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Cite this: Chem. Commun., 2014, 50, 12289 Received 22nd May 2014, Accepted 12th August 2014
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Probing the spatial and momentum distribution of confined surface states in a metal coordination network† Jun Zhang,a Aneliia Shchyrba,b Sylwia Nowakowska,b Ernst Meyer,b Thomas A. Jung*bc and Matthias Muntwiler*a
DOI: 10.1039/c4cc03941f www.rsc.org/chemcomm
The Shockley surface state on Cu(111) reacts sensitively to the perturbation by molecular adsorbates on the surface. In the porous structure of a metal-coordinated molecular network on Cu(111), the surface state is confined to a series of discrete states. Energy and momentum of eigenstates in the pores are related to both the energy dispersion of the free surface state and the geometric and energetic details of the confining barrier formed by the molecular network. The penetration of the confined state into the barrier is found to be sensitive to the constituting architectural elements.
On-surface coordination allows for the versatile and often predictable construction of porous networks if both the metal atoms and the organic linker molecule(s) are adequately chosen.1–9 Thereby surfaces have been equipped with porous confinements to study the host–guest interaction with ad-molecules,10–14 and to modify the electronic surface states of the underlying substrate.15–19 Compared to artificial structures assembled from building blocks with the tip of the scanning tunnelling microscope (STM),20 self-assembled metal coordination facilitates the formation of homogeneous and extended networks. The interaction of molecules or porous networks with the underlying electronic states has been described by models that consider the molecule as a scattering centre for the surface state electrons.21 In recent work, a pseudopotential model that treats the building blocks as scattering barrier with finite height and width has been used to reproduce the observed quantum well state.15,18 Due to the finite potential barriers, electronic coupling between the quantum well states has been evidenced in periodic networks.19,22 By modifying constituents, different quantum dot arrays can form which exhibit tunable electronic and optical properties. On the a
Laboratory for Synchrotron Radiation – Condensed Matter, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland. E-mail: [email protected] b Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland c Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland. E-mail: [email protected] † Electronic supplementary information (ESI) available: Experimental details, additional STM data and details for data analysis. See DOI: 10.1039/c4cc03941f
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other hand, measuring the confinement of the surface state can shed light on the width and the height of the potential barrier.22 There are several factors contributing to the modification of the surface state. Firstly, the interaction between the surface and the adsorbed molecules may shift or quench the surface state in the covered region.23–25 Secondly, the network structure can induce a periodic confinement of the surface state which depends on the lateral size of the pores and on the scattering potential of the molecular barriers.15,18,22,26 These influencing factors have been well demonstrated by angle resolved photoemission spectroscopy (ARPES) and scanning tunnelling spectroscopy (STS) in both real and momentum space on stepped metal surfaces.26–29 However, it is difficult to transpose these combined studies on bare metal substrates to two-dimensional molecular porous networks. Therefore, in the context of molecular networks, there are still open questions concerning the coupling mechanism between the confined quantum dots, and concerning the details of the potential barrier. We use 9,10-dicyanoanthracene (DCA) molecules as building blocks, which have two CN groups bonded to the centre phenyl ring of anthracene. After deposition at room temperature on the Cu(111) surface, the molecules form a regular, porous network (Fig. 1(a)). In the high-resolution STM image we observe that the anthracene backbones point towards the centre of the pores, and that the CN groups are coordinated to Cu adatoms, with reference to earlier work on a similar molecular network.30 The pores exhibit a nearest neighbour distance of 2.08 0.02 nm, which is by one