Quantum Confinement of Hot Image-Potential State Electrons

Schouteden, Koen; Haesendonck, Chris Van

doi:10.1103/physrevlett.103.266805

Cited by 30 publications

(37 citation statements)

References 20 publications

(34 reference statements)

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“…High spatial resolution of an image potential state was achieved by scanning tunneling spectroscopy (STS) [9,10] . The shifts are consistent with a lateral confinement of the electrons as described by textbook (two-dimensional) particle-in-a-box models [14]. Such an assignment assumes atomically flat islands with perfect coordination, though a relation to potential relaxation or reconstruction of the latter has not been made so far [16].…”

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confidence: 71%

“…For this method submolecular resolution was presented only recently [13], but the method has not yet been applied to nanoclusters. On the other hand, STS investigations of such structures yielded significant shifts of the energetic position of image potential states over the nanoislands [14], as well as a quantization due to stacking faults [15]. The shifts are consistent with a lateral confinement of the electrons as described by textbook (two-dimensional) particle-in-a-box models [14].…”

supporting

confidence: 59%

“…On the other hand, STS investigations of such structures yielded significant shifts of the energetic position of image potential states over the nanoislands [14], as well as a quantization due to stacking faults [15]. The shifts are consistent with a lateral confinement of the electrons as described by textbook (two-dimensional) particle-in-a-box models [14]. Such an assignment assumes atomically flat islands with perfect coordination, though a relation to potential relaxation or reconstruction of the latter has not been made so far [16].…”

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Quantitative determination of a nano-object's atom density without atomic resolution

et al. 2014

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We outline a possibility to determine the adatom density of individual nano-objects via measurement of their electronic structure. For this aim, the nonlinear shift of image potential states measured on individual Cu nanoclusters on Ag(100) by low-temperature scanning tunneling spectroscopy is carefully analyzed. The quantitative analysis is confirmed by density-functional theory calculations. A peak width analysis furthermore reveals whether the clusters are purely metallic or alloyed. For nanotechnology a structural control on the nanoscale is essential, because the physical as well as chemical properties of nanoscale objects depend on the exact arrangement of their atoms [1]. As a first step, it is of vital importance for scientists and engineers to resolve the internal structure of the nanosystems to understand and, in a subsequent step, tune the resulting macroscopic properties. The atomic structure of nanoparticles can be determined directly by scanning transmission microscopy (STEM) with high resolution down to 50 pm [2], which shows a two-dimensional projection of the crystal in some high-index direction of particles. With STEM, nanoparticles were imaged three dimensionally [3]. Even single defects within nanoparticles were identified recently [4]. Due to the width of the electron beam, the extraction of the data demands sophisticated procedures.For two-dimensional nanoparticles on surfaces, scanning tunneling microscopy (STM) turned out to be a simple and versatile tool for high resolution imaging. However, atomic resolution is often impossible for discrete entities consisting of only a few atoms, in particular for nanoclusters. These objects have the tendency to be moved or restructured at the tunneling parameters necessary for atomic resolution. On the other hand, structural information of a metal surface is clearly reflected in the energetic positions of its image potential states [5,6]. A Rydberg-like series of these states emerges, when an outside charge polarizes a metal surface and is attracted to the induced polarization charge. As the energy levels of these states are pinned to the vacuum level, they are closely related to the work function, which in turn varies with both the chemical composition of the surface and the surface orientation, and thus with atom density. Surface averaged values of energy, dispersion (and lifetime) of image potential states were extensively probed, first by inverse photoemission (IPES) [7] and later by two-photon photoemission spectroscopy (2PPE) [8]. High spatial resolution of an image potential state was achieved by scanning tunneling spectroscopy (STS) [9,10] . The shifts are consistent with a lateral confinement of the electrons as described by textbook (two-dimensional) particle-in-a-box models [14]. Such an assignment assumes atomically flat islands with perfect coordination, though a relation to potential relaxation or reconstruction of the latter has not been made so far [16]. In this article, we present a method for the analysis of metallic nanostructures ...

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confidence: 59%

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confidence: 99%

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Quantitative determination of a nano-object's atom density without atomic resolution

et al. 2014

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“…1 Nowadays, structures allowing confinement in three dimensions (3D) (quantum corrals, [2][3][4] adatom and vacancy islands, [5][6][7][8][9] and self-organized molecular structures 10 ) and two dimensions (2D) (atomic chains, [11][12][13] and ad-molecule stripes 14 ) have been designed and studied. Many of the above systems are accessible only owing to the scanning tunneling microscopy (STM).…”

