9504 | Phys. Chem. Chem. Phys., 2019, 21, 9504--9511 This journal is© the Owner Societies 2019

Cite this:Phys.Chem.Chem.Phys.,

2019, 21, 9504

Self-ordering of chemisorbed PTCDA moleculeson Ge(001) driven by repulsive forces†

Pavel Kocan, *a Barbara Pieczyrak, b Leszek Jurczyszyn,b

Yoshihide Yoshimoto,c Kazuma Yagyu,d Hiroshi Tochiharad and Takayuki Suzuki d

Realization of future hybrid electronic devices combining organic and inorganic semiconductors

requires a well-defined interface between both components. Such an interface can be formed generally

by self-ordering of organic molecules on inorganic substrates, which is usually hindered by strong

covalent bonds to the semiconductor surface. In this paper, the 3,4,9,10-perylenetetracarboxylic

dianhydride (PTCDA) molecules were unexpectedly found to form a locally self-ordered monolayer on a

strongly interacting semiconductor surface of the Ge(001). Molecular arrangements with preferential

separations between the molecules were observed by the scanning tunneling microscopy at various

coverages of the molecules and substrate temperatures, suggesting strong inter-molecular interaction.

Atomic structures of two paired molecules and their inter-molecular interaction energies in five different

configurations were calculated by density functional theory. Simple Monte Carlo simulations show that

mobility of molecules activated only by the inter-molecular interactions is sufficient to reproduce

the local self-ordering. A dominant inter-molecular interaction between neighboring chemisorbed

molecules has mostly positive energy (destabilizing) except for a single configuration, which leads to the

formation of one-dimensional chains of the molecules and finally a periodic two-dimensional array by

increasing the coverage.

1 Introduction

Utilization of nanostructures grown on solid surfaces in futureelectronic devices requires well-defined and uniform interfacesbetween adsorbates and substrates made of various materials.Such interfaces can be obtained by spontaneous process ofself-ordering. Meanwhile, the adsorbates must have particularproperties, in order to function as the electronic devices afterself-assembling. Because electronic properties of organic moleculescan be tuned by modifying their chemical structures relativelyeasily, they often serve as prefabricated building blocks for theself-assembling.

On weakly interacting surfaces, such as noble metal surfaces,the organic molecules usually diffuse and self-order with oftenintricate inter-molecular interactions.1–3 Meanwhile, stronglyinteracting surfaces, such as those of semiconductors used

massively in the recent electronic chip industry, have highdensities of reactive dangling bonds. Organic molecules aregenerally covalently bonded to these reactive surfaces and theformation of the covalent bonds limits their diffusion andreorientation, hindering self-ordering. However, if the semi-conductor surfaces are passivated by hydrogen or metalatoms,4–6 the organic molecules can diffuse and self-order likeon the weakly interacting surfaces.

The 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA)used in the present study, is a perylene derivative and ann-type organic semiconductor. On weakly interacting surfaces,the PTCDA molecules typically form a herringbone structure,which is a result of inter-molecular interactions of the electro-static origin, often considered as quadrupole–quadrupole and/or hydrogen bond-like ones.7,8 PTCDA has been recentlyreported to form disordered first monolayer on Ge(111)-c(2 � 8)surface at room temperature,9 which is explained by surprisinglyhigh mobility of the molecules on the Ge surface and weak inter-molecular interactions. On rutile TiO2(110), the PTCDA moleculeswere reported to self-order at a deposited amount of nearly onemonolayer.10

In our previous works, we have already determined adsorptionstructures of isolated PTCDA molecules on the Si(001)-2� 111 andGe(001)-2 � 112 surfaces at room temperature with coveragessecuring no influence of inter-molecular interaction. On the

a Charles University, Faculty of Mathematics and Physics, Department of Surface

and Plasma Science, V Holesovickach 2, 180 00, Prague, Czech Republic.