interatomic spacing (0.255 nm) longer than reported earlier.30 Accordingly, we propose a revised adsorption configuration of the molecules as shown in Fig. 1(b). To investigate the effect of confinement on the surface state, dI/dV spectra which are sensitive to the local density of states, have been taken at different positions of the network, as shown in Fig. 1(c). Two features are observed on the spectra: the peak at 0.75 V corresponds to the electronic state derived from a molecular orbital and will be discussed elsewhere; the peak (or shoulder in some of the spectra) at 0.14 V is of highest intensity in the centre of the pore. The dI/dV map obtained at 0.14 V (Fig. 1(d)) reveals a periodic array of high intensity spots with
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Fig. 1 Self-assembled regular structure of DCA on Cu(111) after deposition at room temperature. (a) STM micrograph ( 1.0 V, 100 pA, 20.7 nm 17.4 nm). The arrows mark a domain boundary. Inset: high resolution image ( 0.5 V, 100 pA, 4.6 nm 3.9 nm) measured with a DCA modified tip. A molecular structure model is superimposed. (b) Proposed model of the adsorption configuration with the unit cell highlighted. (c) dI/dV spectra obtained with a metal tip at different locations in the network, as marked in the inset of (a). The dashed black curve was measured on a bare copper region for reference. (d) dI/dV map obtained with a metal tip at 0.14 V (4.6 nm 3.9 nm). The network architecture is superimposed to guide the eyes. The simultaneously obtained STM topography is depicted in Fig. S2, ESI.†
their shape resembling that of the pore. We assign the feature at 0.14 V to a confined surface state derived from the Shockley state of Cu(111). Similar to the concept of a quantum mechanical particle in a box, here the molecules and adatoms play the role of potential walls reflecting and confining the surface state electrons. Scattering of the surface state at the DCA domain border leads to the formation of a standing wave pattern. This suggests that the molecules can act as scattering barriers for the surface state in similarity to step edges.28 While the standing waves on the bare Cu region show the continuum of the surface state band, the confinement inside a pore of the DCA network results in a state which is peaked at a certain momentum and energy (Fig. S3 of the ESI†). The confinement effect of the network can be studied by taking STS above the building blocks: due to imperfect confinement, the confined surface state shows up as a shoulder in the spectra taken above the molecular backbone (red curve in Fig. 1(c)). In contrast, features which could be assigned to the surface state or confined surface state are absent in STS data (Fig. S4(c), ESI†) measured on the close packed DCA assembly. The confined state also shows up at the adatom position but with lower intensity than that at the molecular backbone (Fig. 1(c)). This indicates that the scattering potential is stronger near the adatom due to several possible reasons. Firstly, X-ray Photoelectron Spectroscopy data of the N 1s core level reveal a strong shift by 0.35 eV to a higher binding energy for the adatom-coordinated network with respect to uncoordinated DCA adsorbates. This indicates that negative charge transfer occurs from the molecule to the coordinated adatom.31 Secondly, calculations show that the anthracene backbone is located further away from the surface than the adatom and the CN group.30 In addition to the pores in the interior of regular domains (type C), pores of different size and symmetry are found at
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Fig. 2 Surface state confinement in quantum wells of different size and shape. (a) High resolution STM image taken with a DCA modified tip of the domain boundary region with the proposed assembly structure superimposed ( 0.5 V, 100 pA, 7.5 nm 4.5 nm). (b) STM image ( 1.0 V, 50 pA, 7.0 nm 6.3 nm) of a domain boundary region with different sized pores, which are defined as A and B, respectively. The pores in the domain are labelled C. (c) dI/dV spectra obtained at different locations within the pores marked in (b). The dashed black curve is a reference taken on Cu(111). The onset of the Cu(111) surface state is labelled SS. The spectra show peaks at 0.19 V and 0.17 V for pore A (labelled CSIA and CSIIA), 0.1 V and 0.26 V for pore B (CSIB and CSIIB). The spectrum for pore C is shown for comparison, with its peak labelled CSIC.
