Understanding the photoemission distribution of strongly interacting two-dimensional overlayers

Daniel Lüftner, Simon Weiß, Xiaosheng Yang, Philipp Hurdax, Vitaliy Feyer, Alexander Gottwald, Georg Koller, Serguei Soubatch, Peter Puschnig, Michael G. Ramsey, and F. Stefan Tautz

Phys. Rev. B 96, 125402 – Published 5 September 2017

Abstract

Photoemission tomography (PT), the analysis of the photoemission intensity distribution within the plane wave final-state approximation, is being established as a useful tool for extracting the electronic and geometric structure of weakly interacting organic overlayers. Here we present a simple method for extending PT, which until now has been based on the calculations of isolated molecules. By including the substrate and a damped plane-wave final state, we are able to simulate the photoemission intensity distribution of two-dimensional molecular overlayers with both strong intermolecular and molecule-substrate interactions, here demonstrated for the model system 3,4,9,10-perylene-tetracarboxylic dianhydride (PTCDA) on Cu(100). It is shown that the interaction and hybridization of the lowest unoccupied molecular orbital of PTCDA with substrate states leads to its occupation and the formation of a strongly dispersing intermolecular band, whose experimental magnitude of 1.1 eV and $k$ -space periodicity is well reproduced theoretically.

Received 5 May 2017
Revised 9 August 2017

DOI:https://doi.org/10.1103/PhysRevB.96.125402

Physics Subject Headings (PhySH)

Chemisorption Physisorption

Monolayer films Organic semiconductors Surfaces

Angle-resolved photoemission spectroscopy Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel Lüftner^1,*, Simon Weiß^2,3, Xiaosheng Yang^2,3, Philipp Hurdax¹, Vitaliy Feyer⁴, Alexander Gottwald⁵, Georg Koller¹, Serguei Soubatch^2,3,†, Peter Puschnig¹, Michael G. Ramsey¹, and F. Stefan Tautz^2,3

¹Institut für Physik, Karl-Franzens-Universität Graz, NAWI Graz, Universitätsplatz 5, 8010 Graz, Austria
²Peter Grünberg Institut (PGI-3), Forschungszentrum Jülich, 52425 Jülich, Germany
³Jülich Aachen Research Alliance (JARA), Fundamentals of Future Information Technology, 52425 Jülich, Germany
⁴Peter Grünberg Institut (PGI-6), Forschungszentrum Jülich, 52425 Jülich, Germany
⁵Physikalisch-Technische Bundesanstalt (PTB), Abbestraße 2-12, 10587 Berlin, Germany

^*daniel.lueftner@uni-graz.at
^†s.subach@fz-juelich.de

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Issue

Vol. 96, Iss. 12 — 15 September 2017

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Images

Figure 1
Structural model of the PTCDA/Cu(100) overlayer (from Refs. [32, 44]). The white numbers label the inequivalent carbon and oxygen atoms.
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Figure 2
Schematic sketch of the final state used in our calculation of photoemission intensities. The final state is a plane wave that is damped in the $z$ direction of the unit cell. Above $z_{0}$ the final state is treated as a pure plane wave, and below $z_{0}$ it is exponentially damped by the factor $e^{γ (z - z_{0})}$ , which is shown as the black envelope of the damped plane wave.
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Figure 3
[(a) and (b)] Simulated band maps $I (E_{B}, k_{[01 \bar{1}]})$ of the PTCDA/Cu(100) interface, using a pure plane wave (a) and a damped plane wave (b) with the damping parameter $γ = 0.25 Å^{- 1}$ for the final state, respectively. The insert in panel (a) shows a schematic of the experimental geometry, defining the angle of incidence $α$ , the corresponding polarization vector $A$ , and the momentum vector $k$ for a given emission angle $θ$ . The white box in panel (b) indicates the energy and wave vector range which is considered in more detail in Fig. 5. A photon energy of 31 eV and an angle of incidence of $40^{\circ}$ has been utilized in the simulation of the band map. (c) Differential photoemission intensity band map computed as $(I_{pw} - I_{dpw}) / I_{dpw}$ , where $I_{pw}$ and $I_{dpw}$ are the photoemission intensities calculated within pure plane-wave approximation and using the damped plane wave, respectively.
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Figure 4
(a) Photoemission spectra measured in the $k$ region indicated by the blue and green cricles in panels (b) and (c). (d) Calculated density of states for the PTCDA/Cu(100) heterostructure, projected onto the HOMO and LUMO of PTCDA. [(b) and (c)] Measured momentum maps at the peak energies of $- 1.7 eV$ and $- 0.8 eV$ , respectively. [(e) and (f)] Simulated momentum maps for the HOMO and LUMO of isolated PTCDA, respectively. A photon energy of 35 eV and angle of incidence of $65^{\circ}$ in the plane of incidence containing the $[011]$ direction were used in both the PEEM experiment and the simulation.
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Figure 5
(a) Measured band map $I (E_{B}, k_{[01 \bar{1}]})$ , along the principal azimuth in the $[01 \bar{1}]$ direction. (b) Simulated band map of the PTCDA/Cu(100) heterostructure. The dotted line is merely a guide to the eye. (c) Simulated band map of the freestanding PTCDA layer, with the LUMO centered at the same energy as for the case of PTCDA/Cu(100) heterostructure. [(d)–(f)] Experimental (left halves) and simulated (right halves) momentum maps $I (k_{[01 \bar{1}]}, k_{[011]})$ at the top, middle, and bottom of the band, as indicated by the horizontal lines in panel (b). A photon energy of 31 eV and an angle of incidence of $40^{\circ}$ has been used in both the toroidal analyzer experiment and the simulation.
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