E-mail: pavel.kocan@mff.cuni.cz; Tel: +420 22191 2349b Instytut Fizyki Doswiadczalnej, Universytet Wroclawski, Wroclaw, Polandc Department of Computer Science, The University of Tokyo, Tokyo 113-0033, Japand Department of Electronics Engineering and Computer Science, Fukuoka University,

Fukuoka 814-0180, Japan

† Electronic supplementary information (ESI) available: Additional DFT resultsand animation of considered structural models. See DOI: 10.1039/c9cp01335k

Received 8th March 2019,Accepted 15th April 2019

DOI: 10.1039/c9cp01335k

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Si(001) surface, four dominant molecular configurations withrespect to the surface reconstruction have been observed.On the other hand, in case of the Ge(001) surface, only singlemolecular configuration that is the most stable in the calculatedadsorption energy, has been observed. In the configuration, themolecules are adsorbed in a trough between dimer rows of theGe(001) surface and four carbonyl O atoms form polar covalentbonds with surface Ge atoms. The fact that only one configurationwas observed on the Ge(001) indicates that chemical interactionbetween PTCDA and the substrate is weaker on the Ge(001)surface than on the Si(001) surface, which allows translationand reorientation of PTCDA on the Ge(001) surface.12

Here we report results obtained by deposition of PTCDA onthe Ge(001) surface at higher coverages that is enough to forcethe molecules to interact with each other. Even though thePTCDA molecules are covalently bonded to the Ge(001) surfacewith adsorption energy of B3.6 eV,12 the molecules are foundunexpectedly mobile enough to rearrange and to form self-ordered structures at elevated temperatures at sub-monolayercoverages. The present study demonstrates a very rare case thatthe chemisorbed organic molecules can order on a reactivesemiconductor surface.

2 Experimental

We used an ultra-high vacuum scanning tunneling microscopy(STM) system (JEOL JSTM-4500XT) with the GXSM2 and MK2-A810SPM controller.13 The base pressures in STM and preparationchambers were about 8 � 10�9 and 2 � 10�8 Pa, respectively. TheGe samples (Furuuchi Chemical, 0.3–0.5 O cm) were cleaned byrepeated cycles of Ar ion sputtering and thermal annealing at700 1C until a clean surface was observed by STM prior to thedeposition of the molecules. The sample temperature was mea-sured by an infra-red pyrometer. The PTCDA molecules (TokyoChemical Industry Co., Ltd) were deposited from a quartz crucible.The Ge sample was heated resistively during the PTCDA depositionand held at room temperature (RT) during the STM experiments.

3 Computational method

Interaction of the PTCDA molecules on the Ge(001) surface wassimulated by Density Functional Theory (DFT) calculations asimplemented in VASP package14–16 with the use of plane wavebasis set. To describe the electron–ion interaction the PAWpotentials17,18 were adopted, while the exchange–correlationcontributions were included using generalized gradientapproximation (GGA) in its PBE formulation.19,20 The van derWaals interactions were included using the scheme of Grimme(DFT-D2).21

The used slabs were 6 layers thick with the bottoms of theslabs saturated by hydrogen atoms. The molecules and fourtopmost Ge atomic layers were allowed to relax while the remainingpart of the system was frozen in its bulk-like configuration.The simulated lattice constant of the Ge, a0 = 5.784 Å was used toconstruct the models. The lateral period of the slab and the

simulation cell was 3 � 10 of the 2 � 1 period of the Ge(001)surface, otherwise stated. The cutoff energy of the plane wave basisset was 450 eV. Only the G point was sampled in the first Brillouinzone. Nevertheless, the influence of the applied number of k-pointson the quality of the results was confirmed by double-checkcalculations. The atomic structures of the PTCDA molecules onthe Ge(001) surface were optimized until the maximum residualforces acting on atoms became less than 0.01 eV �1. Interactionenergies of the paired molecules were obtained as Epair + EGe �2 � Elone where Epair, EGe and Elone are the total energies of anadsorbed pair of molecules, a clean relaxed Ge(001) surface and alone adsorbed molecule, respectively.

