Time-resolved photoelectron spectroscopy of mass-selected metal-water clusters

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Time-resolved photoelectron spectroscopy of mass-selected metal-water clusters

Dissertation

zur Erlangung des akademischen Grades Doktor der Naturwissenschaften (Dr. rer. nat.)

durchgeführt an der Universität Konstanz Mathematisch-Naturwissenschaftliche Sektion

Fachbereich Physik

vorgelegt von

Christian Braun

Tag der mündlichen Prüfung: 27. September 2012 Referent: Prof. Dr. Gerd Ganteför

Referent: Prof. Dr. Paul Leiderer

Konstanzer Online-Publikations-System (KOPS) URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-206201

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Zusammenfassung

Die Forschung an massenseparierten Metallclustern hat bereits viele interessante und neuartige Eigenschaften dieser Nanopartikel offenbart, die durch ihre speziellen geo- metrischen und elektronischen Strukturen erklärt werden können. Der praktische Einsatz dieser neuen Sparte der Nanotechnologie gestaltet sich jedoch schwierig, da diese Cluster bis jetzt nicht im präparativen Maßstab hergestellt werden kön- nen. Speziell im Bereich der Photovoltaik und der photochemischen Wasserspaltung könnten Nanostrukturen und Cluster einen wichtigen Beitrag zur Grundlagenfor- schung liefern. Dafür ist die Kenntnis der Dynamik nach Anregung durch Photonen in diesen Nanopartikeln von entscheidender Bedeutung.

Die hier vorgestellte Arbeit behandelt die Untersuchung der Dynamik von kleinen Metallclustern in der Gasphase an welchen Wassermoleküle adsorbiert sind.

Damit sollen die grundsätzlichen Abläufe nach der Anregung durch ein Photon untersucht werden und der initiale Schritt der Wasserspaltung analysiert werden. Dies könnte hilfreich sein um neuartige Photokatalysatoren für die Wasserspaltung zu finden.

Hergestellt werden die Cluster mit einer PACIS (engl. Pulsed Arc Cluster Ion Source). Mithilfe eines Massenspektrometers werden die Cluster nach der Mas- se getrennt. Die Grundzustände der erzeugten Cluster werden mit Photoelektronen Spektroskopie (PES) untersucht, was die Grundlage für die weiteren Untersuchungen darstellt. Die zeitaufgelöste PES ermöglicht einen Zugang zur Dynamik massense- lektierter Cluster in der Gasphase durch eine Pump-Probe Methode.

Verschiedene Metallwassercluster wurden untersucht. An Silberhydroxid mit adsorbierten Wassermolekülen wurden langlebige angeregte Zustände gefunden, was eine Grundvoraussetzung für die photochemische Wasserspaltung ist. Anhand des Systems Au^-(H2O)m wurde ein Vergleich mit dem Model für die Wasserspaltung an Halbleiterpartikeln gemacht; was gezeigt hat, dass thermodynamische und ki- netische Voraussetzungen für die Wasserspaltung näherungsweise erfüllt sind. Am System Au3-(H2O)mdeuten zeitaufgelöste PES Messungen darauf hin, dass die Was- serspaltung realisiert wurde. Zur Untermauerung dieser Ergebnisse werden zur Zeit noch zeitabhängige Dichtefunktionalberechnungen durchgeführt.

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1 Introduction

The development and success of our society is based on the availability of energy.

Without large amounts of readily accessible and cheap energy, the high standard of living we are enjoying today would be impossible. From agriculture to manu- facturing, from transportation of goods to human travel, from telephone to online information; none of these would be possible without a steady supply of energy.

Thus our everyday way of life is unimaginable without it.

In the highly developed countries, the consumption of energy is only slowly increasing [1]. This is explained by the fact that the whole society already has a high standard of living and the increase of energy needs is further reduced by the employment of new energy-efficient technologies. In countries with enormous popu- lations, like China and India for instance, the standard of living for most inhabitants is moderate. However, the current development of these countries is leading to a higher standard of living, which in turn requires a large increase of available energy [1].

Most of the consumed energy is produced by burning fossil fuels, like coal, crude oil and natural gas. The two major problems of these energy carriers are the release of enormous amounts of CO2, which has negative effect on the Earth’s climate, and the limitations of the fossil fuel supplies. Predictions show that oil reserves will run out within the next century [2]. The increase of energy consumption in the developing countries could deplete fossil fuel reserves even faster then predicted. Shortages in the supply of energy would increase the price dramatically and threaten our way of life. Therefore, reliable and clean energy sources have to be found.

Fossil fuels are sources of stored energy from the sun, which has been collected by plants via photosynthesis over millions of years. The total amount of energy stored in all fossil resources corresponds to the solar energy received in just 7 days [3]. The current annual energy consumption of the world is only 0.01 % of the annual energy provided by the sun [3]. Thus, the focus of current research is on directly harvesting the energy provided by the sun.

