Line-on-line organic-organic heteroepitaxy of quaterrylene on hexa-peri-hexabenzocoronene on Au(111)

Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. II. Experimental results

Organic epitaxy is studied experimentally in terms of the correlation of the involved two- and three-dimensional crystallographic lattices.

While the crystal structure of the polymorph phase can be studied in three dimensions conveniently by X-ray methods like grazing-incidence X-ray diffraction (GIXD), the first monolayer is only accessible by surface-sensitive methods that allow the determination of a two-dimensional lattice. Here, GIXD measurements with sample rotation are compared with distortion-corrected low-energy electron diffraction (LEED) experiments on conjugated molecules: 3,4;9,10-perylenetetra­carb­oxy­lic dianhydride (PTCDA), 6,13-pentacene­quinone (P2O), 1,2;8,9-dibenzopentacene (trans-DBPen) and di­cyano­vinyl-quaterthio­phene (DCV4T-Et2) grown by physical vapor deposition on Ag(111) and Cu(111) single crystals. For these molecular crystals, which exhibit different crystallographic lattices and crystal orientations as well as epitaxial properties, the geometric parameters of the three-dimensional lattice are compared with the corresponding geometry of the first monolayer. A comparison of the monolayer lattice from LEED investigations with the multilayer lattices determined by rotated GIXD experiments reveals a correlation between the first monolayer and the epitaxial growth of three-dimensional crystals together with lattice distortions and re-alignment of molecules. The selected examples show three possible scenarios of crystal growth on top of an ordered monolayer: (i) growth of a single polymorph, (ii) growth of three different polymorphs; in both cases the first monolayer serves as template. In the third case (iii) strong lattice distortion and distinct molecular re-alignments from the monolayer to epitaxially grown crystals are observed. This is the second part of our work concerning the correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. In the first part, the theoretical basis has been derived which provides a mathematical relationship between the six lattice parameters of the three-dimensional case and the three parameters obtained for the two-dimensional surface unit cell, together with their orientation to the single-crystalline substrate. In this work, a combined experimental approach of GIXD and LEED is introduced which can be used to investigate the effect of the epitaxial monolayer on the structural properties of molecular crystals grown on top.

Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. I. Theory

A general formalism to determine the surface unit cell of a three-dimensional crystallographic lattice is presented.

The epitaxial growth of molecular crystals at single-crystalline surfaces is often strongly related to the first monolayer at the substrate surface. The present work presents a theoretical approach to compare three-dimensional lattices of epitaxially grown crystals with two-dimensional lattices of the molecules formed within the first monolayer. Real-space and reciprocal-space representations are considered. Depending on the crystallographic orientation relative to the substrate surface, proper linear combinations of the lattice vectors of the three-dimensional unit cell result in a rhomboid in the xy plane, representing a two-dimensional projection. Mathematical expressions are derived which provide a relationship between the six lattice parameters of the three-dimensional case and the three parameters obtained for the two-dimensional surface unit cell. It is found that rotational symmetries of the monolayers are reflected by the epitaxial order. Positive and negative orientations of the crystallographic contact planes are correlated with the mirror symmetry of the surface unit cells, and the corresponding mathematical expressions are derived. The method is exemplarily applied to data obtained in previous grazing-incidence X-ray diffraction (GIXD) measurements with sample rotation on thin films of the conjugated molecules 3,4;9,10-perylenetetra­carb­oxy­lic dianhydride (PTCDA), 6,13-pentacene­quinone (P2O), 1,2;8,9-dibenzopentacene (trans-DBPen) and di­cyano­vinyl-quaterthio­phene (DCV4T-Et2) grown by physical vapor deposition on Ag(111) and Cu(111) single crystals. This work introduces the possibility to study three-dimensional crystal growth nucleated by an ordered monolayer by combining two different experimental techniques, GIXD and low-energy electron diffraction, which has been implemented in the second part of this work.