4 Results and discussion4.1 Observed molecular arrangements

Fig. 1 shows filled- (a) and empty- (b) states STM images afterdeposition of PTCDA at 180 1C. The deposited amount ofPTCDA is B0.06 ML, which is relatively small, but enough toobserve the effect of the inter-molecular interaction (1 MLcorresponds to the surface completely covered by the molecules,i.e. 7.83 � 1013 cm�2). The observed STM images of both isolatedand paired PTCDA molecules are very similar to each other (forexample, see that indicated by arrowheads for isolated and thoseindicated by green squares with a label ‘‘3’’ for paired moleculesin the figure). Thus, we postulate that the presence of othermolecules in the neighboring positions does not change themolecular configuration of its adsorption structure significantly.Using our previous results,12 the molecules are oriented parallelwith dimer rows of the 2 � 1 reconstruction. As we show later inFig. 2, inter-molecular interaction between two paired molecules,which are adsorbed at neighboring troughs on both sides of onedimer row, is important for local self-ordering.

From Fig. 1 we can classify the paired molecules by theirrelative separations along the [110] direction that are measuredusing Ge dimers as a grid. The corresponding models areshown in Fig. 2, details can be found in ESI.† Number labelsin Fig. 1 and 2 denote the relative separation between twopaired molecules in the [110] direction in the 2 � 1 unit length.For example, the paired molecules indicated by a blue squarewith a label ‘‘2’’ in Fig. 1 are separated from each other by twounit lengths in the [110] direction, and its structural modelcorresponds to the configuration in the center of the Fig. 2 witha label ‘‘2’’. From our previous study,12 it is known that theadsorption of one PTCDA molecule directly affects four Gedimers in either side of the molecule, that is eight Ge dimersin total. In particular, eight Ge atoms of each eight dimers,which are closer to the molecule, appear to interact with themolecule: four Ge atoms form polar covalent Ge–O bonds withcorresponding four O atoms at the corner of carbonyl groups ofthe PTCDA molecule. The four Ge atoms take the buckled-downposition. The other four Ge atoms are close to edge C atoms ofthe perylene core of the PTCDA molecule but there seems to beno apparent formation of covalent chemical bonds between theGe and C atoms.12 Thus, in the case of the configuration ‘‘4’’,

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there is no Ge dimer affected directly by both molecules.Besides, their STM images seem very similar to those of theisolated PTCDA molecules: typical ‘‘H’’ shape at filled- (Fig. 1a)and four-dots-square shape at empty-states (Fig. 1b), respectively.Therefore, the configuration ‘‘4’’ can be regarded as two isolatedmolecules rather than the paired molecules.

The STM images of the configuration ‘‘3’’ show almost nodifference from the isolated ones at empty-states, but show avisible darker line between the two paired molecules at filled-states, as indicated by a dotted white arrow. This can beexplained by the saturation of both dangling bonds of the Gedimer marked by a blue dotted oval in configuration ‘‘3’’ ofFig. 2 upon formation of two Ge–O covalent bonds.

The case of the configuration ‘‘2’’ is clearly different fromthe above cases – the empty-state STM image of each moleculein this pair has only one 2-fold rotational symmetry (2), while

an isolated molecule has the two mirror symmetries perpendi-cular to each other (2 mm), as shown in Fig. 1. In ref. 12 wefound by means of the DFT calculations several adsorptionstructures of the isolated PTCDA molecule on the Ge(001) thathave almost the same adsorption energies. Some of thesestructures are asymmetric with respect to the center line ofthe trough (see Fig. 5a of ref. 12), while the most stable one isalmost symmetric. Differences among the adsorption struc-tures are only buckling angles of eight affected Ge dimers.Thus, we considered that the actual structure at RT thermallyfluctuates between two equivalent asymmetric adsorptionstructures, in addition to the most stable almost-symmetricone, which results in the 2 mm symmetry imaged by the STM.Presence of a neighboring molecule can, however, freeze thethermal fluctuations, which then causes the reduction of theobserved symmetry from 2 mm to 2.