Various methods exist to convert the energy provided by the sun into applicable

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However, the production of hydrogen and oxygen out of water still demands the consumption of high amounts of energy. Therefore, new methods to produce hydrogen and oxygen directly from sunlight are desirable, which would facilitate the so-called hydrogen economy [5]. In this economy, the energy carrier is basically water, which can be split into hydrogen and oxygen via sunlight for storing energy. This energy can be released when needed by employing fuel cells to convert it into electrical energy and water. The main advantages of this energy carrier are its cleanliness and that the energy supply is basically unlimited. However, a major problem is based on todays poor hydrogen storage materials, [6]. One way to circumvent this problem could be the use of methanol instead of hydrogen, which constitutes the idea of the methanol economy [6]. The production of methanol from atmospheric CO2and hydrogen is possible with the application of suitable photocatalysts[7]. The advantages are the large availability of CO2 and the fact that the energy is stored in a convenient liquid fuel. The greatest obstacle for these two economies is, however, the development of the photocatalysts for generating hydrogen and methanol.

The current method for producing hydrogen from water with sunlight is to use a photochemical cell. Fujishima and Honda discovered the photocatalytic activity of TiO2 in 1971 [8, 9]. Since then, over 130 materials have been employed in the photochemical splitting of water [10]. These photocatalysts are semiconductors and their electronic band structure is used for creating a situation where the reduction and oxidation of water to produce H2 and O2 is possible. The photon absorbed by the photocatalyst produces an electron-hole pair, where the electron in the conduc- tion band serves as a reducer to produce H2 and the hole serves as an oxidatizer to produce O2 [11]. Achieving overall water splitting requires an energy gap of at least 1.23 eV [11], which would theoretically allow the harvesting of almost all photons provided by the sun. The current problems of the photochemical water dissociation are that the materials for these catalysts are expensive, show insufficient light absorption [12] and inefficient charge transfer [13].

A new approach to tackle these problems is to employ nanotechnology meth-

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ods; one example of which is to use small metal clusters as novel photocatalysts, as will be described in this thesis. Clusters are the agglomeration of a certain number of atoms, ranging from two to thousands. The main idea of this approach is that the metal cluster serves as an antenna for efficient absorption of light (photons) and allows, due to its size, for a fast and efficient transfer of the energy for dissociation directly to the adsorbed water molecule.

The properties of clusters are governed by the geometrical and electronic structure and can differ strongly from atoms and bulk materials. The starting point for the systematic investigation of clusters can be seen as the discovery of the geometric and electronic magic clusters [14, 15]. In the beginning of the research on clusters, the main experimental tools to obtain information about the properties in the gas phase were mass spectrometry and photoelectron spectroscopy (PES) [16]. The comparison with sophisticated calculations was invaluable to obtain an insight into the electronic and geometrical structures. The deposition of clusters on surfaces enabled chemical investigation of the catalytic activity [17, 18] and direct access to the geometric structure with scanning tunneling microscopy (STM) [19, 20]. The- ory and experiment went hand in hand to discover the properties of clusters. In the size regime of small clusters (2 ≤ n ≤ 100) each atom counts since the properties may change considerably when adding one atom to a clusters[21]. This is, e.g., the case for metal clusters, which become semiconducting for a small number of atoms [22, 23]. A further example that cluster size matters has been found for the chemical reactivity of small gold and silver clusters, which was found to be strongly size-dependent [24–26]. One of the most unexpected discoveries was the catalytic activity of deposited gold clusters [27–31].

Investigations of the relaxation dynamics of clusters became possible with the advent of ultrafast lasers. In a pump-probe scheme, the relaxation dynamics after excitation with one photon became experimentally accessible. Ahmed H. Zewail and his group have been the first the employ femtosecond lasers for the investigation of chemical bonds in molecules. Their research developed the field of femtochemistry [32, 33] and has been honored with a Nobel prize for chemistry in 1999. The most important method in this field is time-resolved photoelectron spectroscopy (TR- PES). This method allows direct access to changes of the electronic structure in the cluster during the relaxation process or triggered chemical reaction.

In this work, TRPES is employed to investigate mass selected metal-water clusters in the gas phase in order to follow the excited states and screen the spectra for evidence of photodissociation of water molecules. The results of this research could be used as a model system for studying the dissociation process facilitated

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results are summarized and also an outlook on future experiments possible with the current experimental setup is included.

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2 Basic Concepts

In this chapter the basic theoretical concepts for interpretation of the experimental results are introduced. In the first section, fundamental considerations about metal clusters are presented, where the shell model for spherical and distorted clusters is introduced. In the following section, photoelectron spectroscopy (PES) is discussed by employing the single particle picture and the quantum mechanical model.

PES is one of the most important experimental tools for the investigation of clusters. In this work the applied experimental method is time-resolved photoelectron spectroscopy (TRPES). TRPES is a tool that allows direct access to the cluster dynamics, considered in subsection 2.2.3. The different processes that are possible after photoexcitation of a cluster are discussed in the last section.