Searching for New Polymorphs by Epitaxial Growth

The formation of unknown polymorphs due to the crystallization at a substrate surface is frequently observed. This phenomenon is much less studied for epitaxially grown molecular crystals since the unambiguous proof of a new polymorph is a challenging task. The existence of multiple epitaxial alignments of the crystallites together with the simultaneous presence of different polymorphs does not allow simple phase identification. We present grazing incidence X-ray diffraction studies on conjugated molecules like perylenetetracarboxylic dianhydride (PTCDA), pentacene, dibenzopentacene (trans-DBPen), and dicyanovinylquater-thiophene (DCV4T-Et2) grown by physical vapor deposition on single crystalline surfaces like Ag(111), Cu(111), and graphene. A new method for indexing the observed Bragg peaks allows the determination of the crystallographic unit cells so that the type of crystallographic phase can be clearly identified. This approach even works when several polymorphs are simultaneously present within a single sample as shown for DCV4T-Et2 on Ag(111). Additionally, epitaxial relationships between the epitaxially grown crystallites and the single crystalline surfaces are determined. In a subsequent step, the experimental data are used for the crystal structure solution of an unknown polymorph, as shown for the example trans-DBPen grown on Cu(111).

Classification of epitaxy in reciprocal and real space: rigid versus flexible lattices

Early investigations of epitaxy focused on inorganic adsorbates consisting of atoms or few-atom molecules, where commensurate registries are predominantly encountered. Expanding such studies to larger (organic) molecules has revealed hitherto unknown types of epitaxy with coherence between adlayer and substrate lattices in just one direction. Here we review recent contributions to the fundamental understanding and modeling of epitaxy. By sorting the ideas brought forward in the literature and amending some basic algebraic considerations a universal scheme for the classification of lattice epitaxy is presented. Ultimately, the occurrence of the different types of epitaxy is made plausible by easy-to-grasp energetic arguments.

Determination and correction of distortions and systematic errors in low-energy electron diffraction

We developed and implemented an algorithm to determine and correct systematic distortions in low-energy electron diffraction (LEED) images. The procedure is in principle independent of the design of the apparatus (spherical or planar phosphorescent screen vs. channeltron detector) and is therefore applicable to all device variants, known as conventional LEED, micro-channel plate LEED, and spot profile analysis LEED. The essential prerequisite is a calibration image of a sample with a well-known structure and a suitably high number of diffraction spots, e.g., a Si(111)-7×7 reconstructed surface. The algorithm provides a formalism which can be used to rectify all further measurements generated with the same device. In detail, one needs to distinguish between radial and asymmetric distortion. Additionally, it is necessary to know the primary energy of the electrons precisely to derive accurate lattice constants. Often, there will be a deviation between the true kinetic energy and the value set in the LEED control. Here, we introduce a method to determine this energy error more accurately than in previous studies. Following the correction of the systematic errors, a relative accuracy of better than 1% can be achieved for the determination of the lattice parameters of unknown samples.

Inhomogeneous relaxation of a molecular layer on an insulator due to compressive stress

We discuss the inhomogeneous stress relaxation of a monolayer of hexahydroxytriphenylene (HHTP) which adopts the rare line-on-line (LOL) coincidence on KCl(001) and forms moiré patterns. The fact that the hexagonal HHTP layer is uniaxially compressed along the LOL makes this system an ideal candidate to discuss the influence of inhomogeneous stress relaxation. Our work is a combination of noncontact atomic force microscopy experiments, density functional theory and potential energy calculations, and a thorough interpretation by means of the Frenkel-Kontorova model. We show that the assumption of a homogeneous molecular layer is not valid for this organic-inorganic heteroepitaxial system since the best calculated energy configuration correlates with the experimental data only if inhomogeneous relaxations of the layer are taken into account.

On the Origin of the Energy Gain in Epitaxial Growth of Molecular Films

The material properties of organic thin films depend strongly on their order. The different types of epitaxy may complicate the exploration of the large variety of ordered systems and its exploitation in potential electronic devices. In this Letter, we develop a coherent description of the driving force that creates epitaxial systems. We focus on flat-lying organic adsorbates and explain the energy gain in commensurate, point-on-line, and line-on-line epitaxy. We use potential energy maps to visualize our concept and to derive a relation that allows anticipating epitaxial growth from low-energy electron diffraction (LEED) data. A unified description facilitates the identification and interpretation of experimentally observed adsorbate structures, whereas the rationalized expectation from LEED means a considerable speed gain if suitable candidates for organic-organic epitaxy are searched for in a combinatory approach.