Fig. 2 Possible relative positions of the two paired molecules in adjacent troughs of the 2 � 1 reconstruction. The molecular configurations areoptimized by DFT. Only top-most Ge atoms and molecules are shown. Relative interaction energies of each configuration calculated by DFT andreferenced to configuration ‘‘4’’ are given on top of each configuration.

Fig. 1 STM images of Ge surface at low-coverage (B0.06 ML) of PTCDA molecules deposited at T B 180 1C. Sample voltages are (a) �1.2 V and(b) +1.2 V. Image size is 22 � 22 nm2.

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Other possible configurations, ‘‘0’’ and ‘‘1’’ in Fig. 2, werenot observed at this relatively small coverage. We also did notobserve the paired molecules in a same trough with relativeseparation shorter than 5 lattice units (a) at this coverage.Configurations with separations from 0a to 3a would result inoverlapping of the molecules in mismatch with a preferredinteraction with the substrate. Molecules with separation of 4awould not overlap but we can expect a strong repulsion betweennegatively charged O atoms.22

An empty-states STM image after the PTCDA deposition withincreased coverage of B0.4 ML at 220 1C is shown in Fig. 3a.A magnified STM image of the area indicated by a dottedsquare in Fig. 3a is shown in Fig. 3b, where positions of thePTCDA molecules and the Ge dimers are indicated by overlaidlayouts. Most of the molecules preserve the basic configura-tions with respect to the Ge substrate. Neighboring moleculesform the pairs like those shown in Fig. 2, except that severalmolecules form rather 1-D molecular chains. The numberswritten in Fig. 3b denote relative separations between twoneighboring molecules along the [110] direction in the samemanner as in Fig. 2. The configuration ‘‘2’’ is dominant insidethe 1-D molecular chain. Considering paired molecules in asame trough, the shortest observed relative separation at thiscoverage was 4a, even though it is very rare. The configurationof paired molecules in a same trough with separation of 5a wasfound B10 � more often than that with separation of 4a. Fewirregular features present on the image can be possibly explainedby interaction of molecules with surface defects. We note thatdeposition at relatively low temperatures o180 1C resulted inappearance of irregular and often fuzzy features, which could beinterpreted as clusters of overlapping molecules, even though theirdetailed analysis would be difficult.

Fig. 4a shows an empty-states STM image after the PTCDAdeposition of B0.8 ML at 220 1C, which is the highest inves-tigated coverage in the present study. We can distinguish areas

with locally ordered 2-D molecular array coexisting with thatof less ordered or irregular molecular array. A magnified STMimage of the ordered molecular array indicated by a dottedsquare in Fig. 4a is shown in Fig. 4b, where positions of thePTCDA molecules and the Ge dimers are indicated by overlaidlayouts again. The tendency to form such molecular chains canbe already observed at lower coverage of B0.4 ML, as explainedabove in Fig. 3. The STM image of the molecules in the ordered2-D molecular array is the same as that within the 1-D mole-cular chain in the configuration ‘‘2’’ (Fig. 2). Thus we canpropose that the 2-D molecular array is simply composed ofthe 1-D chains. The configuration between neighboring 1-Dmolecular chains corresponds to ‘‘4’’ (see ‘‘4’’ in small yellowcircle in Fig. 4b), which indicates there is almost no inter-molecular interaction between them as shown in Fig. 2. Theunit cell of the 2-D molecular array corresponds to a matrix of6 02 2

� �, but for simplicity is denoted as 6� 2

ffiffiffi2p

R45� here-

after. This super-cell is indicated by a blue parallelogram inFig. 5a.

From the experimental facts shown above, it is evident thatthe PTCDA molecules form locally ordered 2-D molecular arrayson the Ge(001). Two main aspects will be further discussedbelow: (1) what is the driving force of the molecular ordering,i.e. what inter-molecular interactions are responsible? (2) Thelocal ordering cannot be achieved without sufficient mobility ofthe molecules on the surface. What is a kinetic pathway leadingto the observed structure?

