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Nanoscale Imaging of Charge Carrier and Exciton Trapping at Structural Defects in Organic Semiconductors Christoph Große, Olle Gunnarsson, Pablo Merino, Klaus Kuhnke, and Klaus Kern Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b00190 • Publication Date (Web): 12 Feb 2016 Downloaded from http://pubs.acs.org on February 15, 2016
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Nano Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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Nano Letters
Nanoscale Imaging of Charge Carrier and Exciton Trapping at Structural Defects in Organic Semiconductors Christoph Große,∗,† Olle Gunnarsson,† Pablo Merino,† Klaus Kuhnke,† and Klaus Kern†,‡ †Max-Planck-Institut f¨ ur Festk¨orperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany ´ ‡Ecole Polytechnique F´ed´erale de Lausanne, 1015 Lausanne, Switzerland E-mail: [email protected] Abstract Charge carrier and exciton trapping in organic semiconductors crucially determine the performance of organic (opto-)electronic devices, such as organic field-effect transistors, light-emitting diodes, or solar cells. However, the microscopic origin of the relevant traps generally remains unclear, as most spectroscopic techniques are unable to simultaneously probe the electronic and morphological structure of individual traps. Here, we employ low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) as well tight-binding calculations derived from ab initio calculations to image the localized electronic states arising at structural defects in thin C60 films (< 10 ML). The spatially and spectrally resolved STM-induced luminescence at these states reveals an enhanced radiative decay of excitons, which is interpreted in terms of the local symmetry lowering and the trapping of excitons by X-traps. The combined mapping of the STM-induced luminescence, electronic structure, and morphology thus
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provides new insights into the origin and characteristics of individual exciton traps in organic semiconductors and offers new avenues to study charge carrier and exciton dynamics on molecular scales.
Keywords C60 ; STM; STM-induced luminescence; X-traps
Main text Structural disorder and deviations from perfect crystallinity often limit the performance and capabilities of organic semiconductors in organic devices 1,2 . The charge carrier mobility, for example, typically decreases with diminishing degree of order 3–5 . Temperature and gate voltage dependent measurements 6,7 suggest that charge transport in ordered organic semiconductors occurs via successive trapping of charge carriers by a distribution of localized gap states and their subsequent release into higher-energy delocalized states 8 . Photoluminescence and absorption spectra – sensitive to the electronic structure seen by excitons, that is, electron–hole pairs – corroborate the presence of local traps and indicate a similar increase in their density 9–12 as well as a decreasing exciton diffusion 13,14 with increasing number of structural defects. Such exciton traps have been observed in many organic materials 9,15–18 and can even dominate their emission characteristics 19,20 . However, their precise identity generally remains a mystery because of the limited spatial resolution of spectroscopic techniques and the missing structural information. For this reason, such exciton traps, resulting from structural defects instead of specific electronic states of chemical impurities, are commonly referred to as X-traps 21 . A fundamental understanding of charge carrier and exciton traps in organic solids thus requires a comprehensive investigation of their morphology, electronic structure, and their emission characteristics on the scale of individual molecules. For this purpose, C60 is an ideal model system. Because of its rigid and highly symmetric 2 ACS Paragon Plus Environment
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structure, individual C60 molecules exhibit only one stable conformation and can be grown epitaxially 22 , which both limit the number of microstates. Furthermore, at a temperature of 90 K solid C60 exhibits an orientational glass transition, below which each C60 molecule resides in one of two possible orientations 23 , resulting in bipolar or merohedral disorder 24 . In the thermodynamically most stable P orientation, bonds between two hexagons oppose a pentagonal face of the neighboring molecules; while in the slightly less stable H orientation, these bonds oppose a hexagonal face of the neighboring molecules. The abundance of both orientations is given by their Boltzmann distribution at the glass transition temperature and their energy difference of ∼10 meV 25 . Last but not least, the molecular orbitals of the free molecule remain essentially intact in the solid; hence, the charge hopping between individual molecules can be calculated by rather inexpensive methods, such as tight-binding approaches 26,27 . Here, we investigate the molecular orientations as well as the local electronic structure at the surface of thin C60 films (< 10 ML) by scanning tunneling microscopy (STM). Local disorder and structural defects in the surface layer are found to