e − kz ) is indepen-dent on y andd F y d y ≈ kF z , d F z d z ≈ − kF z . (2)Using that µ i = α ii F i and inserting (2) in (1), we obtain∆ E ≈ − Bµ z − Cµ z − α yy F B = k ( M yy − M zz ) / α zz and C = ( α yy − α zz ) / α zz . molecule M yy M zz α xx α zz B Ca.u. a.u. a.u. a.u. eV/D eV/D
2P -46.2 -57.3 217.4 68.2 0.558 0.0686P -135.7 -168.4 1257.6 190.5 0.589 0.0625A -82.6 -101.4 645.2 115.2 0.557 0.0845PV -145.3 -180.1 2052.9 207.8 0.574 0.090TABLE I: PBE quadrupole moments ( M yy , M zz ), polarizabil-ities ( α xx , α zz ) as well as B and C coefficients (see text) fordifferent molecules. Table I compiles the values of the relevant param-eters for 2P and three other representative molecules(6P, 5A=pentacene, 5PV=penta-phenylene-vinylene), allwidely used in organic opto-electronics. Though theanisotropy of α can be quite significant, the termquadratic in µ z in (3), originating from the inductionenergy, is negligible against the linear term (i.e., thequadrupolar contribution) for weak fields. Hence, theanalytical model fully recovers the numerical results ofFig. 3b. A linear fit to the data in Fig. 3b for 2P pro-vides a slope of -0.48 eV/D in very good agreement withthe value expected from Table I.The analytical treatment suggests that the electro-static scenario found for 2P is of general validity. In-deed, the full numerical analysis confirms this for 6P, 6A,and 5PV. A global optimization for molecules of this sizecannot be carried out using first-principles methods onlyand, usually, semi-empirical approximations have to beemployed [17]. The QM/PPC approach is instead non-empirical because the only parameter (q) is fixed froma first-principles (PBE/PW) calculations. We thus wereable to perform the same global scan of the PES as for2P. Fig. 4a demonstrates that the linear relation betweeninteraction energy and vertical dipole moment is a com-mon feature for this class of non-polar molecules. Even,the slope of the curves is almost the same (-0.46 ÷ -0.58eV/D), consistent with the similar values of B in Tab. I. -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 µ z [D] -0.6-0.4-0.200.2 I n t e r ac ti on E n e r gy [ e V ] θ [degree] -0.6-0.4-0.20 I n t e r ac ti on E n e r gy [ e V ] a)b) ∆ y FIG. 4: Interaction energy for 6P, 5A and 5PV onZnO(10¯10) in QM/PPC. a) Linear relation between molecule-substrate interaction energy and induced vertical dipole mo-ment. b) Interaction energy versus rotation angle, only theminimum values from all x - and y -positions scanned areshown. Inset (color-online): Orientation of 6P at the globalminimum shown on a colormap of the z -component of thesurface electric field. Although the linear energy-dipole relation holds for allthese molecules, the specific alignment on the substratecan be substantially different. This is documented in Fig.4b, where the energy is plotted as a function of θ at x -and y -positions with minimized energy. In contrast to2P, the PES of both 6P and 5PV exhibits deep globalminima at θ = 0, clearly separated by 140 meV and 330meV, respectively, from other arrangements. Not onlythe orientation but also the lateral position of the ad-sorption site is uniquely defined, with y ≈ x = 0 for both 5PV and 6P. Thus, as illustrated in theinset for 6P, the energy is minimized when the long axisof the molecule matches with the lines of largest posi-tive F z , where the electrostatic coupling and thus µ z aremaximized. The longer the molecule, the more stablethe alignment. The PES of 5A is instead less deep andstructured. In contrast to 6P/5PV, no preferred orien-tation can be thus anticipated here. This finding can berationalized by the fact that 5A has no carbon atoms ex-actly on the long molecular axis which can be most easilypolarized by the electric field, as it is for 6P/5PV.In conclusion, we found that the periodic dipolar elec-tric field of the ZnO(10¯10) surface plays a key role in the adsorption of typical oligomers. When the molecules ex-hibit an axially oriented π -electron system, a well-definedmolecular alignment, stabilized by energies larger than100 meV against reorientation, is established, as observedexperimentally for 6P [7]. The electrostatic coupling ischaracterized by a linear relation between the molecule-substrate interaction energy and the induced verticalmolecular dipole moment, which can be employed to pre-dict and/or to design the molecular orientation on thesurface. Moreover, this dipole moment is directly associ-ated with workfunction changes [18], and thus providesa tool for engineering the energy level adjustment of in-organic/organic hybrid structures [7]. Finally, we notethat the single-molecule adsorption described above willbe perpetuated and will result in molecular assembliesreflecting the topology of the surface field. Althoughthe induced dipole moment is modified by depolariza-tion effects [18, 19], this energy scale is certainly signif-icantly smaller than the electrostatic molecule-substratecoupling controlling the alignment on the surface. There-fore, we believe that our findings define a route towardsthe realization of highly-ordered self-assembled arrays ofoligomer/polymers on ZnO(10¯10) and similar surfaces.We thank R. Ahlrichs for providing us with the TUR-BOMOLE program package, M. Sierka, G. Heimel andI. Ciofini for discussions. This work is partially fundedby the ERC Starting Grant FP7 Project DEDOM (no.207441). [1] S. Blumstengel, S. Sadofev, and F. Henneberger, New J.Phys. , 065010 (2008).[2] R. Lin et al., J. Chem. Phys. , 321 (2002).[3] C. W¨oll, Prog. Surf. Sci. , 55 (2007).[4] C. Catlow et al., J. Comput. Chem. (2008).[5] M. Law et al., Nat. Mater. , 455 (2005).[6] S. Dag and L.-W. Wang, Nano Letters , 4185 (2008).[7] S. Blumstengel et al., Phys. Chem. Chem. Phys. ,11642 (2010).[8] F. Labat, I. Ciofini, and C. Adamo, J. Chem. Phys. ,044708 (2009).[9] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996).[10] S. Grimme, J. Comput. Chem. , 1787 (2006).[11] See supplementary material XXXX for computational de-tails and a simple model for the surface periodic dipolarelectric field.[12] A. M. Burow et al., J. Chem. Phys. ,266106 (2008).[15] Bending and inter-ring torsion or tilt with respect to thesurface plane do certainly increase the total energy andcan be thus safely ignored.[16] A. Buckingham et al., Chem. Rev. , 963 (1988).[17] J. D. Gale and A. L. Rohl, Mol. Sim. (2003). [18] A. Natan et al., Adv. Mater. , 4103 (2007).[19] M. Piacenza, S. D’Agostino, E. Fabiano, and F. Della Sala, Phys. Rev. B80