4.2 Inter-molecular interaction

Relative inter-molecular interaction energies among the con-figurations ‘‘0’’, ‘‘1’’, ‘‘2’’, ‘‘3’’ and ‘‘4’’ shown in Fig. 2 havebeen calculated using the DFT with respect to the interactionenergy of the configuration ‘‘4’’, in which case the inter-molecular

Fig. 3 (a) A STM image of Ge surface at B0.4 ML coverage of PTCDA deposited at T B 220 1C. Sample voltage is +1.6 V, image size is 35 � 35 nm2 (b) anenlarged image of the rectangular area marked in (a). Overlaid layouts of some molecules and Ge dimers are added in (b), the numbers indicateseparations between the molecules along the [110] direction.

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interaction energy is assumed to be negligible.23 In Fig. 2, largerpositive (negative) interaction energy means more destabilizing(stabilizing) than two isolated molecules, as defined in Fig. 1 ofref. 24. The assumption of negligible inter-molecular interactionof the configuration ‘‘4’’ is based on the following: (1) deformationof both paired molecules and the reacted dimers in configuration‘‘4’’ is the same as that of an isolated adsorbed molecule (Fig. S1,ESI†). (2) Also the local density of states projected onto the orbitalsof carbonyl O atoms and of reacted Ge atoms are very similar inthe case of the isolated adsorbed molecule and the molecules inconfiguration ‘‘4’’ (Fig. S3, ESI†). (3) The electrostatic interactionof the molecules in configuration ‘‘4’’ is negligible.22 Becauseconfigurations anologous to ‘‘1’’ to ‘‘4’’ but with the pairedmolecules in a same trough (not shown here) were not statisticallysignificant, we did not analyze them using DFT.

On the weakly interacting surfaces, inter-molecular interactionbetween the PTCDA molecules can be described as a combinationof two electrostatic forces: (1) between molecular quadrupoles25,26

and (2) hydrogen bonds.2,8 In the former, a quadrupole momentis dominantly a result of charge redistribution within anhydride

groups, with O atoms charged negatively and C atoms positively.In the latter, the interaction is more directional and localizedbetween carbon–hydrogen groups and oxygen atoms. In thepresent case, the interaction of the molecules with the Gesubstrate is rather strong,12 which significantly influences theinter-molecular interaction, as discussed below. However, theirelectrostatic interaction can be comparable to that betweengas-phase molecules, because the dominant charge distribu-tion inside the molecules does not change significantly byadsorption (Fig. S2, ESI†).

According to the DFT results, the configuration ‘‘0’’ is themost destabilizing with the interaction energy of 1.04 eV, wheremolecules are adsorbed in the nearest neighboring positions.Because their distance would be so small, they must have asteric hindrance in addition to the quadrupole–quadrupolerepulsion. Distance of the nearest H atoms are between 1.83and 1.86 Å in the relaxed structure, which is less than two vander Waals radii (2.18–2.4 Å) in organic crystal structures.27

Therefore, their geometries are slightly deformed from that ofthe isolated molecule to minimize the sum of inter-molecular

Fig. 4 (a) STM image of Ge surface at B0.8 ML coverage of PTCDA deposited at T B 220 1C. Sample voltage is +1.6 V, image size is 30 � 22 nm2 (b) anenlarged image of the rectangular area marked in (a). Overlaid layouts of some ordered molecules and Ge dimers are added in (b), the numbers indicateseparations between the molecules along the [110] direction.

Fig. 5 Molecular arrangement of the ordered PTCDA superstructure after optimization by DFT. (a) Top view with the grey, red and white spheresrepresenting C, O and H atoms having van der Waals radii, respectively. The 6� 2

ffiffiffi2p

R45� unit cell is indicated by a blue parallelogram. (b) Overhead ball-and-stick model of the structure model in (a) showing distortion of molecules and buckling of dimers. Note that the dimer row direction is perpendicularto that in (a). Only top-most of Ge atoms and molecules are shown.