result in spatially localized split-off states within the band gap of the film. The STM-induced luminescence at these states reveals a locally enhanced radiative decay of excitons, which suggests that these states act as traps for charge carriers as well as for excitons. Tight-binding calculations of the films, parameterized to ab initio calculations 26,27 and based on the experimentally observed molecular orientations in the surface layer, reproduce these split-off states and identify local changes in the hopping integrals as their origin. Figure 1a depicts a typical STM image of the states derived from the highest occupied molecular orbital (HOMO) of the C60 molecules in an about six molecular layers (ML) thin film. Previous STM studies have shown that the orientation of the surface molecules can be determined by comparing the observed orbital patterns with calculated projections of a free C60 molecule 28–33 . At bias voltages < −2.5 V, three main orientations can be identified (cf. Fig. 1a): Molecules with a three-lobed pattern, which results from a hexagonal face of
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the molecules pointing toward the STM tip, molecules with a more intensive oval pattern, arising from a bond between two hexagonal faces, and molecules with a triangular pattern, resulting from a bond between a hexagonal and a pentagonal face. The derived orientations of the surface molecules are depicted in Fig. 1b. In the upper part, the molecules form a (2 × 2) superlattice (red rhombus), which has been also observed for C60 multilayers on Si(100) 28 and on thin NaCl films 33 . The molecular orientation in this (2 × 2) superlattice matches the lowest-energy, (111)-terminated low-temperature bulk structure of C60 , in which all molecules reside in a P orientation. Each of the four molecules in the unit cell can be described by a single rotational angle around one of the four equivalent crystallographic [111] axes. In addition, a small fraction of molecules reside in a second, only ∼10 meV 25 less stable H orientation, which can be described by a second setting angle along the same [111] axes. A comparison of the expected molecular orientations with those derived in Fig. 1b reveals that the molecules depicted by black pictograms exist in this second most stable H orientation. The fraction of surface molecules with an H orientation in the Fig. 1a (15 %) well agrees with the fraction of H molecule in the bulk (16.5 % 23 ). Molecule 1 (red pictogram) is the only
Figure 1: Orientation of the surface molecules of a ∼6 ML C60 film on Ag(111). (a) Constant height current image of the HOMO-derived states (Uset = −3 V). (b) Schematic molecular orientations determined from panel a. Gray pictograms indicate molecules in the thermodynamically most stable P orientation within the (2 × 2) superstructure (red rhombus); black pictograms indicate molecules in the slightly less stable H orientation. Molecule 1 (red) deviates from these two orientations at the respective lattice site and appears slightly higher than the other surface molecules. (c) Simulated STM image of the HOMO-derived states. The normalized LDOS maps in panel a and c are displayed with the logarithmic gray scales shown on the right-hand side.
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surface molecule that occurs in neither a P nor an H orientation. In topography images at bias voltages < −2.5 V, that is, at energies of the HOMO-derived bands, this molecule seems to protrude by ∼0.02 nm and exhibits the same orbital pattern as its upper left and lower right neighbors. The discussion below will show that this small protrusion results from a C60 molecule in a non-equilibrium configuration or an underlying neutral impurity. Figure 1c displays the simulated STM image of the HOMO-derived band (see methods section) based on the orientation of the surface molecules defined in Fig. 1b, with molecule 1 being lifted by 0.02 nm. For bias voltages close to the onsets of the HOMO- and LUMO- (lowest unoccupied molecular orbital) derived bands, individual localized states appear (Fig. 2a,b). Whereas the state close to the LUMO-derived band (Fig. 2b) possesses its spatial maximum on the slightly raised C60 molecule 1, the much more intense state close to the HOMO-derived band (Fig. 2a) is mostly localized on the neighboring molecule 2. A comparison of the dI /dV spectra on both molecules with those on C60 molecules several nanometers away (gray curve in Fig. 2c) demonstrate that these states lie in the band gap of the C60 surface. Moreover, the energy split-off from the HOMO-derived band is much larger than the one from the LUMO-derived band. We observed similar localized split-off states also at other structural defects, such as dislocations and domain boundaries 34 . In the latter case, imaging of the corresponding split-off states by constant height dI /dV maps requires a much more sophisticated analysis due to the spatial variations in the topographic height however. The calculated energy and spatial distribution of the highest occupied state of the system sensitively depend on the molecular orientation in the surface layer and the layer beneath. Therefore, we calculated the electronic structure of the system for all permutations of the two possible orientations of the twelve nearest neighbors of molecule 2 in the second layer. Interestingly, only 19 of the 212 possible permutations result in a predominant localization of the highest occupied state as well as a local density of states (LDOS) maximum on molecule 2, which illustrates the high sensitivity to the precise molecular arrangement. In the major-