As mentioned in chapter 1, clusters connect the physics of atoms to the physics of bulk materials. In this intermediary region the properties of the cluster do not scale linearly with size; instead, strong and nonmonotonous changes are observed [34]. In some cases even novel properties are found, as is the case of deposited gold nanoparticles showing catalytic activity. This behavior is unexpected, since gold is the most inert metal. In the initial investigations it was believed that moderate sized gold nanoparticles were responsible for catalytic activity. However, more detailed experiments revealed that even smaller gold clusters actually exhibit the catalytic activity [35]. In order to understand these properties of nanoparticles and clusters much theoretical and experimental work has been undertaken over the last 4 decades.

These two branches often went hand in hand to deepen the understanding of the properties of nanoparticles and clusters.

Classification of clusters is best performed by considering the material they are made of, as the material dictates the interaction between the atoms (or molecules) of a cluster. It can be realized as follows:

• noble gas:

The interaction that hold these clusters together is the Van der Waals force.

• metal:

Metallic bonding is the main interaction that governs the properties in these clusters.

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experimental method exists that allows direct access. Information about the cluster structure can be obtained by comparing experimental results of mass spectrometry and photoelectron spectroscopy (PES) to theoretical calculations. The most simple case for understanding the geometrical structure of a cluster is found in noble gas clusters, as the interaction is weak and only nearest neighbors interact. According to the Rule of Friedel [36], the structure that exhibits the most nearest neighbor interactions has the highest binding energy. This situation is found for the icosahedron structure, which is presented in its smallest sizes in figure 2.1.

Figure 2.1: Examples of icosahedron structures, for which the binding energy of a noble gas cluster is maximized. (Taken from [37].)

In these structures, the atoms organize themselves in closed layers called geometric shells. This configuration restricts the amount of atoms constituting the clusters to certain numbers (13, 55, 147, 309, 561, ... from left to right in the figure 2.1). These clusters are called geometric magic clusters, as they exhibit high binding energy and thus high stability. In mass spectra of Krypton and Argon clusters, the most abundant cluster sizes are found to be exactly these magic clusters [36].

This confirms the high stability of these clusters under the drastic conditions during cluster formation in the cluster source.

Additionally, there are further cluster sizes with pronounced peak intensities in mass spectra of noble gas clusters. Which can be explained by the filling of sub shells, where the cluster exhibits an elevated binding energy as well.

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2.1 Metal Clusters

The geometrical structure of metal clusters cannot be understood quite as easily as for the noble gas cluster. The interaction within the clusters is governed by the loosely bound valence electrons of the atoms constituting the cluster. Therefore, the electronic structure within the cluster has to be well known in order to understand the geometrical structure.

The electronic structure of an atom is well understood and it can be described by discrete electronic states that arise from the Coulomb potential of the protons in the core. These electronic states are filled up with the electrons under consideration of Pauli’s exclusion principle. In bulk metals, the electronic structure is very different as compared to the electronic structure of the atom. The periodic structure of the atoms in the bulk metal results in the convergence of the electronic states into a band structure. This change in electronic structure from atom to bulk is illustrated for aluminum in figure 2.2.

Figure 2.2: The evolution of the electronic states of aluminum in dependence as a function of the number of atoms arranged together. In the single atom case, there are two distinct states for the 3s and 3p electrons. If more atoms are put together the states split up until a band of states is reached in the bulk. EB is the binding energy and EF the fermi energy. (Taken from [38].)

In solid state physics, a very successful model to describe metals is the Som- merfeld model. In this model, the quasi-free valence electrons are described as an electron gas distributed over the whole bulk and the ion cores are substituted by a uniform positive potential. This type of model is called Jellium model and is very successful in describing the properties of bulk materials in solid state physics. Thus it is not surprising this model gives reasonable results for clusters as well.

Clusters can neither be simply described by the electronic structure of an

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from ion cores is assumed to be smeared out over the whole cluster, similar to the Jellium model in solid state physics.

The density of atoms in a cluster is constant in the center and drops quit fast to zero at the edge of the cluster. This density distribution is similar to the density distribution in the nucleus of atoms and thus the same potential can be employed to approximate the potential of the ion cores. This is the case of the Wood-Saxon potential, whose shape is between the harmonic potential and the square potential.

The calculation of the electronic states in a spherical symmetric cluster requires the solution of the three-dimensional single-particle Schrödinger equation with the Woods-Saxon potential. The resulting electronic states are subsequently filled with the available number of valence electrons, similar to the filling of shells in nuclear or atomic physics.

The electronic states calculated for the harmonic, Woods-Saxon and square potential are presented in figure 2.3. The shell number for the harmonic oscillator (n) and the shell number (ν) and the angular momentum (l) for the Wood-Saxon and Square-Well potential are indicated on the left and right side of the figure, respectively. The number above the energy levels indicates how many electrons can populate this particular state. Note that the quantum numbers describing the electronic states in cluster physics follow the convention in nuclear physics.

The reason is that the potential in the atomic shell model is point like and in nuclear physics and cluster physics the potential has a non-negligible size. A set of energetically degenerated states is called shell, similar to the shells in the atom and the nucleus. Clusters with a completely filled electronic shell are particularly stable and are therefore said to have a magic number of electrons, similar to the convention of the geometric magic number. In case of a filled geometric and electronic shell, the cluster is called doubly magic. The electronic shell closing was verified by various experiments; as an example, in the mass spectrum of sodium clusters the magic numbers have been confirmed [15].

