Tracing the film structure of an organic semiconductor with photoemission orbital tomography

Abstract

Photoemission orbital tomography (POT) is a powerful tool for investigating the orbitals and electronic band structure of oriented layers of organic molecules. In many cases, POT allows conclusions to be drawn regarding the geometric structure, but so far it has been mainly applied to (sub)monolayers and rarely to bilayers, raising the question of whether POT can also provide structure information for thicker films. Here, we use POT to analyze the band dispersion in up to eight layers of $α$-sexithiophene (6T) adsorbed on Cu(110)-p($2\times1$)O. This linear oligomer turns out to be a textbook example that exemplifies the concepts of intra- and intermolecular band dispersion in molecules. Moreover, the rich band and orbital structure information available from POT for this system enables us to trace subtle changes in the crystal structure as a function of layer thickness. Specifically, we find that the periodicity of an intermolecular band changes with film thickness, revealing an increase of the intralayer distance between the molecules with the number of layers. At the same time, the momentum distribution of photoemission from the highest occupied molecular orbital of 6T discloses a decrease of the molecular tilt angle. Following the evolution of tilt angle and lattice constant with layer thickness, we observe -- purely based on electronic structure data -- that the surface-templated monolayer structure relaxes into the structure of bulk 6T crystals. The experimental findings agree well with the results of density functional theory calculations.

Figures (10)

