Electron confinement in chlorine based quantum corrals

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Partially commensurate and incommensurate structures

In most of the systems formation of commensurate structure is followed by further adsorption and compression of halogen monolayer. At this stage the 2D halogen lattice is compressed and a partially commensurate or incommensurate structure is formed. In such kind of lattice the adsorbed atoms occupy different adsorption sites on the surface and part of them are placed in energetically unfavorable sites. Compression continuously increases with surface coverage. There are two different scenarios of compression – uniform compression and nonuniform compression.
In the former case halogen lattice is compressed uniformly as a hole. The density of adsorbed atoms on the surface remains uniform whereas the average interatomic distances decrease. Almost all halogen atoms occupy adsorption sites that are not energetically most favorable. Uniform compression can be either isotropic or uniaxial – see Figure 1.6a. For uniaxial compression a few domains with different direction of compression can be formed, depending on the symmetry of the substrate: three domains on (111) face and two domains on (100) face – see Figure 1.6b. There can be only one domain on the anisotropic (110) face. Scenario of uniform compression is realized in that system where the lateral adsorbate-adsorbate interaction is much stronger than adsorbate-substrate interaction.
A more complex scenario is realized in the systems with comparable lateral and transversal interactions. A nonuniform compression becomes energetically favorable in such case. As opposite to uniform compression a periodic system of domains with commensurate structure is formed. Neighboring domains are separated by a narrow region with increased density of halogen atoms called « heavy domain walls » – see Figure 1.7a. In the case of nonuniform compression most of adsorbed atoms remain in their energetically most favorable positions since commensurate structure is not disturbed inside domains. All compression is concentrated within domain walls where adsorbed atoms have to be arranged denser than in the commensurate structure and occupy different (and energetically less favorable) sites. The number of domain walls continuously increases (on the contrary, the width of domains decreases) with halogen coverage [65].

Cl/Cu(111) system

From previous studies [5,69,74,102] Cl/Cu(111) is known to form ordered and stable structures at room temperature.It has been shown that it forms a (√3×√3)R30° structure on Cu(111) surface at coverage θ = 0.33 ML. According to EXAFS and PED measurements chlorine occupy fcc hollow adsorption site [36,37]. This measurements were confirmed by DFT calculations [47,103]. At higher chlorine coverage θ > 0.33 ML compression of (√3×√3)R30° lattice starts and a domain-wall structure is formed [5,69,74].
The structure of low-coverage chlorine layer (θ < 0.33 ML) and the very first stage of (√3×√3)R30° lattice compression are unknown and still needs experimental study.

Cl/Ag(111) system

This system was studied for the first time by Rovida et al. in 1974 [90] using LEED measurement. Distorted (3×3) diffraction pattern was reported for saturated chlorine monolayer, explained by the authors as a corrosion layer. According to Bowker and Waugh [91] TDS spectra from chlorinated Ag(111) surface consists of two peaks. One of them (760 K) was attributed to monolayer desorption whereas another one (670 K) to silver chloride desorption.
The Ag(111) surface covered by chlorine has been studied by LEED [15,69,90,92,93,91,94], EXAFS [15,31], and room-temperature STM [95]. Besides this, DFT calculations [48,96,97,98] were used to investigate chlorine interaction with silver surface. It was found that at room-temperature adsorption of chlorine a diffuse (√3×√3)R30° LEED pattern is observed first [15,69,91], which is followed by a complex pattern described by different authors as (10×10) [15,69], (17×17) [95] or double-diffraction from epitaxial AgCl(111) layer [93,91]. In fact all the authors observed LEED patterns similar to that reported by Rovida et al. in [90]. Bowker and Waugh [91] desribe two diffraction patterns for almost saturated chlorine layer. The first one (structure ―C‖) contains fractional-order spots 0.28 and 0.72 (in the units of substrate reciprocal lattice vectors) wich is in agreement with data from the study of Rovida et al. [90]. Further chlorine adsorption transform structure ―C‖ to ―D‖ which contains only 0.72 spots. Wu et al. [94] also reported observation of structure ―D‖ for saturated chlorine monolayer. The only STM study [95] of chlorine adsorption on Ag(111) surface was done at room temperature. Poor spatial resolution due to high mobility of chlorine atoms at 300 K made it impossible to determine exact atomic structure of saturated monolayer. The authors had to use FTT transform of STM images to determine periodicity of chlorine layer.
A low-temperature LEED and EXAFS study of Cl/Ag(111) was done by Shard and coworkers [15]. A sharp (√3×√3)R30° LEED pattern was observed for surface temperatures less than 190 K and chlorine coverage = 0.33 ML. For higher chlorine coverage splitting of diffraction spots similar to that in Cl/Cu(111) [74], I/Cu(111) [73,74], I/Ag(111) [58], I/Au(111) [89] systems is reported. For saturated monolayer the authors observed the same LEED pattern as in [90].
To conclude, in spite of rather long study of chlorine adsorption on Ag(111) surface there are still doubts about exact atomic structure of saturated chlorine layer. The structure of compressed (√3×√3)R30° lattice is not determined either. The knowledge of the exact atomic structure in the first stages of Cl adsorption could be therefore of important interest for catalysis. This was one of the motivations of our work.