In the consideration of the electronic states in a cluster mentioned above, the

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2.1 Metal Clusters

Figure 2.3: The energetic level structure as calculated for the harmonic potential (left), the Woods-Saxon potential (middle) and the square well potential (right) are given. On the left, the shell number (n) for the harmonic potential is provided and on the right the shell number (ν) and the angular momentum (l) of the states in the Wood-Saxon and square well potential are provided. The numbers above the levels indicate the number of electrons that can populate the level. (Taken from reference [39].)

electron-electron interaction has been neglected. A more accurate method for describing clusters is the self-consistent Jellium model, which is similar to the Hatree- Fock method in atomic physics. In this method, the interaction of electrons is included in an effective potential of the ion cores. The starting point in this model is to assume a reasonable potential. The three-dimensional single-particle Schrödinger equation is then solved for this initial potential. The resulting electronic level structure is used to calculate a new effective potential. In case that this new effective potential is identical to the initial one, the best potential is found. If the new effective potential is different to the initial potential, the Schrödinger equation is solved with the newly generated effective potential until these potentials are identical. The results of calculations for the sodium 40 cluster are presented in figure 2.4. The effective potential for this cluster is similar to the Wood-Saxon potential and the number of electrons in one shell is the same as in the case of the Wood-Saxon potential (see

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Figure 2.4: This level scheme was obtained from self-consistent Jellium calculations.

The shape of the potential is similar to the Woods-Saxon potential and the level scheme has the same distribution of states, however the energy differences between the states are different. (Taken from [38].)

2.1.2 Clemenger-Nilsson Shell Model

In the shell model presented in the previous subsection, the clusters were assumed to be spherical. This, however, is only true for clusters with completely filled shells.

Since a cluster can maximize the binding energy by deformation, the spherical symmetry is lost. This is expressed by the Jan-Teller Theorem [40] for clusters.

Clemenger was the first to incorporate deformed potentials in the calculation of the electronic states of clusters with half-filled shells [41]. For this purpose, he adapted the Nilsson model of nuclear physics [42], which was broadly used to estimate the shape and level structure of distorted nuclei.

In the Clemenger-Nilsson model, the potentials for calculating the electronic states are different for the three dimensions. The cluster is treated like an ellipsoid, where the volume is kept constant when going from a sphere to an ellipsoid.

The model is simplified by constraining the shapes to spheroids. In spheroids, the dimensions of two axis are the same (R_x =R_y), where R is the semi-axis of the ellipsoid. The distortion from the spherical symmetry is expressed with the distortion parameter η= 2^R_R^z_z^−R_+R^x_x.

The procedure for calculating the electronic states in the case of a spheroid is the same as for the shell model in the previous subsection. The shell model for spherical clusters predicts more stable clusters for closed electronic shells. In addition to that, the Clemenger-Nilsson shell model predicts stable clusters for the

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2.1 Metal Clusters closing of sub-shells. Evidence of this fact can be seen as a fine structure in the distribution of the abundance of the cluster sizes in mass spectra, e.g. for sodium clusters [15].

Figure 2.5 (a) presents the shapes of the electronic states as predicted by the Clemenger-Nilsson model. These shapes are compared to more accurate calculations using an ab initio quantum-chemical method, presented in figure 2.5 (b). The change in geometry from prolate to oblate as predicted by the Clemenger-Nilsson model is also observed in the more accurate geometric structures obtained from the quantum- chemical calculations.

Figure 2.5: In (a) the electronic structure of small clusters as proposed by the Clemenger-Nilsson model is presented. (b) shows the structures deduced by ab initio quantum-chemical calculations. In this accurate description of the cluster the transition from prolate to oblate structures is also found, which provides further credibility for the results of the simple model. (Taken from [39].)

The Clemenger-Nilsson diagram readily provides access to single particle energy levels of clusters with differently filled electronic shells. This diagram is presented in figure 2.6, where the energy levels are displayed as a function of the distortion parameter η. The minimal total energy of a cluster with a certain number of electrons is represented by an open circle in the diagram. The level structure is obtained by drawing a vertical line through the open dot with the desired number of electrons. The intersections of the vertical line with the lines of the level position provide the electronic level structure. The level structure for closed shell clusters is included in the Clemenger-Nilsson diagram, where the distortion parameter is zero.

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Figure 2.6: In the Clemenger-Nilsson diagram, as presented here, the energy level structure of the distorted clusters is displayed depending on the distortion parameter η. The empty circles denote the position of distortion according to the shell filling, which is indicated by the number next to the circles. The level scheme for a specific shell filling is obtained by drawing a vertical line through the empty circle. The intersections of this line with the level curves provide the level scheme. (Taken from [39].)