domain boundaries (Fig. 2(a)). To compare the confinement effect in the different pores, we also measure STS in two types of pores at domain boundaries (type A and B) shown in Fig. 2(b). Spectra taken at different positions of two typical pores both exhibit two peaks, 0.19 V and 0.17 V for pore A, 0.1 V and 0.26 V for pore B, as shown in Fig. 2(c). We assign the two peaks observed in pore A and B to the first and second eigenstates of the confinement. This can be seen more clearly in the spatial variation of the peak intensity shown in Fig. 3. Close to the first peak position of each pore, the dI/dV map shows a dome-like shape inside the pore (Fig. 3(a–c)), corresponding to the spatial distribution of the first eigenstate. However, the image obtained close to the second peak position of pore A (Fig. 3(d)) shows a donut shape, indicating that the peak corresponds to the second eigenstate. For pore B, the dI/dV image of the second peak (Fig. 3(e)) also shows a donut shape, but only along the long axis direction of the pore due to the elongated shape of the confining region. The spatial extent of the eigenstates observed in different pores is evident from the line profiles in Fig. 3(g–i). The eigenstates shift to higher energy with decreased pore size, as expected for a particle in a box, similar to observations in a covalently bonded network.32 We analyse the confinement in the pores by using the quantum mechanical model of a particle in a two-dimensional box with finite barriers. Accordingly, we expect a discrete series of states inside each pore where energy and momentum (or wave vector) of the eigenstates are defined by the spatial extent of the potential well. Wave vectors are calculated from the reciprocal area of the potential well and a shape factor.33–35 The energy-momentum relation deduced from the analysis of the eigenstates in different pores is plotted in Fig. 4(c). Details of the analysis are shown in Section 7 of ESI.† Since we do not know the effective pore size a priori, we calculate
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Fig. 3 Spatial distribution of the confined states in pores of different size and symmetry. (a–e) dI/dV maps at voltages close to the peak positions shown in Fig. 2. (f) Simultaneously obtained STM image ( 0.5 V, 70 pA, 5.6 nm 5.6 nm). The positions for molecular backbone and adatoms have been superimposed to guide the eyes. Bias voltages and peak labels as defined in Fig. 2 are included. The letters A, B and C indicate the type of pores, and mark the interesting region in the maps. (g–i) Profiles along the lines shown in corresponding dI/dV maps in the upper panels.
wave vectors for two limiting cases: the red data points correspond to the largest possible well size (red outlines in Fig. 4 and Fig. S6, ESI†) where the edges are centred at the molecules; the blue markers are based on a well size (blue outlines in Fig. 4 and Fig. S6, ESI†) closely following the area of the pores in the STM images. Although measured in different pores, the data points nicely follow a freeelectron like parabola which resembles that of the Shockley state (Fig. 4(c)). The effective mass is increased to between 0.47 me and 0.75 me, depending on the definition of the pore boundary, and the band bottom shifts up by 80 meV. We understand this behaviour in the following qualitative picture: the confined states essentially derive from the surface state, modulated by an envelope function induced by the confinement. The envelopes can be approximated by solving the ¨dinger equation of a finite potential well with the