Scanning tunneling microscopy and spectroscopy

As mentioned above LEED analysis is very often not sufficient to resolve the surface structure and local probe in real space is needed. In this thesis most of the discovered surface structures were therefore decoded with the help of Scanning Tunneling Microscopy. Figure 2.7 shows the block diagram of a scanning tunneling microscope [4, 7, 8]. A sharp metal tip placed on the piezoelectric drive is used to probe the surface. Electrons can tunnel between the surface and STM tip when they are sufficiently close to each other (~ 10 Å). A small bias voltage (from a few millivolts to several volts) between the tip and the surface give rise to the appearance of tunnel current (up to a few nano amps). A high-resolution (up to atomic resolution) map of local electron density can be obtained when scanning the surface with the tip. This requires fulfillment of two conditions: 1) spatial position of the tip has to be controlled with precision less than 0.1 Å; 2) the tip has to be extremely sharp – ideally it should be atomically sharp. The first condition is fulfilled by the use of precise piezoelectric drivers for tip movement together with efficient vibro  technical problem that was studied before [9, 10]. In our work we often saved time by using PtIr tips simply cut in air. Then the tips were prepared in situ inside STM by using voltage pulses (10 volts for few seconds) and/or gentle contact with a metallic surface (see Section 2.6). One has to note that this procedure was especially reliable for low temperature measurements as the tip apex is much more stable than at room temperature even when covered by gold cluster.
The tunneling process can be described from Figure 2.8 which illustrates the energy diagram between the tip and the surface. Electron density of states (DOS) on the tip is shown on the left of diagram. For simplicity tip DOS is supposed to be featureless. A bias voltage V is applied to the sample relative to the grounded tip (as in case of Omicron LT STM). The DOS of the sample surface is shown on the right of diagram. All the states below Fermi level are marked in red. The tunnel current is generated by electrons passing the tunnel barrier from the left to the right.
In the s-wave function approximation at T = 0 and for small bias voltage (Tersoff-Hamann approximation) the tunnel current It is proportional to the number of electrons tunneling through the barrier between 0 and applied voltage V: eVIts (E)t (E eV )T (E,eV , z)dE (2.9).

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Basics of density functional theory

On the base of experimental data structural models for the surfaces modified by chlorine action where proposed. DFT calculations were used to test them and discriminate eventually between several possible ones.
Density functional theory is one of the most powerful approaches for theoretical study of systems with large number of atoms [16, 17, 18].
The main concept of this theory consists in the following: all the properties of a many body system in a ground state are uniquely determined by the spatial distribution of its electron density [17]. This statement can be proved mathematically and is known as the first Hohenberg-Kohn theorem. In the usual quantum-mechanical description the N-particle system state is set by 3N independent variables. The Hohenberg-Kohn approach reduces the number of independent variables down to only 3 spatial coordinates of electron density function n(x,y,z).
The energy of the system (together with its other properties) is a functional of electron density n(x,y,z). The energy functional reaches its minimum for those n(x,y,z) which corresponds to the ground state of the system. This is the second Hohenberg-Kohn theorem [17].
DFT approach is usually used together with Kohn-Sham formalism. Within the framework of Kohn-Sham formalism the intractable many-body problem of interacting electrons in the external potential of atomic nuclei is reduced to a tractable problem of non-interacting electrons moving in an effective potential. This effective potential includes both static potential of atoms and interaction between all the electrons. The total energy of the system can be written as: [] [] [] [] (2.12).
where T[n] is the kinetic energy of electrons, U[n] – potential energy of electrons in static potential of atomic nuclei and V[n] is the effective potential of electron-electron interaction. Here every term is the functional of electron density n(x,y,z).
Let us suppose that n(x,y,z) depends on a certain parameter a. It can be, for example, lattice parameter of a crystal or the angle between two chemical bonds in a molecule. We can minimize functional E[n] by varying parameter a and calculating each time the new value of the energy. Corresponding value amin = a0 is the equilibrium lattice constant or angle between chemical bonds and Emin[n] = E0 is the total energy of the system in the ground state.
However in practice another approach instead of minimization the functional E[n] is used. The ground state problem of a many-body system can be reduced to the solution of a single particle Schrödinger equation [17]: * ( )+ ( ) ( ) (2.13).