2.2 Photoelectron Spectroscopy

Photoelectron spectroscopy (PES) is a vastly applied experimental method that enabled researchers to obtain invaluable insights in various fields of research. The method is based on the photoelectric effect, in which one quanta of light absorbed by the material leads to the emission of exactly one electron. The correct interpretation of this effect was found by Albert Einstein [43], who was awarded the Noble Prize in 1921.

The typical setup of a PES experiment consists of a well defined light source, the material to be investigated, a kinetic energy analyzer and a detector for the pho- toemitted electrons. The energy distribution of the electrons contains information about the electronic structure of the material. Depending on the light source, different PES methods are distinguished. When applying an ultraviolet photon source, the

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2.2 Photoelectron Spectroscopy method is called ultraviolet photoemission spectroscopy (UPS). With this method, the valence levels of a surface or molecules on the surface can be investigated. The scanning of the detector over different angles with respect to the surface constitutes the method of angle-resolved photoelectron spectroscopy (ARPES). This method allows direct access to the band structure of bulk materials. When x-ray photon sources are used, the method is called x-ray photoelectron spectroscopy (XPS). Here, the core levels of atoms are probed, which provides information about the chemical environment of the atom.

All these methods investigate solid state specimens, where a high photoelectron count rate is easily achieved. This high count rate facilitates measurements of PES spectra in reasonable time scales. Investigation of clusters in the gas phase requires very intense light sources, since the target density is extremely small as compared to a solid state specimen [16]. The only light sources that provide sufficient intensities are lasers. However, commercial laboratory lasers have a limitation on the available photon energy, where the highest achieved photon energy is 7.9 eV with an excimer laser [44]. Due to this limitation, only the highest occupied electronic states of a cluster are accessible with lasers. This is the major reason that most of the research on clusters is performed with anionic clusters. The extra electron often occupies a weakly bound state and is therefore easily accessible. The strength of this electron binding energy is represented by the electron affinity (EA) of the cluster. In small metal clusters, the EA ranges from about 1 eV to 4 eV, which are values easily accessible by lasers.

In the following two subsections, two models for the interpretation of photoelectron spectra of clusters are presented. The single-particle picture is a straight forward model, that soon reaches its limitations to explain actual measurements.

With the quantum mechanical model, the spectra can be understood in more detail.

However, the interpretation of photoelectron spectra is often ambiguous and has to be compared to theoretical calculations of the cluster to reach conclusive results. In the last subsection the idea of time-resolved experiments is illustrated.

2.2.1 Single-Particle Picture

In the photoemission process, one photon transfers its whole energy (E_photon =hν) to one electron. If the energy of the electron after the absorption of a photon is higher then the vacuum energy it can leave the cluster and be measured with a detector. In the single-particle picture the electron leaves the cluster without interacting with the other electrons that are present in the cluster [45]. This is a very crude approximation, but it nevertheless provides a very instructive picture

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single photoemission processes and provides information about the electronic structure of the cluster. In figure 2.7 the transition from cluster states to a photoelectron spectrum is shown.

Figure 2.7: The connection of the electronic states and the photoelectron spectrum is illustrated here. The photons (blue arrows) with energy Ehn excite electrons from three states above the vacuum energy (Evac), from where the electrons leave the cluster.

The measurement of an electronic state results in a peak in the photoelectron spectrum that can have various intensities and widths. The intensity of the peak depends on the number of electrons in the measured state, the probability for the detachment process to occur, the symmetry of the probed state and the used photon energy [46]. The width of the peak can not be explained by the single particle-

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2.2 Photoelectron Spectroscopy picture. Employing the quantum mechanical model for PES (see subsection 2.2.2) provides insight into the width of the peak.

Consideration of all electrons in a cluster is mandatory for understanding the features in photoelectron spectra. The cluster is excited from an N electron initial state into an N-1 electron final state. Experimental results can often be explained by taking into account final state effects that occur during the photoemission process [47–49]. Three of these effects are explained below:

• Relaxation:

The detachment of one electron results in a change of the charge state in the clusters. The binding energy of the remaining electrons is increased due to a reduction in screening. This released binding energy is transferred to the detached electron.

• Multiplet Splitting:

The remaining electrons in a state may combine to different spin and angular momentum states. The energy difference between the states results in multiple peaks in the photoelectron spectrum.

• Shake-Up Process:

In the detachment process the outgoing electron excites another electron into another state. The energy that is required for exciting the electron is missing in the kinetic energy of the detected photoelectron.

2.2.2 Quantum Mechanical Model

In the quantum mechanical model of the photoemission process, all electrons are considered and the motion of the atomic nuclei in the cluster can not a priori be neglected. As the nuclei of atoms are much heavier then the electrons, the electronic processes happen instantly in comparison to nuclear motion. Within the Born-Oppenheimer approximation, the movement of the atoms in a cluster can be neglected for the consideration of the photoemission process. This approximation implies that the energy levels obtained with PES correspond to the geometric structure of the anionic cluster. The geometric structure of the neutral cluster can be different, which makes the assignment of peaks in the photoelectron spectra to electronic states of the neutral cluster more complex.