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repulsion and the deformation energies. Meanwhile, a positiveinteraction energy of 0.55 eV was obtained by DFT between thepaired molecules in the configuration ‘‘1’’. The relatively higherpositive interaction energies for the configurations ‘‘0’’ and ‘‘1’’agree with the experimental fact that they are absent at lowercoverages (see Fig. 1 and 3).

On the other hand, the paired molecules are stabilized onlyin the configuration ‘‘2’’, whose calculated energy is �0.12 eV.The stabilization is mainly of electrostatic origin, becauseattractive Od�–Hd+ interaction is dominating over repulsiveOd�–Od� and Hd+–Hd+ interactions.22 However, if two gas-phase molecules were located in the same separation andorientation to the configuration ‘‘2’’ without the Ge substrate,the inter-molecular interaction energy would be about �0.4 eV.22

Thus their adsorption onto the Ge surface weakens their inter-molecular interaction as a whole by including all factors likemolecular deformation, buckling of the Ge dimers, charge transferbetween molecules and the Ge surface and so on.

The configuration ‘‘3’’ is slightly destabilizing with theinteraction energy of 0.1 eV. For two gas-phase molecules withthe same separation and orientation as in the configuration‘‘3’’ the inter-molecular interaction energy would be slightlynegative (stabilizing).22 Thus, again their adsorption onto theGe substrate influences the inter-molecular interaction. Bothtwo Ge atoms in one Ge dimer indicated by a blue dotted oval inconfiguration ‘‘3’’ of Fig. 2 cannot take the preferred buckleddown position simultaneously because of the O–Ge–Ge–Obonding, which could result in the slightly positive interactionenergy. Absence of the buckling can be recognized on detailedstructural images of the configuration ‘‘3’’ (Fig. S1, ESI†).In general, dimers that have two molecules at both sides andare affected by the two molecules, either directly by bonded Oatom or by the proximity of a perylene core, are flat (no buckling).The dimers affected only at one side are always buckled with thelower Ge atoms of the dimers being closer to the molecule. Thisbuckling initiates the zigzag chain running out of the molecules,if not disturbed by presence of other molecules (in STM images,see Fig. 1a) or by the size of the supercell (in DFT23).

Metal atomic chains on the Si(001)2 � 1 surface were reportedto grow by the so-called surface polymerization reaction.28 In thecase of the metal chains, saturation of one of the two danglingbonds on one surface dimer by an adsorbed metal atom induceshigher chemical reactivity of the other remaining dangling bondon the same dimer, which becomes preferential adsorption sitesfor other diffusing metal atoms. It is also reported that a moleculechemisorbed to one of the two dangling bonds on one surfacedimer activates the other unsaturated dangling bond on the samedimer in a similar way.29,30 Adsorption of a PTCDA molecule onthe Ge(001) surface creates four equivalent possible preferentialadsorption sites for another PTCDA molecule to form the geo-metry of the configuration ‘‘2’’. If such a pair is formed once, thepreferential adsorption sites are limited only in the directionalong the growing chain, due to distortion of the molecules inthe configuration ‘‘2’’. This makes the growth of the present 1-Dmolecular chains analogical to the surface polymerizationreaction,28 even though the nature of present inter-molecular

interaction is much different from that of the surface polymeriza-tion reaction.

The ordered structure with 6� 2ffiffiffi2p

R45� periodicity shownin Fig. 5 that was experimentally observed as shown in Fig. 4 iscomposed of such chains of molecules with the configuration‘‘2’’ in a packing without repulsion between the chains. Fromthe STM images we cannot exclude another possible configu-ration of the ordered structure with all molecules rotated by 901with respect to the model shown in Fig. 5. According to DFTcalculation, the structure analogous to configuration ‘‘4’’ butwith the molecules rotated by 901 is around 3.0 eV less stable,which shows that the molecules do not change orientation atthe higher coverages.