shape and Schro dimensions of the blue outlines in Fig. 4(a) (see Section 8 in ESI†). The calculation shows that the energetic position of the observed states is sensitive to the overlap integral of the wave function with the potential barrier in the molecular network. This is similar to the confinement of the surface state on vicinal Cu(111) where the periodic potential of the step array induces the opening of a band gap at the Brillouin zone boundary and a shift of the band bottom which is proportional to the height of the potential barrier.26,36 Similar to the observation of a delocalized state by ARPES,19 we would expect the formation of a periodic band structure also in the present case, with possible band gaps at the high symmetry points X1 and X2 marked in Fig. 4(c). We observe that the confined state extends into the region covered by the molecular backbone (Fig. S3(c), ESI†). However, we believe that our data are not suitable to
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Fig. 4 Effective confinement and E(k) derived from STS spectra taken in pores of different size. (a, b) STM image and structural model of two limiting well sizes for pores A, B and C. (c) Energy dispersion plot of the confined state and quadratic curve fits. Red and blue colours correspond to the large and small well size in (a) and (b). The fits yield an effective mass of 0.47 0.03 me, bottom of the dispersion 0.364 0.027 eV for the large well size, and 0.75 0.03 me, 0.355 0.019 eV for the small well size, respectively. The black dashed curve is the energy dispersion of the surface state of bare Cu(111) with E0 = 0.44 eV, m* = 0.40 me. Two highsymmetry points of the surface Brillouin zone (shown in the inset) are marked by vertical lines. The data points are obtained from five different types of pores including pore A, B and C, which are shown in Fig. S6, ESI.†
analyse such a delocalized state because they were partly measured in irregular pores which are not part of the periodic lattice, and because the uncertainty in the calculation of kJ renders an assignment of electronic bands impossible. In any case, the observed shift of the band bottom of 80 meV represents a probe of the potential inside the pores and of the confining barrier of the molecular network. Such modification can include contributions from the Pauli repulsion between the porous network and the electrons, and charge transfer/ redistribution at the adsorbate–substrate interface.23,37 In conclusion, we have studied the spatial distribution and the energy dispersion of the confined quantum states in a supramolecular porous network. STS data interpreted both in real and reciprocal spaces indicate the modulation of the intrinsic surface state in the confined space of the pores. The energy levels of the confined states depend on the chemical components of the metal– organic network which enclose the pores, making them sensitive probes of the electrostatic potential, or of the energy levels of the frontier orbitals in the confining molecules. This work was supported by the PSI-FELLOW/COFUND program. Partial funding from the Swiss National Science Foundation, the Swiss Nanoscience Institute (among others, grant no. 200020-137917, 206021-113149, 206021-121461), and the Swiss Federal Institute for Materials Testing and Research is gratefully acknowledged. The authors would like to thank the founding partners of the PEARL beamline, in particular P. Aebi, R. Fasel, and T. Greber for scientific and technical advice. We also gratefully acknowledge discussions with F. Baumberger.