In the photoemission process the cluster loses an electron, making a transition from a negatively charged cluster initial state (X^-) into either a neutral cluster state (X) or an electronically excited neutral cluster state (A). In the consideration of

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Figure 2.8: In this level scheme, the electronic potential curve depending on a general reaction coordinate is drawn for three cases. The anionic cluster (X^-), the neutral cluster (X) and the excited neutral cluster (A) potential curves (red) along with vibrational states (green) are displayed. The electron is excited with a photon (blue arrow) into various vibrational states of X and A. The intensity of the resulting peak depends on the overlap of the vibrational wave function (Franck-Condon Principle). (Adapted from [38].)

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2.2 Photoelectron Spectroscopy Assuming that the cluster is cold before the photoemission process, the electron is in the vibrational ground state of the anionic cluster (X^-). The electron is excited by a photon with the energyhν (blue arrow). In the case that the electron is photo detached, the cluster is left in a certain electronic and vibrational state of the neutral (X) or excited neutral cluster (A). Because the electronic processes are very fast, the levels of the remaining electrons in the neutral cluster relax to the equilibrium position and the energy that might be released is given to the outgoing electron.

Thus the binding energy value measured from the photoelectron corresponds to the level structure of the neutral cluster in the geometry of the anionic cluster.

Different vibrational states of the neutral or excited neutral cluster can be reached by the photoemission process, as is seen in figure 2.8. Each of these processes contributes to a peak in the photoelectron spectrum. In the case that the difference in energy between these peaks is smaller than the resolution of the kinetic energy analyzer, the resulting peak will be broader than the resolution of the analyzer.

High resolution measurements can resolve the individual vibrational peaks [50, 51].

The intensity of the peaks in the spectrum can be interpreted via the Franck- Condon principle [52, 53]. It states that the probability for the transition to occur depends on the overlap of the initial and final state wave functions. In the example provided in figure 2.8, the PES peaks with the highest intensity are for the transitions into the vibrational level n=2 of the neutral cluster and into the vibrational level n=1 of the excited neutral cluster, where the wave functions of the initial and final states present the largest overlap. Vertical transitions in the potential curves plot (like in figure 2.8) are called adiabatic transitions since no heat (vibrational energy) is released. Within the Born-Oppenheimer approximation all transitions are adiabatic.

Restrictions for the possible transitions are given by the quantum mechanical selection rules. Since the electron can have any angular momentum and parity when leaving the cluster, most of the transitions are possible. The selection rule for the spin has to be considered as the electron carries a spin of 1/2 [49].

In the comparison of experimentally obtained spectra to calculations the following energy values are often used, which are indicated by arrows in figure 2.8.

• Adiabatic Detachment Energy (ADE):

This is the energy difference between the electronic and vibrational ground state of the anion and the electronic and vibrational ground state of the neutral cluster. In PES measurements, the ADE is not always observed as the ground state of the neutral and anionic cluster not always have exactly the same reaction coordinate.

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This is the energy released when a neutral cluster binds an electron. In this adiabatic consideration, the cluster ends up in an highly excited vibrational state.

2.2.3 Time-Resolved Photoelectron Spectroscopy

Accessing the dynamics of clusters requires the application of ultrashort laser pulses, as many processes happen on the femtosecond time scale. Since there are no detec- tors that exhibit such a good time resolution, methods have to be applied that do not need to detect the time dependent signal directly. In the pump and probe concept this is done by transferring the time dependent signal into multiple measurements at different time delays between the pump and probe pulse. In this method the temporal resolution is only limited by the laser pulse duration and the smallest time delay step.

With time-resolved photoelectron spectroscopy (TRPES), the dynamics of a cluster after being excited by a photon can be studied. TRPES is realized by applying two laser pulses with variable time delay between them to perform PES in a pump-probe scheme. Figure 2.9 (a) presents the level structure scheme of this process. The cluster is brought to an excited state by the pump pulse (red arrow in figure 2.9 (a)). The time-dependent population of this excited state can be investigated with the probe pulse (blue arrows in 2.9 (a)), as sketched in figure 2.9 (b). The two laser pulses are separated by means of a dichroic mirror and the time delay is provided by a mechanical delay line. The pulses are subsequently superimposed and irradiate the clusters in order to perform PES measurements at multiple time delays between the pump and probe pulse. The dynamics of the cluster can be extracted from the time-dependent peak intensity corresponding to the temporal evolution of the excited state.

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2.3 Dynamics in Clusters

Figure 2.9: In (a) the schematic level scheme of the single particle picture is shown, where the pump photon (red arrow) can excite one state and the probe pulse (blue arrows) is measuring the electronic states. In (b) the general concept of pump and probe experiments is presented. The pump pulse excites an electronic state and the probe pulse measures the temporal evolution of this excited state.

2.3 Dynamics in Clusters

The relaxation dynamics of photoexcited electronic states in clusters differs from the dynamics observed in atoms and bulk materials. The differences are explained by the unique electronic and structural situation of the various cases. Because molecules have similar electronic structures as clusters the same dynamics are observed.