Low surface coverage (θ < 0.33 ML)

Figure 3.3 shows an STM image of Au(111) surface after adsorption of a small amount of Cl at 300 K. One can see that chlorine atoms first tend to decorate atomic steps. This observation conform results of DFT calculations by Liu et al. [8] that showed significant increase of adsorption energy for chlorine atoms on the step edge compared to flat terrace.
Along this single chlorine atoms can be seen on terrace (Figure 3.3). They are imaged in STM as protrusions. Most of adsorbed atoms are randomly distributed over the surface and are separated by large (> 7 Å) distances from each other. Few of the adsorbed atoms form pairs with smaller interatomic distance. Surprisingly even at such extra-low surface coverage formation of Figure 3.3. STM image (277×275 Å2; It = 1 nA; Us = –780 mV, T = 5 K) of Ag(111) surface covered with 0.02 ML of chlorine. Chlorine atoms decorating atomic step can be clearly seen. (I) – single Cl atoms, (II) – dimers of Cl atoms, (III) –chains-trimers of Cl atoms,r: Figure 3.4. STM images (330×330 Å2; It = 1 nA; Us = –780 mV, T = 5 K, treatment was used) demonstrating: (a–f) formation of chains from Cl atoms; (g–i) nucleation of a 2D commensurate (√3×√3)R30° structure atomic chains is observed. The nearest-neighbor distances in such chains are 4.4-4.5 Å. The tendency to form chains becomes more evident at higher coverage. A series of STM images of Ag(111) surface during continuous increase of surface chlorine coverage in the range 0.03-0.31 ML is shown on Figure 3.4. The images were treated to make clearer the distribution of chlorine atoms over the surface. As one can see chlorine atoms tend to form single-atom chains. The density of chains increases together with chlorine coverage but adsorbed atoms avoid formation of island with compact structure.
It can be clearly seen from Figure 3.4 that commensurate (√3×√3)R30° structure starts to form on the surface when chlorine coverage approaches 0.33 ML, which is in agreement with our LEED data and results of previous study [6]. According to [6] this structure is formed at surface temperatures less than 190 K. Table 3.1 contains results of DFT calculations of adsorption energy for chlorine atoms on Ag(111) surface. The calculations were done for surface coverage 0.33 ML, with chlorine atoms forming (√3×√3)R30° structure. An fcc three-fold hollow site is energetically most favorable, followed by hcp hollow site which has 10 meV lower adsorption energy.

Table of contents :

1. Halogen interaction with metal surfaces: bibliographic review
1.1 General considerations
1.2 Monolayer of chemisorbed halogen atoms
1.2.1 Halogen-substrate interaction
1.2.2 Halogen-halogen lateral interaction
1.2.3 Disordered phase: θ < 0.2 – 0.4 ML
1.2.4 Commensurate structures
1.2.5 Partially commensurate and incommensurate structures
1.2.6 Saturated monolayer structure
1.2.7 Surface reconstruction
1.3 The subject of this thesis
1.3.1 Cl/Cu(111) system
1.3.2 Cl/Ag(111) system
1.3.3 Cl/Au(111) system
1.4 Conclusion
2. Experimental and theoretical methods used in present study
2.1 Introduction
2.2 Experimental setup
Chlorine inlet system
2.3 Preparation of clean metal surfaces
2.4 Low-energy electron diffraction
Splitting of diffraction spots
2.5 Scanning tunneling microscopy and spectroscopy
Scanning tunneling spectroscopy
2.6 Experimental procedure
2.7 Basics of density functional theory
2.9 DFT calculations procedure
3. Ag(111) surface under molecular chlorine action
3.1 General description of the system
3.2 Low surface coverage (θ < 0.33 ML)
3.3 Compression of commensurate (√3×√3)R30° structure (0.33<θ<0.42ML)
3.4 The (3×3) structure
3.5 Saturated chlorine layer: Ag3Cl7 clusters
3.6 Conclusion
4. Au(111) surface under molecular chlorine action
4.1 Low coverage (from 0 to 0.33 ML)
4.1.1 Preferential adsorption and atomic chain formation
4.1.2 Removal of the reconstruction
4.1.3 Quasi hexagonal lattice of nano pores
4.1.4 Thermal stability of nano porous lattice
4.2 Honeycomb structure formation (θ > 0.33 ML)
4.2.1 AuCl2 and (AuCl2)2 nucleation on the Au(111) surface
4.2.2 Pseudo honeycomb lattice
4.3 Conclusion
5. Comparison of the structural phase transitions on (111) face of Cu, Ag and Au under chlorine action
5.1 Cu(111) surface under molecular chlorine action
5.1.1 Introduction – LEED data
5.1.2 Appearance of the commensurate structure (θ <0.33 ML)
5.1.3 Compression of commensurate lattice (θ > 0.33 ML)
5.2 Comparison of structural phase transitions on (111) face of Cu, Ag and
Au under chlorine action
5.3 Conclusion
6. Electron confinement in chlorine based quantum corrals
6.1 Scientific background on surface electron confinement
6.1.1 Surface states
6.1.2 Scattering of surface states by impurities and surface defects
6.1.3 Quantum corrals
i) Fabrication of quantum corrals
ii) Understanding the standing-wave pattern
6.1.4 Scattering of bulk electrons by the surface structures
6.2 Spectral properties of Cl based quantum corrals
6.2.1 Evidence of electron confinement
6.2.2 Local spectroscopy on quantum corrals
A. measurement of quantized states in Cl nano pores
B: Size and shape effects on quantized states inside the pores
C: Failure of the « particle in a box model »
6.3 Conclusion
Bibliography 

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