Ordering of the PTCDA molecules potentially prepares theground for polymerization of the molecules by covalent bondsbetween the molecules after their proper functionalization.31

Further research in this direction is awaited.

4.3 Kinetic aspects

A simple Monte Carlo simulation has been carried out to getinsight into kinetic aspects of the formation of the observedarrangement of the PTCDA molecules. In the directionperpendicular to the Ge dimer rows, a molecule has to passthrough one of metastable positions above the dimer row.Adsorption energies in these positions were calculated to bemore than 1 eV higher than that in the most stable position inthe trough in case of PTCDA adsorbed on the Si(001) surface.11

Therefore, we consider diffusion of the molecules only in thedirection parallel to the Ge dimer rows.

The net interaction energy Ec of each molecule was calculatedas the sum of inter-molecular interaction energies. Only themolecules separated less than five-unit length in the [110]direction, located in the same or neighboring troughs, wereconsidered. For paired molecules in the neighboring troughs,the inter-molecular interaction energies calculated by DFT wereused, whose configurations and the energy values are shownin Fig. 2. Meanwhile, for paired molecules in the same trough,the inter-molecular interaction energy was assumed to beproportional linearly to the distance between the molecularcenters, where its proportionality factor was adjusted so thatit becomes 5 eV for completely overlapped molecules, and1 eV for those separated by 4-unit length, in order to preventmolecules from overlapping during the simulation. This is asimple way to implement repulsion of a steric hindrancebetween the molecules, being consistent with the experimentalobservation of few (no) molecules in a same trough with relativeseparation of 4 (shorter than 4) unit lengths, respectively,at 0.4 ML coverage and at temperature of 220 1C.

The simulation proceeded as follows: first, molecules wererandomly placed on a 100 � 50 rectangular grid with periodicboundary conditions (see Fig. 6a and d for 0.4 and 0.8 MLcoverage, respectively, where one white rectangle correspondsto one molecule, which occupies 4 � 1 in the 100 � 50 grid).Then, one molecule was selected randomly and moved toadjacent position according to a standard Metropolis algorithm32

in which probability of the molecular movement is the lesser of 1 or

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exp(�DE/kT) where DE is the difference between the net interactionenergies before and after the movement, k is the Boltzmannconstant and temperature T = 500 K. Note that realistic diffusionbarriers are not considered in this simplified model. The randomselection and movement were repeated for 100 attempts permolecule, from which 14.8 and 5.5 attempts per molecule weresuccessful in case of 0.4 and 0.8 ML coverage, respectively.

Fig. 6b and e show simulated molecular arrangements afterthe energy minimization for 0.4 and 0.8 ML coverage, respectively.The molecular distributions are more uniform than the initialrandom distributions shown in Fig. 6a and d. Furthermore, thelocal ordering is evident on the simulated images.

In order to elucidate influence from the long thermal diffu-sion of isolated molecules, we have tested another modifiedmodel, in which the movement was not realized if the moleculewas in energetically favorable or neutral position before themovement, i.e. Ec r 0. In this way isolated non-interactingmolecules cannot diffuse. Kinetically this simulation corre-sponds to a higher activation barrier for movement of isolatedmolecules, and significantly lower activation barriers for that of

non-isolated unfavorable molecular configurations like thoseconsisting of mixture of ‘‘0’’, ‘‘1’’ and ‘‘3’’. In the model wesuppose these barriers are low enough to be easily overcomethermally. The lowering of barriers can be rationalized by apositive interaction energy between nearby molecules (exceptfor configuration ‘‘2’’) which assists in breaking Ge–O bondsduring the molecular movement. Results of the simulation areshown in Fig. 6c and f. Because molecular arrangement inFig. 6b and e looks similar to that in Fig. 6c and f, respectively,long thermal diffusivity of isolated molecules is not necessaryto achieve the final arrangements. The extent of the ordering at0.4 and 0.8 ML coverage in the both simulated images wellreproduces the experimentally observed arrangements seen inthe insets of Fig. 6c and f, respectively.