Notes and references 1 J. V. Barth, G. Costantini and K. Kern, Nature, 2005, 437, 671–679. 2 A. Langner, S. L. Tait, N. Lin, R. Chandrasekar, V. Meded, K. Fink, M. Ruben and K. Kern, Angew. Chem., Int. Ed., 2012, 51, 4327–4331.
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ChemComm 21 L. Gross, F. Moresco, L. Savio, A. Gourdon, C. Joachim and K.-H. Rieder, Phys. Rev. Lett., 2004, 93, 056103. ¨rter, F. J. Garcı´a de Abajo, D. Ecija, 22 K. Seufert, W. Auwa S. Vijayaraghavan, S. Joshi and J. V. Barth, Nano Lett., 2013, 13, 6130–6135. ¨ller, R. Bertschinger, M. Wahl, A. Bendounan, 23 A. Scheybal, K. Mu P. Aebi and T. Jung, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 79, 115406. 24 B. W. Heinrich, L. Limot, M. V. Rastei, C. Iacovita, J. P. Bucher, D. M. Djimbi, C. Massobrio and M. Boero, Phys. Rev. Lett., 2011, 107, 216801. 25 E. Annese, J. Fujii, I. Vobornik and G. Rossi, J. Phys. Chem. C, 2011, 115, 17409–17416. 26 F. Baumberger, T. Greber, B. Delley and J. Osterwalder, Phys. Rev. Lett., 2002, 88, 237601. ´rez-Dieste, V. Repain, S. Rousset, 27 A. Mugarza, A. Mascaraque, V. Pe F. Garcı´a de Abajo and J. Ortega, Phys. Rev. Lett., 2001, 87, 107601. ¨rgi, O. Jeandupeux, A. Hirstein, H. Brune and K. Kern, Phys. 28 L. Bu Rev. Lett., 1998, 81, 5370–5373. 29 J. Ortega, J. Lobo-Checa, G. Peschel, S. Schirone, Z. Abd El-Fattah, M. Matena, F. Schiller, P. Borghetti, P. Gambardella and A. Mugarza, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 115425. 30 G. Pawin, K. L. Wong, D. Kim, D. Sun, L. Bartels, S. Hong, T. S. Rahman, R. Carp and M. Marsella, Angew. Chem., Int. Ed., 2008, 47, 8442–8445. 31 T.-C. Tseng, C. Urban, Y. Wang, R. Otero, S. L. Tait, M. Alcamı´, D. Ecija, M. Trelka, J. M. Gallego, N. Lin, M. Konuma, U. Starke, ¨ll, M. A. Herranz, F. Martı´n, N. Martı´n, A. Nefedov, A. Langner, C. Wo K. Kern and R. Miranda, Nat. Chem., 2010, 2, 374–379. ¨ckerlin, M. Matena, T. Ivas, 32 A. Shchyrba, S. C. Martens, C. Wa ¨hr, T. A. Jung and L. H. Gade, Chem. Commun., H. Wadepohl, M. Sto 2014, 50, 7628–7631. 33 J. Li, W.-D. Schneider, R. Berndt and S. Crampin, Phys. Rev. Lett., 1998, 80, 3332–3335. 34 J. Li, W.-D. Schneider, S. Crampin and R. Berndt, Surf. Sci., 1999, 422, 95–106. 35 R. Temirov, S. Soubatch, A. Luican and F. S. Tautz, Nature, 2006, 444, 350–353. 36 F. Baumberger, M. Hengberger, M. Muntwiler, M. Shi, J. Krempasky, L. Patthey, J. Osterwalder and T. Greber, Phys. Rev. Lett., 2004, 92, 016803. ¨vel, Phys. Rev. B: Condens. Matter 37 T. Andreev, I. Barke and H. Ho Mater. Phys., 2004, 70, 205426.
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COMMUNICATION
Cite this: Chem. Commun., 2014, 50, 12289 Received 22nd May 2014, Accepted 12th August 2014
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Probing the spatial and momentum distribution of confined surface states in a metal coordination network† Jun Zhang,a Aneliia Shchyrba,b Sylwia Nowakowska,b Ernst Meyer,b Thomas A. Jung*bc and Matthias Muntwiler*a
DOI: 10.1039/c4cc03941f www.rsc.org/chemcomm
The Shockley surface state on Cu(111) reacts sensitively to the perturbation by molecular adsorbates on the surface. In the porous structure of a metal-coordinated molecular network on Cu(111), the surface state is confined to a series of discrete states. Energy and momentum of eigenstates in the pores are related to both the energy dispersion of the free surface state and the geometric and energetic details of the confining barrier formed by the molecular network. The penetration of the confined state into the barrier is found to be sensitive to the constituting architectural elements.