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confidence: 99%

Theoretical study of constant current scanning tunneling spectroscopy in Pb overlayers

et al. 2011

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We present a theoretical study of the constant current scanning tunneling spectroscopy of quantum well states localized in Pb(111) overlayers on Cu(111) surfaces. The distance-voltage characteristic of the tunneling junction is obtained with a mixed approach. The wave packet propagation technique is applied to describe electron tunneling from the tip into the sample, and the density functional calculations provide the necessary inputs for the one-dimensional model potential representation of the system. The excited-state population decay mechanisms via inelastic electron-electron and electron-phonon interactions are taken into account with a bias-dependent absorbing potential introduced in the metal. Our results are in good agreement with recent experimental studies [Phys. Rev. Lett. 102, 196102 (2009), Phys. Rev. B 81, 205438 (2010)] over the energy range where the free-electron description of the Pb overlayer used here applies. We find that at high bias the quantum well states experience a Stark energy shift and partially acquire a character of field emission resonances. The present model study also sheds light at the experimentally observed departure of the energies of the quantum well states from the particle-in-a-box prediction for the bias above 4 eV. The measured trend can be consistently explained as due to the departure of the realistic Pb band structure in the -L direction from free-electron parabola when the electron momentum approaches the point.

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“…In this case, the atomic structure of the islands is unclear, the size cannot be varied, and the clusters are not entirely stable during the measurement. An intriguing feature is the coupling between the IPSs on neighboring nanostructures to molecule-like states [3,6,13].IPSs on graphene (gr) are of special interest: On fundamental grounds, they share a common origin with specific states of related materials [14] as the interlayer state of graphite, or superatomic states of fullerenes [13]. As a consequence of graphene's 2D-character a splitting of the IPSs into Ψ (n + ) and Ψ (n − ) has been predicted for freestanding [14] and observed for epitaxial graphene weakly coupled to SiC [15, 16].…”

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Mapping Image Potential States on Graphene Quantum Dots

et al. 2013

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Free electron like image potential states are observed in scanning tunneling spectroscopy on graphene quantum dots on Ir(111) acting as potential wells. The spectrum strongly depends on the size of the nanostructure as well as on the spatial position on top, indicating lateral confinement. Analysis of the substructure of the first state by spatial mapping of constant energy local density of states reveals characteristic patterns of confined states. The most pronounced state is not the ground state, but an excited state with a favorable combination of local density of states and parallel momentum transfer in the tunneling process. Chemical gating tunes the confining potential by changing the local workfunction. Our experimental determination of this workfunction allows to deduce the associated shift of the Dirac point.PACS numbers: 73.63.Hs, 73.22.Pr, Confinement of electrons in nanostructures leads to quantum size effects as a size-dependent electronic structure and atom-like states (characterized by a set of quantum numbers). Recently, first experiments regarding the confinement of image potential states (IPSs) using the spatial resolution of the scanning tunneling microscope (STM) have been performed [1-6], transcending pioneering studies based on two photon photoemission (2PPE) [7,8]. IPSs are unoccupied states in an attractive image charge Coulomb potential between the Fermi level E F and the vacuum level E F + Φ given by the local work function Φ. Perpendicular to the surface they feature a hydrogen-like spectrum (characterized by a quantum number n) which converges to E F + Φ [9], parallel to it a two dimensional electron gas (2DEG) forms with a continuous distribution of parallel momentum k for the case of extended systems. The resulting states can be labeled Ψ (n) (k) with energies E (n) (k). In STM, IPSs appear as peaks in the local density of states (LDOS) measured while retracting the tip from the surface. As they are Stark-shifted due to the electric field between tip and sample [10] they are often referred to as field emission resonances (FERs).Confinement effects for IPSs can be induced by nanostructures fulfilling four conditions: (i) the corresponding potential well must have a sufficient depth of ∆Φ = Φ out − Φ in [2], a large ∆Φ provides strong confinement; (ii) a well-defined shape; (iii) an established preparation that allows to adjust the size in a wide range; (iv) stability under the high STM bias voltage U . Whereas previous work provides fascinating first insights into quantum size effects for IPSs, no study yet matches all four conditions: In [3] a first hint at a size dependence of the energies of IPSs confined to Co islands on Au(111) is visible, however here the size variation was less than an order of magnitude. Atom-like patterns have been observed above stacking-fault tetrahedra on Ag(111) [5], still ∆Φ is so small that the resulting weak confinement only acts on the IPSs lowest in energy. The system NaCl on metal is promising as it shows a large ∆Φ. However, up to now there is no...

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Quantum Confinement of Hot Image-Potential State Electrons

Cited by 30 publications

References 20 publications

Quantitative determination of a nano-object's atom density without atomic resolution

Quantitative determination of a nano-object's atom density without atomic resolution

Theoretical study of constant current scanning tunneling spectroscopy in Pb overlayers

Mapping Image Potential States on Graphene Quantum Dots

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