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ity of cases, the highest LDOS occurs on other surface molecules, most often on the slightly lifted molecule 1. Furthermore, we note that the packing of molecules in a face-centered cubic (fcc) lattice a priori enables two different lattice positions for the molecules in the second layer. However, for the alternative lattice sites of the second layer, i.e., the reverse succes-
Figure 2: Electronic structure at the edge of the HOMO- and LUMO-derived band (same area as in Fig. 1). (a) Constant height dI /dV map of the HOMO-derived split-off state and (b) the LUMO-derived split-off state. The bias voltage is denoted at the top right of each map. (c) dI /dV spectra acquired on molecule 1 (red), molecule 2 (blue), and a reference molecule in the highly-ordered region marked by the white cross in panel a,b. (d) Simulated dI /dV spectra at these sites, (e) map of the highest occupied electronic state, and (f) map of the lowest unoccupied state. The normalized localized density of states (LDOS) maps in panel a,b,e,f are displayed with the logarithmic color scales displayed at the bottom.
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sion of fcc layers, none of the 212 permutations result in an LDOS maximum on molecule 2. These results suggest that the combined approach of experiments and calculations enables determination of the molecular position and orientation in the second layer, which is typically inaccessible in STM. Figure 2e,f show the calculated STM map of the highest occupied state and the lowest unoccupied state of the system, respectively, for the orientation that leads to the best agreement with the experimental data. The corresponding configuration of the molecules in the surface layer and the layer beneath is encoded in Fig. 3. The simulated spectra and maps qualitatively reproduce the experimentally observed splitting and localization of electronic states caused by the molecular arrangement. The different energy scales in both the experiment and the calculation primarily have two origins: (I) the calculated band gap is underestimated as many-body effects are neglected and (II) the experimental band gap is overestimated because of the band bending of the C60 states due to the electric field within the STM junction. We now discuss the origin of the observed split-off states. As mentioned above, the majority of C60 molecules are in the thermodynamically most stable P orientation. Therefore, the electronic structure is primarily determined by the charge carrier hopping between molecules in a P orientation. Molecules in the slightly less stable H orientation can be regarded as perturbations of the periodic electronic structure by varying the local hopping integrals, that is, the spatial overlap of wavefunctions between neighboring molecules. The larger the local changes of the hopping integrals caused by these deviations from perfect order, the larger is the local perturbation and thus the splitting of electronic states from the band center. Figure 3 depicts the summed changes of the hopping integrals between adjacent molecules, compared to the thermodynamically most stable crystal structure (for details see methods section). Indeed, all molecules with a H orientation (black dots) cause changes in the local hopping integrals and thus in the local electronic structure. The strongest changes of the HOMO-derived hopping integrals (Fig. 3a) arise around molecule 1 and 2, with the maximum difference (black segment) occurring between these two molecules. This explains the obser-
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vation of the highest occupied state in this region. For the LUMO-derived states (Fig. 3b), none of the hopping integral changes is particularly large. Instead, the maximum changes occur on all molecules with a hexagon-pentagon bond pointing upwards (cf. Fig. 1b). On molecule 1, which exhibits the highest LDOS both in experiment and calculation, however, the variations in the hopping integrals are less pronounced. Hence, the high LDOS observed on molecule 1 most likely arises from its elevated position. It is noteworthy that the absolute changes of the LUMO-derived hopping integrals are only about half as large as in the case of the HOMO-derived states, most likely due to their lower degeneracy. This fact is in good agreement with the weaker localization of the LUMO-derived split-off state as well as their weaker splitting from the conduction band. In the following, we demonstrate that the observed structural defect sites cause a locally enhanced radiative recombination of excitons by investigating the STM-induced luminescence around the split-off states. Previous studies have shown that the highly localized current in STM can be used to stimulate the electroluminescence from single molecules 35,36 , molecular nanocrystals 37–39 , and molecular films 40,41 . For bias voltages