In the case of an atom, an electron can be excited into a discrete electronic state, from where it generally decays into the lowest unoccupied electronic level while emitting a photon. This photon emission occurs since there is no other relaxation meachnism available for the electron in an atom. The population of the excited state is best described by an exponential decay function, as the decay is a statistical process. For energy differences between the involved states in the order of eV, the decay time is in the nanosecond regime [54].

In case of bulk materials (especially metals) the density of electrons is generally high. Thus electron-electron interactions govern the relaxation process, which is generally much faster then the decay in atoms. Time constants down to the femtosecond regime are observed [55]. Additionally, a slower decay process is possible since the bulk is constituted by many atoms in an ordered fashion. This structure allows for electron-phonon interaction, which results in relaxation times within the picosecond regime.

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In figure 2.10, the possible processes after a cluster is excited by a photon are summarized.

Figure 2.10: The processes that are possible after excitation by a photon are sketched.

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2.3.1 Wave Packet Motion

According to the uncertainty principle the short pulse length of femtosecond laser pulses yields very broad spectral bandwidth [56]. Absorption of such a femtosecond laser pulse can therefore lead to the excitation of many closely spaced vibrational states. In the case of no coherence loss, these vibrational states can form a wave packet that moves back and forth in the potential well of the excited state, as is illustrated in figure 2.11. In theory, the motion of this wave packet could con- tinue indefinetely. In reality, the excited states undergo relaxation processes and, depending on the time constant of these processes, the wave packet motion can be measured or not [57]. Most of the examples of wave packet motion were observed for small molecules/clusters, where no fast relaxation processes are available. In larger molecules or clusters fast relaxation processes dominate the relaxation dynamics.

Figure 2.11: Many vibrational levels of the excited state (V1) are populated by the pump pulse (hn). These vibrational states can form a wave packet that moves in the potential of the excited state. (Adapted from [57].)

2.3.2 Relaxation Processes

The time constant of the relaxation processes depends on the electronic level structure and the phononic level structure of the cluster. Because the position of atoms in a cluster is not rigid, the distances between them can vary and influence its level structure, as discussed in subsection 2.1.2 for the simple case of the shell model. The simplest case for illustrating the electronic level structure of a cluster as a function of the position of the atoms is the dimer. In this case, the levels can be drawn

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• Photoemission (PE):

In the case that the coupling between the electronic ground state energy surface and excited state energy surface is neglible no fast relaxation processes are possible. Then, the only possible relaxation process is the emission of a photon.

This process is the only radiative process in the relaxation dynamics in clusters.

The time constant for this process is on the nanosecond time scale similar to the dynamics in atoms.

• Intramolecular Vibrational Redistribution (IVR):

In this process the energy of the initially excited vibrational states is distributed to all accessible vibrational degrees of freedom within the same electronic state. The energy transfer is mediated by coupling of the molecular vibrational states and after a certain time an equilibrium is reached. The time constant of the redistribution is on the order of picoseconds to nanoseconds [58]. In the case that the energy of the photon is absorbed in a chemical bond, it can be broken after the energy is redistributed to many vibrational states [57]. This process is called indirect photodissociation, in contrast to direct photodissociation, which is described in subsection 2.3.3.

• Internal Conversion (IC):

The transfer from electronic energy into vibrational energy of a different electronic state is called internal conversion. This process occurs due to nonadiabatic coupling between the different electronic and vibrational (vibronic) levels. Nonadiabatic implies that the motion of the atoms can not be neglected, as was considered in the Born-Oppenheimer approximation in the description of the photoemission process.

Internal conversion occurs when the energy potential surface of the ground and excited states are close to each other, as illustrated in figure 2.12. In this case, the wave functions of the vibronic states may overlap and thus a non-radiative transition from the excited state to the ground state is possible. The rate of

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2.3 Dynamics in Clusters the transition depends on the overlap of the wave functions of the involved states. Typical time constants range from about 100 fs to tens of picoseconds [59].

Internal conversion describes the transition between states of the same multiplicity. For states with different multiplicity, e.g. from singlet to triplet, the transition is mediated by spin-orbit coupling and is called inter-system crossing (ISC).

Figure 2.12: The potential energy surface of a ground state (GS) and an excited state (S1) of a protein are presented as a function of two reaction coordinates.

An electron is excited into the excited state by a photon (green arrow).

The electron follows the energy surface, which implies that the geometry of the cluster changes. At the point where the surfaces are close to each other, the overlap of the states is non-zero and a non-radiative transition into the ground state becomes possible, which is indicated by two green arrows. (Adapted from [59].)

• Conical Intersection (CI):

The energy surfaces of the ground and excited state are energetically degenerate at the point where they intersect each other. This can happen for a specific cluster geometry. If there exists nonadiabatic coupling between the ground and excited states, the situation is called a conical intersection, where the vibronic coupling becomes strong. The wave packet formed after photoexcitation follows the potential curve to the conical intersection and a non-radiative transition into the ground state occurs. This situation is presented in figure 2.13 for the pryazine molecule. Due to the strong coupling, the time constants for conical intersections are on the order of tens of femtoseconds [60].