• Figure 1: (a) Chemical structure of $\alpha$-sexithiophene (6T). The length $a$ of a single thiophene unit (1T) is indicated. (b) DFT-calculated structure of a monolayer (ML) of 6T adsorbed on Cu(110)-p($2\times1$)O, viewed from the top and along the $x$ ($\equiv [\overline{1}10]$) and $y$ ($\equiv [001]$) directions. In the upper part, the Cu(110)-p($2\times1$)O substrate is shown without molecules. (c) Side view of the 6T bulk structure, as found by Horowitz et al.Horowitz1995. The tilt angles $\beta$ of the molecular plane against the surface plane are indicated in panels (b) and (c).
• Figure 2: Band maps (a)-(c) along and (d)-(f) perpendicular to the long molecular axis of 6T for (a), (d) the experiment on a 4 ML 6T film, (b), (e) the DFT calculation for a single molecule, and (c), (f) the DFT calculation for bulk 6T. $E_{\rm F}$ is the experimental Fermi level. The calculated maps are shifted in energy such that the HOMO is aligned with the experimentally measured HOMO in panel (a). The vacuum level in the single-molecule calculation is at $E-E_{\rm F}=3.3$ eV. To aid comparison with the experiment, in the band maps in panels (b), (c), (e) and (f) two rotational domains are considered. In both cases (single molecule and bulk), the tilt angle of the bulk structure ($\beta=\pm 31$$\rm ^{\circ}$ against the $xy$ plane) is used. In panels (a) and (d), $k$ vectors corresponding to the lengths $(2)a$ of the (bi)thiophene units (Brillouin zone (BZ) boundaries in case of an infinite polythiophene chain ($\infty$T)) and the intermolecular distance $b$ in the 4 ML experiment are indicated. The value for $b$ is a result of the analysis in section \ref{['sec:Coverage']} (see Tab. \ref{['tab:Fitting_results']}). In panels (e) and (f), the intensity is increased in parts of the band maps in order to make more molecular levels visible.
• Figure 3: (a) DFT-calculated HOMO$-$1 of a single thiophene unit (1T). The atoms in the ring are numbered to enable clear identification. (b) Momentum maps and wave functions, both derived from a single-molecule DFT calculation, of the 6T orbitals that contribute to the nonbonding quasiband. These orbitals can be constructed from combinations of a 1T HOMO$-$1 at each unit. Solid vertical lines mark approximate nodal planes, see main text for details. (c) Band map calculated for a single 6T molecule (vacuum level at $E-E_{\rm F}=3.3$ eV as in Fig. \ref{['fig:Intra/Intermolecular_dispersion']} (b)). Orbital energies of HOMO (H) to HOMO-11 (H11) are marked. The sinusoidal lines serve as guides for the eye to highlight the two minibands (see main text for details). Solid (dashed) white marks at $n \pi/a$ ($n\pi/(2a)$) indicate $k_y$ vectors belonging to the 1T (2T) periodicity. (d) Wave functions and momentum maps, both derived from a single-molecule DFT calculation, of the 6T orbitals that contribute to the bonding quasiband. These orbitals can be constructed from combinations of a 1T HOMO at each unit. Dotted vertical lines mark nodal planes deriving directly from the 1T HOMO, solid vertical lines mark nodal planes arising from the combination of 1T HOMOs at neighboring units. (e) DFT-calculated HOMO of a single thiophene unit (1T). (f) DFT-calculated HOMO$-$1 and HOMO$-$2 of bithiophene (2T). (g) DFT-calculated HOMO and HOMO$-$3 of 2T. To aid comparison with experiments (in which two rotational domains are always present), the energy and momentum maps in panels (b), (c) and (d) were generated for a pair of single molecules with tilt angles $\beta=\pm 38$$\rm ^{\circ}$ against the $xy$ plane.
• Figure 4: (a) DFT-calculated (for bulk 6T) and (b) measured (for the 4 ML film) band maps. The calculated band map was energy-shifted such that the HOMOs in experiment and theory align. White solid lines mark the centers of the quasibands. The white dashed line marks the position where the center of the bonding quasiband (relative to the nonbonding quasiband) would be expected if only the energy difference between the underlying 1T orbitals (HOMO and HOMO$-$1, single-molecule calculation) was considered. (c) Calculated (bulk) and (d) measured (4 ML) momentum maps, recorded at the energies marked by colored lines in the left margins of panels (a) and (b). In the leftmost map in panel (d), a gray arrow indicates the projection of the light direction into the $k_x$,$k_y$ plane. (e) Direct comparison of calculated (bulk, top) and measured (4 ML, bottom) momentum maps taken at the energies marked by the colored lines in the right margins of panels (a) and (b).
• Figure 5: 3D representation of the $E(k_x,k_y)$ band measured for a 4 ML film. To generate this representation, the data of the full $I(E_\mathrm{b}, k_x,k_y)$ data cube in the relevant energy range were processed as follows: First, each $k_x$,$k_y$ map was symmetrized. Then, pre-smoothing was performed in 3D by applying a Gaussian filter. Next, a curvature filter was applied using an analogous formula to Eq. (14) in Ref. Zhang2011, but in three dimensions (see Appendix \ref{['Appendix:3D_curvature']}). The necessary derivatives were obtained using Savitzky-Golay filters SavGol19642020SciPy. Finally, all intensity values below 35% of the maximum intensity were removed in order to reduce the background and only focus on the $E(k_x,k_y)$ band. The following parameters were used: Pre-smoothing: $\sigma_{k_x} = \sigma_{k_y} = 10$ and $\sigma_E = 1$; Curvature filtering: $C_k = 0.05$ Å$^{-2}$, $C_E = 0.01$ eV$^2$, window length and polynomial order in the Savitzky-Golay filter SavGol19642020SciPy: 100 and 2 for the $k$ axes, and 20 and 2 for the $E$ axis. The opacity as well as the color depends on the intensity values. The opacity of a single data point varies from 0 to 0.5 and the color from dark blue to yellow. To enable a view into the band, data points with negative $k_x$ and $k_y$ values are not shown. A cut through the dataset at $E\,-\,E_{\mathrm{F}}\,=\,-4.0$ eV (dotted lines) is shown in the $k_x$, $k_y$ plane at $E\,-\,E_{\mathrm{F}}\,=\,-4.4$ eV. Note that, in contrast to the $E(k_x,k_y)$ band, the opacity for the $k_x$, $k_y$ map ranges from 0 to 1. The layered structure in vertical direction is a consequence of the finite energy steps in the measured data cube. While mainly the first BZ is shown in the figure, at $k_y$ = 0 and $k_x\,<\,-0.6$ Å$^{-1}$ the edge of the $E(k_x,k_y)$ band in the neighboring BZ is visible as well.