Communication
Nanoscale Imaging of Charge Carrier and Exciton Trapping at Structural Defects in Organic Semiconductors Christoph Große, Olle Gunnarsson, Pablo Merino, Klaus Kuhnke, and Klaus Kern Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b00190 • Publication Date (Web): 12 Feb 2016 Downloaded from http://pubs.acs.org on February 15, 2016
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Nano Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
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Nano Letters
Nanoscale Imaging of Charge Carrier and Exciton Trapping at Structural Defects in Organic Semiconductors Christoph Große,∗,† Olle Gunnarsson,† Pablo Merino,† Klaus Kuhnke,† and Klaus Kern†,‡ †Max-Planck-Institut f¨ ur Festk¨orperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany ´ ‡Ecole Polytechnique F´ed´erale de Lausanne, 1015 Lausanne, Switzerland E-mail: [email protected] Abstract Charge carrier and exciton trapping in organic semiconductors crucially determine the performance of organic (opto-)electronic devices, such as organic field-effect transistors, light-emitting diodes, or solar cells. However, the microscopic origin of the relevant traps generally remains unclear, as most spectroscopic techniques are unable to simultaneously probe the electronic and morphological structure of individual traps. Here, we employ low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) as well tight-binding calculations derived from ab initio calculations to image the localized electronic states arising at structural defects in thin C60 films (< 10 ML). The spatially and spectrally resolved STM-induced luminescence at these states reveals an enhanced radiative decay of excitons, which is interpreted in terms of the local symmetry lowering and the trapping of excitons by X-traps. The combined mapping of the STM-induced luminescence, electronic structure, and morphology thus
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provides new insights into the origin and characteristics of individual exciton traps in organic semiconductors and offers new avenues to study charge carrier and exciton dynamics on molecular scales.
Keywords C60 ; STM; STM-induced luminescence; X-traps
Main text Structural disorder and deviations from perfect crystallinity often limit the performance and capabilities of organic semiconductors in organic devices 1,2 . The charge carrier mobility, for example, typically decreases with diminishing degree of order 3–5 . Temperature and gate voltage dependent measurements 6,7 suggest that charge transport in ordered organic semiconductors occurs via successive trapping of charge carriers by a distribution of localized gap states and their subsequent release into higher-energy delocalized states 8 . Photoluminescence and absorption spectra – sensitive to the electronic structure seen by excitons, that is, electron–hole pairs – corroborate the presence of local traps and indicate a similar increase in their density 9–12 as well as a decreasing exciton diffusion 13,14 with increasing number of structural defects. Such exciton traps have been observed in many organic materials 9,15–18 and can even dominate their emission characteristics 19,20 . However, their precise identity generally remains a mystery because of the limited spatial resolution of spectroscopic techniques and the missing structural information. For this reason, such exciton traps, resulting from structural defects instead of specific electronic states of chemical impurities, are commonly referred to as X-traps 21 . A fundamental understanding of charge carrier and exciton traps in organic solids thus requires a comprehensive investigation of their morphology, electronic structure, and their emission characteristics on the scale of individual molecules. For this purpose, C60 is an ideal model system. Because of its rigid and highly symmetric 2 ACS Paragon Plus Environment
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structure, individual C60 molecules exhibit only one stable conformation and can be grown epitaxially 22 , which both limit the number of microstates. Furthermore, at a temperature of 90 K solid C60 exhibits an orientational glass transition, below which each C60 molecule resides in one of two possible orientations 23 , resulting in bipolar or merohedral disorder 24 . In the thermodynamically most stable P orientation, bonds between two hexagons oppose a pentagonal face of the neighboring molecules; while in the slightly less stable H orientation, these bonds oppose a hexagonal face of the neighboring molecules. The abundance of both orientations is given by their Boltzmann distribution at the glass transition temperature and their energy difference of ∼10 meV 25 . Last but not least, the molecular orbitals of the free molecule remain essentially intact in the solid; hence, the charge hopping between individual molecules can be calculated by rather inexpensive methods, such as tight-binding approaches 26,27 . Here, we investigate the molecular orientations as well as the local electronic structure at the surface of thin C60 films (< 10 ML) by scanning tunneling microscopy (STM). Local disorder and structural defects in the surface layer are found to result in spatially