Epitaxy and Molecular Organization on Solid Substrates

Abstract

The recent emergence of molecular films as candidates for functional electronic materials has prompted numerous investigations of the underlying mechanisms responsible for their structure and formation. This review describes the role of epitaxy in molecular organization on crystalline substrates. A much‐needed grammar of epitaxy is presented that classifies the various modes of epitaxy according to transformation matrices that relate the overlayer lattice to the substrate lattice. The different modes of epitaxy can be organized hierarchically to reflect the balance of overlayer–substrate and molecule–molecule energies. In the case of molecular overlayers, the mismatch of overlayer and substrate symmetries commonly leads to coincident epitaxy in which some of the overlayer lattice points do not reside on substrate lattice points. Analyses of numerous reported epitaxial molecular films reveal that coincidence is quite common even though, based on overlayer–substrate interface energies alone, not as energetically favorable as commensurism. The prevalence of coincidence can be attributed to overlayer elastic constants, associated with molecule–molecule interactions within the overlayer, that are larger than the elastic constants of the overlayer–substrate interface. This condition facilitates prediction of the epitaxial configuration and overlayer structure through simple and comparatively efficient geometric modeling that does not require the input of potential energies, while revealing the role of phase coherence between the overlayer and substrate lattices.

Commensurate monolayers on surfaces: Geometry and ground states

“…28,31 Another possible application concerns the structure of intercalated crystals, where the three-dimensional Fourier expansion describes the field felt by a foreign element introduced inside of a crystal. 32 The computer codes for generating all commensurate structures for a given coverage range and the Fourier sequence associated with each structure on ͑111͒ and ͑100͒ surfaces are available upon request from the author.…”

“…One expects lower energy structures to have higher symmetry, although this would require that the Fourier amplitudes be strictly decaying. Although this seems to be the case for some physisorption systems, 17,18 many examples of higher-order commensurate structures exist in the experimental literature on atomic and molecular adsorption, 5,9,11,13,21,22,[27][28][29] where the stability should be mainly determined by the contribution of the high-order Fourier terms. Furthermore, the knowledge of the Fourier amplitudes for any particular system ͑i.e., obtained from DFT calculations͒ could allow better interpretation of the translational symmetry of commensurate monolayers in addition to the fitting of the LEED spectra.…”

“…The theory presented in this work could probably be extended to treat coincident organic molecule epitaxy, 28 where the molecule-surface potential has been shown to dominate the structure formation. 28,31 Another possible application concerns the structure of intercalated crystals, where the three-dimensional Fourier expansion describes the field felt by a foreign element introduced inside of a crystal.…”

Late growth stages and post-growth diffusion in organic epitaxy: PTCDA on Ag(111)

“…While the structure and epitaxy has been thoroughly studied for several model systems, such as PTCDA [1,2,3,4,5,6,7,8], on Ag(111) the growth dynamics and evolution of the resulting morphology have been less systematically investigated. Importantly, even for a system with well-defined monolayer epitaxy, the later stages of the growth (after a certain threshold thickness) can, of course, exhibit islanding (Stranski-Krastanov (SK) growth) and a very rough resulting morphology.…”

Comprehensive study of the potential energy surface minima of a monolayer on (111) surface

“…[14][15][16] Monolayers formed at well-ordered surfaces show a wide variety of ordered structures: simple commensurate, uniaxially compressed, and complex incommensurate with domain walls among others. 7,17,18 Even when analytic expressions for the interactions of a monolayer-surface system are known, i.e., for Xe-Pt͑111͒, 19,20 the determination of the global minimum is still a formidable task. 21 That is, although molecular dynamics could be employed with a large system size to determine the most probable minimum of an adsorbatesubstrate system, 22 this approach suffers from the finite-size effect and requires an initial guess, making the search process biased.…”