On-surface coordination allows for the versatile and often predictable construction of porous networks if both the metal atoms and the organic linker molecule(s) are adequately chosen.1–9 Thereby surfaces have been equipped with porous confinements to study the host–guest interaction with ad-molecules,10–14 and to modify the electronic surface states of the underlying substrate.15–19 Compared to artificial structures assembled from building blocks with the tip of the scanning tunnelling microscope (STM),20 self-assembled metal coordination facilitates the formation of homogeneous and extended networks. The interaction of molecules or porous networks with the underlying electronic states has been described by models that consider the molecule as a scattering centre for the surface state electrons.21 In recent work, a pseudopotential model that treats the building blocks as scattering barrier with finite height and width has been used to reproduce the observed quantum well state.15,18 Due to the finite potential barriers, electronic coupling between the quantum well states has been evidenced in periodic networks.19,22 By modifying constituents, different quantum dot arrays can form which exhibit tunable electronic and optical properties. On the a
Laboratory for Synchrotron Radiation – Condensed Matter, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland. E-mail: [email protected] b Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland c Laboratory for Micro- and Nanotechnology, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland. E-mail: [email protected] † Electronic supplementary information (ESI) available: Experimental details, additional STM data and details for data analysis. See DOI: 10.1039/c4cc03941f
This journal is © The Royal Society of Chemistry 2014
other hand, measuring the confinement of the surface state can shed light on the width and the height of the potential barrier.22 There are several factors contributing to the modification of the surface state. Firstly, the interaction between the surface and the adsorbed molecules may shift or quench the surface state in the covered region.23–25 Secondly, the network structure can induce a periodic confinement of the surface state which depends on the lateral size of the pores and on the scattering potential of the molecular barriers.15,18,22,26 These influencing factors have been well demonstrated by angle resolved photoemission spectroscopy (ARPES) and scanning tunnelling spectroscopy (STS) in both real and momentum space on stepped metal surfaces.26–29 However, it is difficult to transpose these combined studies on bare metal substrates to two-dimensional molecular porous networks. Therefore, in the context of molecular networks, there are still open questions concerning the coupling mechanism between the confined quantum dots, and concerning the details of the potential barrier. We use 9,10-dicyanoanthracene (DCA) molecules as building blocks, which have two CN groups bonded to the centre phenyl ring of anthracene. After deposition at room temperature on the Cu(111) surface, the molecules form a regular, porous network (Fig. 1(a)). In the high-resolution STM image we observe that the anthracene backbones point towards the centre of the pores, and that the CN groups are coordinated to Cu adatoms, with reference to earlier work on a similar molecular network.30 The pores exhibit a nearest neighbour distance of 2.08 0.02 nm, which is by one interatomic spacing (0.255 nm) longer than reported earlier.30 Accordingly, we propose a revised adsorption configuration of the molecules as shown in Fig. 1(b). To investigate the effect of confinement on the surface state, dI/dV spectra which are sensitive to the local density of states, have been taken at different positions of the network, as shown in Fig. 1(c). Two features are observed on the spectra: the peak at 0.75 V corresponds to the electronic state derived from a molecular orbital and will be discussed elsewhere; the peak (or shoulder in some of the spectra) at 0.14 V is of highest intensity in the centre of the pore. The dI/dV map obtained at 0.14 V (Fig. 1(d)) reveals a periodic array of high intensity spots with
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Fig. 1 Self-assembled regular structure of DCA on Cu(111) after deposition at room temperature. (a) STM micrograph ( 1.0 V, 100 pA, 20.7 nm 17.4 nm). The arrows mark a domain boundary. Inset: high resolution image ( 0.5 V, 100 pA, 4.6 nm 3.9 nm) measured with a DCA modified tip. A molecular structure model is superimposed. (b) Proposed model of the adsorption configuration with the unit cell highlighted. (c) dI/dV spectra obtained with a metal tip at different locations in the network, as marked in the inset of (a). The dashed black curve was measured on a bare copper region for reference. (d) dI/dV map obtained with a metal tip at 0.14 V (4.6 nm 3.9 nm). The network architecture is superimposed to guide the eyes. The simultaneously obtained STM topography is depicted in Fig. S2, ESI.†