localized split-off states within the band gap of the film. The STM-induced luminescence at these states reveals a locally enhanced radiative decay of excitons, which suggests that these states act as traps for charge carriers as well as for excitons. Tight-binding calculations of the films, parameterized to ab initio calculations 26,27 and based on the experimentally observed molecular orientations in the surface layer, reproduce these split-off states and identify local changes in the hopping integrals as their origin. Figure 1a depicts a typical STM image of the states derived from the highest occupied molecular orbital (HOMO) of the C60 molecules in an about six molecular layers (ML) thin film. Previous STM studies have shown that the orientation of the surface molecules can be determined by comparing the observed orbital patterns with calculated projections of a free C60 molecule 28–33 . At bias voltages < −2.5 V, three main orientations can be identified (cf. Fig. 1a): Molecules with a three-lobed pattern, which results from a hexagonal face of
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the molecules pointing toward the STM tip, molecules with a more intensive oval pattern, arising from a bond between two hexagonal faces, and molecules with a triangular pattern, resulting from a bond between a hexagonal and a pentagonal face. The derived orientations of the surface molecules are depicted in Fig. 1b. In the upper part, the molecules form a (2 × 2) superlattice (red rhombus), which has been also observed for C60 multilayers on Si(100) 28 and on thin NaCl films 33 . The molecular orientation in this (2 × 2) superlattice matches the lowest-energy, (111)-terminated low-temperature bulk structure of C60 , in which all molecules reside in a P orientation. Each of the four molecules in the unit cell can be described by a single rotational angle around one of the four equivalent crystallographic [111] axes. In addition, a small fraction of molecules reside in a second, only ∼10 meV 25 less stable H orientation, which can be described by a second setting angle along the same [111] axes. A comparison of the expected molecular orientations with those derived in Fig. 1b reveals that the molecules depicted by black pictograms exist in this second most stable H orientation. The fraction of surface molecules with an H orientation in the Fig. 1a (15 %) well agrees with the fraction of H molecule in the bulk (16.5 % 23 ). Molecule 1 (red pictogram) is the only
Figure 1: Orientation of the surface molecules of a ∼6 ML C60 film on Ag(111). (a) Constant height current image of the HOMO-derived states (Uset = −3 V). (b) Schematic molecular orientations determined from panel a. Gray pictograms indicate molecules in the thermodynamically most stable P orientation within the (2 × 2) superstructure (red rhombus); black pictograms indicate molecules in the slightly less stable H orientation. Molecule 1 (red) deviates from these two orientations at the respective lattice site and appears slightly higher than the other surface molecules. (c) Simulated STM image of the HOMO-derived states. The normalized LDOS maps in panel a and c are displayed with the logarithmic gray scales shown on the right-hand side.
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surface molecule that occurs in neither a P nor an H orientation. In topography images at bias voltages < −2.5 V, that is, at energies of the HOMO-derived bands, this molecule seems to protrude by ∼0.02 nm and exhibits the same orbital pattern as its upper left and lower right neighbors. The discussion below will show that this small protrusion results from a C60 molecule in a non-equilibrium configuration or an underlying neutral impurity. Figure 1c displays the simulated STM image of the HOMO-derived band (see methods section) based on the orientation of the surface molecules defined in Fig. 1b, with molecule 1 being lifted by 0.02 nm. For bias voltages close to the onsets of the HOMO- and LUMO- (lowest unoccupied molecular orbital) derived bands, individual localized states appear (Fig. 2a,b). Whereas the state close to the LUMO-derived band (Fig. 2b) possesses its spatial maximum on the slightly raised C60 molecule 1, the much more intense state close to the HOMO-derived band (Fig. 2a) is mostly localized on the neighboring molecule 2. A comparison of the dI /dV spectra on both molecules with those on C60 molecules several nanometers away (gray curve in Fig. 2c) demonstrate that these states lie in the band gap of the C60 surface. Moreover, the energy split-off from the HOMO-derived band is much larger than the one from the LUMO-derived band. We observed similar localized split-off states also at other structural defects, such as dislocations and domain boundaries 34 . In the latter case, imaging of the corresponding split-off states by constant height dI /dV maps requires a much more sophisticated analysis due to the spatial variations in the topographic height however. The calculated energy and spatial distribution of the highest occupied state of the system sensitively depend on the molecular orientation in the surface layer and the layer beneath. Therefore, we calculated the electronic structure of the system for all permutations of the two possible orientations of the twelve nearest neighbors of molecule 2 in the second layer. Interestingly, only 19 of the 212 possible permutations result in a predominant localization of the highest occupied state as well as a local density of states (LDOS) maximum on molecule 2, which illustrates the high sensitivity to the precise molecular arrangement. In the major-