A physisorbed state of PTCDA on TiO2 at low coverageshas been reported to transform to a chemisorbed state atmonolayer coverage.10 This is different from the present case,because adsorption structure of an isolated molecule is verysimilar to that of the molecules in the ordered array. Theadsorbed PTCDA molecules might be in some weakly-bondedprecursor states with short life-time firstly. Then, within theshort life-time, the molecules would search the stable positionsby the lateral movements. We cannot exclude existence ofsuch short-time precursor states of PTCDA on Ge(001), whichcould facilitate the ordering process, however the Monte Carlosimulations suggest that such mechanism is not required.

From the Monte Carlo simulations we can derive conditionsresulting in growth of ordered arrays in case of moleculeschemisorbed on surfaces. The first condition is a strong enoughpreference for a molecular configuration with the lowest inter-action energy, here represented by the configuration ‘‘2’’. Thiscondition applies also for conventional self-ordering on weaklyinteracting surfaces. The second is that all the other configura-tions have positive interaction energy (destabilizing). In the pre-sent case, the forces that make those configurations destabilizingare mostly the repulsion between negatively charged O atoms(in configurations ‘‘0’’ and ‘‘3’’) and the steric hindrance(in configurations ‘‘0’’ and ‘‘1’’). These forces must be strongenough to overcome kinetic barriers for molecular movementto configurations with lower interaction energy and thus acti-vating the process of self-ordering. It is noted here that even themovement from the configuration ‘‘3’’ to ‘‘2’’ is due to repulsiveforces between negatively charged oxygen atoms, although itseems attractive with respect to the paired molecules. Mobilityof isolated molecules is not necessary, but molecular coveragemust be sufficient to stimulate the self-ordering.

5 Conclusions

Arrangements of the PTCDA molecules deposited at 180–220 1Con the Ge(001) surface at coverages of 0.06–0.8 ML, where inter-molecular interactions are important, were investigated by STM.The arrangements clearly indicated mobility of the molecules,leading to local self-ordering by adjusting their relative positions.The inter-molecular interaction energies were calculated by DFTfor the two paired molecules in adjacent troughs of the Ge(001)

Fig. 6 Monte Carlo simulations of PTCDA on Ge(001) for (a–c) coverage0.4 ML, (d–f) coverage 0.8 ML. (a and d) are as-deposited (initial) moleculararrangements. (b, e) and (c, f) are arrangements after energy minimizationusing Metropolis algorithm and limited mobility of molecules, respectively.Insets in (c and f) show corresponding STM images. The dimer rows runhorizontally in the simulated images.

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This journal is© the Owner Societies 2019 Phys. Chem. Chem. Phys., 2019, 21, 9504--9511 | 9511

surface, as a function of relative separation in the [110] direction.Only one configuration was found to have negative interactionenergy (stabilizing) in the calculation, which corresponds to thatwith the separation of 2-unit length. The self-ordering is dom-inantly induced by repulsive forces between the molecules in theirclose proximity. Simple Monte Carlo simulations showed that theobserved arrangements can be reproduced by molecular movementsto adjacent positions activated by the inter-molecular interaction.Preference for a molecular configuration with the lowest interactionenergy plays a critical role for the formation of the 2D ordered arrayof the PTCDA molecules on a reactive Ge(100) surface.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported in part by funds (Grant No. 185008 &177105) from the Central Research Institute of FukuokaUniversity and in part by Grants-in-Aid for Scientific Research(Grant No. 15K04630) from MEXT, Japan. P. K. acknowledgessupport from Czech Science Foundation (contract no.16-15802S). B. P. and L. J. acknowledge support from WroclawUniversity (Grant No. 1010/S/IFD/18). Numerical calculationswere performed at the Interdisciplinary Centre for Mathe-matical and Computational Modeling of the University ofWarsaw, under Grants No. GB73-18 and GA73-20.

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