their shape resembling that of the pore. We assign the feature at 0.14 V to a confined surface state derived from the Shockley state of Cu(111). Similar to the concept of a quantum mechanical particle in a box, here the molecules and adatoms play the role of potential walls reflecting and confining the surface state electrons. Scattering of the surface state at the DCA domain border leads to the formation of a standing wave pattern. This suggests that the molecules can act as scattering barriers for the surface state in similarity to step edges.28 While the standing waves on the bare Cu region show the continuum of the surface state band, the confinement inside a pore of the DCA network results in a state which is peaked at a certain momentum and energy (Fig. S3 of the ESI†). The confinement effect of the network can be studied by taking STS above the building blocks: due to imperfect confinement, the confined surface state shows up as a shoulder in the spectra taken above the molecular backbone (red curve in Fig. 1(c)). In contrast, features which could be assigned to the surface state or confined surface state are absent in STS data (Fig. S4(c), ESI†) measured on the close packed DCA assembly. The confined state also shows up at the adatom position but with lower intensity than that at the molecular backbone (Fig. 1(c)). This indicates that the scattering potential is stronger near the adatom due to several possible reasons. Firstly, X-ray Photoelectron Spectroscopy data of the N 1s core level reveal a strong shift by 0.35 eV to a higher binding energy for the adatom-coordinated network with respect to uncoordinated DCA adsorbates. This indicates that negative charge transfer occurs from the molecule to the coordinated adatom.31 Secondly, calculations show that the anthracene backbone is located further away from the surface than the adatom and the CN group.30 In addition to the pores in the interior of regular domains (type C), pores of different size and symmetry are found at
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Fig. 2 Surface state confinement in quantum wells of different size and shape. (a) High resolution STM image taken with a DCA modified tip of the domain boundary region with the proposed assembly structure superimposed ( 0.5 V, 100 pA, 7.5 nm 4.5 nm). (b) STM image ( 1.0 V, 50 pA, 7.0 nm 6.3 nm) of a domain boundary region with different sized pores, which are defined as A and B, respectively. The pores in the domain are labelled C. (c) dI/dV spectra obtained at different locations within the pores marked in (b). The dashed black curve is a reference taken on Cu(111). The onset of the Cu(111) surface state is labelled SS. The spectra show peaks at 0.19 V and 0.17 V for pore A (labelled CSIA and CSIIA), 0.1 V and 0.26 V for pore B (CSIB and CSIIB). The spectrum for pore C is shown for comparison, with its peak labelled CSIC.
domain boundaries (Fig. 2(a)). To compare the confinement effect in the different pores, we also measure STS in two types of pores at domain boundaries (type A and B) shown in Fig. 2(b). Spectra taken at different positions of two typical pores both exhibit two peaks, 0.19 V and 0.17 V for pore A, 0.1 V and 0.26 V for pore B, as shown in Fig. 2(c). We assign the two peaks observed in pore A and B to the first and second eigenstates of the confinement. This can be seen more clearly in the spatial variation of the peak intensity shown in Fig. 3. Close to the first peak position of each pore, the dI/dV map shows a dome-like shape inside the pore (Fig. 3(a–c)), corresponding to the spatial distribution of the first eigenstate. However, the image obtained close to the second peak position of pore A (Fig. 3(d)) shows a donut shape, indicating that the peak corresponds to the second eigenstate. For pore B, the dI/dV image of the second peak (Fig. 3(e)) also shows a donut shape, but only along the long axis direction of the pore due to the elongated shape of the confining region. The spatial extent of the eigenstates observed in different pores is evident from the line profiles in Fig. 3(g–i). The eigenstates shift to higher energy with decreased pore size, as expected for a particle in a box, similar to observations in a covalently bonded network.32 We analyse the confinement in the pores by using the quantum mechanical model of a particle in a two-dimensional box with finite barriers. Accordingly, we expect a discrete series of states inside each pore where energy and momentum (or wave vector) of the eigenstates are defined by the spatial extent of the potential well. Wave vectors are calculated from the reciprocal area of the potential well and a shape factor.33–35 The energy-momentum relation deduced from the analysis of the eigenstates in different pores is plotted in Fig. 4(c). Details of the analysis are shown in Section 7 of ESI.† Since we do not know the effective pore size a priori, we calculate
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Fig. 3 Spatial distribution of the confined states in pores of different size and symmetry. (a–e) dI/dV maps at voltages close to the peak positions shown in Fig. 2. (f) Simultaneously obtained STM image ( 0.5 V, 70 pA, 5.6 nm 5.6 nm). The positions for molecular backbone and adatoms have been superimposed to guide the eyes. Bias voltages and peak labels as defined in Fig. 2 are included. The letters A, B and C indicate the type of pores, and mark the interesting region in the maps. (g–i) Profiles along the lines shown in corresponding dI/dV maps in the upper panels.