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ity of cases, the highest LDOS occurs on other surface molecules, most often on the slightly lifted molecule 1. Furthermore, we note that the packing of molecules in a face-centered cubic (fcc) lattice a priori enables two different lattice positions for the molecules in the second layer. However, for the alternative lattice sites of the second layer, i.e., the reverse succes-
Figure 2: Electronic structure at the edge of the HOMO- and LUMO-derived band (same area as in Fig. 1). (a) Constant height dI /dV map of the HOMO-derived split-off state and (b) the LUMO-derived split-off state. The bias voltage is denoted at the top right of each map. (c) dI /dV spectra acquired on molecule 1 (red), molecule 2 (blue), and a reference molecule in the highly-ordered region marked by the white cross in panel a,b. (d) Simulated dI /dV spectra at these sites, (e) map of the highest occupied electronic state, and (f) map of the lowest unoccupied state. The normalized localized density of states (LDOS) maps in panel a,b,e,f are displayed with the logarithmic color scales displayed at the bottom.
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sion of fcc layers, none of the 212 permutations result in an LDOS maximum on molecule 2. These results suggest that the combined approach of experiments and calculations enables determination of the molecular position and orientation in the second layer, which is typically inaccessible in STM. Figure 2e,f show the calculated STM map of the highest occupied state and the lowest unoccupied state of the system, respectively, for the orientation that leads to the best agreement with the experimental data. The corresponding configuration of the molecules in the surface layer and the layer beneath is encoded in Fig. 3. The simulated spectra and maps qualitatively reproduce the experimentally observed splitting and localization of electronic states caused by the molecular arrangement. The different energy scales in both the experiment and the calculation primarily have two origins: (I) the calculated band gap is underestimated as many-body effects are neglected and (II) the experimental band gap is overestimated because of the band bending of the C60 states due to the electric field within the STM junction. We now discuss the origin of the observed split-off states. As mentioned above, the majority of C60 molecules are in the thermodynamically most stable P orientation. Therefore, the electronic structure is primarily determined by the charge carrier hopping between molecules in a P orientation. Molecules in the slightly less stable H orientation can be regarded as perturbations of the periodic electronic structure by varying the local hopping integrals, that is, the spatial overlap of wavefunctions between neighboring molecules. The larger the local changes of the hopping integrals caused by these deviations from perfect order, the larger is the local perturbation and thus the splitting of electronic states from the band center. Figure 3 depicts the summed changes of the hopping integrals between adjacent molecules, compared to the thermodynamically most stable crystal structure (for details see methods section). Indeed, all molecules with a H orientation (black dots) cause changes in the local hopping integrals and thus in the local electronic structure. The strongest changes of the HOMO-derived hopping integrals (Fig. 3a) arise around molecule 1 and 2, with the maximum difference (black segment) occurring between these two molecules. This explains the obser-
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vation of the highest occupied state in this region. For the LUMO-derived states (Fig. 3b), none of the hopping integral changes is particularly large. Instead, the maximum changes occur on all molecules with a hexagon-pentagon bond pointing upwards (cf. Fig. 1b). On molecule 1, which exhibits the highest LDOS both in experiment and calculation, however, the variations in the hopping integrals are less pronounced. Hence, the high LDOS observed on molecule 1 most likely arises from its elevated position. It is noteworthy that the absolute changes of the LUMO-derived hopping integrals are only about half as large as in the case of the HOMO-derived states, most likely due to their lower degeneracy. This fact is in good agreement with the weaker localization of the LUMO-derived split-off state as well as their weaker splitting from the conduction band. In the following, we demonstrate that the observed structural defect sites cause a locally enhanced radiative recombination of excitons by investigating the STM-induced luminescence around the split-off states. Previous studies have shown that the highly localized current in STM can be used to stimulate the electroluminescence from single molecules 35,36 , molecular nanocrystals 37–39 , and molecular films 40,41 . For bias voltages