wave vectors for two limiting cases: the red data points correspond to the largest possible well size (red outlines in Fig. 4 and Fig. S6, ESI†) where the edges are centred at the molecules; the blue markers are based on a well size (blue outlines in Fig. 4 and Fig. S6, ESI†) closely following the area of the pores in the STM images. Although measured in different pores, the data points nicely follow a freeelectron like parabola which resembles that of the Shockley state (Fig. 4(c)). The effective mass is increased to between 0.47 me and 0.75 me, depending on the definition of the pore boundary, and the band bottom shifts up by 80 meV. We understand this behaviour in the following qualitative picture: the confined states essentially derive from the surface state, modulated by an envelope function induced by the confinement. The envelopes can be approximated by solving the ¨dinger equation of a finite potential well with the shape and Schro dimensions of the blue outlines in Fig. 4(a) (see Section 8 in ESI†). The calculation shows that the energetic position of the observed states is sensitive to the overlap integral of the wave function with the potential barrier in the molecular network. This is similar to the confinement of the surface state on vicinal Cu(111) where the periodic potential of the step array induces the opening of a band gap at the Brillouin zone boundary and a shift of the band bottom which is proportional to the height of the potential barrier.26,36 Similar to the observation of a delocalized state by ARPES,19 we would expect the formation of a periodic band structure also in the present case, with possible band gaps at the high symmetry points X1 and X2 marked in Fig. 4(c). We observe that the confined state extends into the region covered by the molecular backbone (Fig. S3(c), ESI†). However, we believe that our data are not suitable to
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Fig. 4 Effective confinement and E(k) derived from STS spectra taken in pores of different size. (a, b) STM image and structural model of two limiting well sizes for pores A, B and C. (c) Energy dispersion plot of the confined state and quadratic curve fits. Red and blue colours correspond to the large and small well size in (a) and (b). The fits yield an effective mass of 0.47 0.03 me, bottom of the dispersion 0.364 0.027 eV for the large well size, and 0.75 0.03 me, 0.355 0.019 eV for the small well size, respectively. The black dashed curve is the energy dispersion of the surface state of bare Cu(111) with E0 = 0.44 eV, m* = 0.40 me. Two highsymmetry points of the surface Brillouin zone (shown in the inset) are marked by vertical lines. The data points are obtained from five different types of pores including pore A, B and C, which are shown in Fig. S6, ESI.†
analyse such a delocalized state because they were partly measured in irregular pores which are not part of the periodic lattice, and because the uncertainty in the calculation of kJ renders an assignment of electronic bands impossible. In any case, the observed shift of the band bottom of 80 meV represents a probe of the potential inside the pores and of the confining barrier of the molecular network. Such modification can include contributions from the Pauli repulsion between the porous network and the electrons, and charge transfer/ redistribution at the adsorbate–substrate interface.23,37 In conclusion, we have studied the spatial distribution and the energy dispersion of the confined quantum states in a supramolecular porous network. STS data interpreted both in real and reciprocal spaces indicate the modulation of the intrinsic surface state in the confined space of the pores. The energy levels of the confined states depend on the chemical components of the metal– organic network which enclose the pores, making them sensitive probes of the electrostatic potential, or of the energy levels of the frontier orbitals in the confining molecules. This work was supported by the PSI-FELLOW/COFUND program. Partial funding from the Swiss National Science Foundation, the Swiss Nanoscience Institute (among others, grant no. 200020-137917, 206021-113149, 206021-121461), and the Swiss Federal Institute for Materials Testing and Research is gratefully acknowledged. The authors would like to thank the founding partners of the PEARL beamline, in particular P. Aebi, R. Fasel, and T. Greber for scientific and technical advice. We also gratefully acknowledge discussions with F. Baumberger.
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