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Figure 2.13: The ground and excited state energy surface of the molecule pryazine is presented. At the conical intersection these two energy surfaces become energetically degenerate where the coupling between them is very strong. In these cases very fast relaxation times for excited electrons are observed. (Adapted from [61].)

Except PE, all possible relaxation processes are non-radiative and describe the redistribution of the electronic energy deposited in the cluster by the photon into vibrational energy. This is equivalent to heating of the cluster. If the deposited energy is high enough, an electron can be emitted in a thermionic emission process.

2.3.3 Photochemical Reactions

Processes where photons trigger chemical reactions or reactions that are only possible with the help of photons are called photochemical reactions. In femtosecond experiments, such reactions can be observed down to the level where the movement of the atoms during the reaction can be followed. The possible photochemical reactions are discussed below:

• Direct photodissociation:

In the case of direct photodissociation, the electron is excited directly or indi- rectly from a stable ground state (solid line in figure 2.14) of the cluster into an anti-bonding state, also called dissociative state (dashed line in figure 2.14).

After excitation into the dissociative state, the reaction coordinate adjusts until a stable state is reached. In the case of an anti-bonding state, the stable situation is reached after the dissociation of the cluster has occurred. Direct photodissociation of clusters or molecuels deposited on bulk metals is rarely seen, because the excited state lifetimes are extremely fast due to the many electrons present in these systems. In isolated clusters and molecules, much longer lifetimes appear and also direct photodissociation is found.

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• Indirect photodissociation:

An indirect dissociation is achieved when the weakly bound excited state is intersected by a dissociative state. The dissociative state is then reached via conical intersection and the cluster dissociates. The situation of direct and indirect dissociation is sketched in figure 2.14 for the oxygen molecule, where the potential curves are presented. With an excitation of a 157 nm photon the molecule can be excited to dissociative states (dashed lines) or to a weakly binding excited state (upper solid line). Conical intersection between the excited state and the dissociative states leads to an indirect dissociation.

Figure 2.14: Potential curves for the oxygen molecule. The ground state is excited with a 157 nm photon either into a weakly bound excited state (solid line) or into a dissociative state (dashed lines). (Adapted from [57].)

• Isomerization:

Isomers are different geometrical structures of the same cluster. In the ground state energy surface there may exist two energetic minima, thus two stable configurations are possible. The chemical reaction here is the switching from one geometry to the other by means of absorption of a photon. Presented in figure 2.15 is the case of stilbene, where photoisomerization has been observed.

The potential energy curves are displayed as a function of a general reaction coordinate, in this case the angle between two parts of the molecule. The excited state curve has a minimum (P) exactly at the maximum of the ground state energy curve. After excitation, the wave packet moves to the minimum

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Figure 2.15: Potential energy curves of the stilbene molecule are presented. After excitation by one photon, both geometrical structures, Trans and Cis can be reached. (Adapted from [62]).

(P), which lies directly between the two possible geometrical structures (Trans and Cis). Due to vibronic transitions into the ground state, the molecule can end up in one of both structures, with highly excited vibrational modes.

• Electron Transfer:

Forming and breaking bonds in clusters and molecules is mediated by the transfer of electrons. One particular chemical reaction in which the absorption of a photon can trigger a chemical reaction is the harpooning reaction [63]:

M +RX →M⁺+ (RX)⁻→M X +R .

Here, M is an alkali or alkaline earth atom and RX a halide molecule or an organic halide [57]. In this reaction, the ionic intermediates are formed via conical intersection of the neutral and the ionic states. The cross section for this reaction to occur is much larger if M is in an excited state. Therefore, photoexcitation can trigger this reaction [64].

• Proton Transfer:

Another chemical reaction that can be triggered by absorption of a photon is

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the following:

AH· · ·B +hν →AH^∗· · ·B →A^−∗· · ·HB⁺

In this reaction, A is an aromatic molecule, B is a cluster of alkaline molecules with a high proton affinity and H is a hydrogen atom. After photoexcitation, the proton can move to the cluster of alkaline molecules due to the high proton affinity of B [65, 66].

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3 Experimental Setup and Methods

In this chapter the experimental setup and methods are presented. The overall setup is described in the first section, followed by a detailed description of the methods in the subsequent sections.

3.1 Experimental Setup

In general, setups for investigating clusters in the gas phase can be classified according to the mode of operation as continuous [50, 51] and pulsed [67, 68]. Here, the pulsed method is used since the dynamics of particular cluster sizes are of interest.

To this end, a particular cluster size has to be irradiated by two light pulses with various time delays. Thus the cluster has to rest at the interaction point with the light for a finite amount of time, which is only possible if the experiment is done in a pulsed fashion.

The setup used here has a typical layout for experiments investigating clusters in the gas phase. These setups generally consist of vacuum chambers to produce and separate the clusters, an optical setup for investigation and the electronics and computers to control the experiment and collect the recorded data. Figure 3.1 shows a schematic drawing of the overall setup used for obtaining most of the data presented in this work. Note that electronics and computers are not shown for simplicity. The main parts of this setup are the cluster source, mass separation, electron analyzer, laser system and optical setup, which will be explained in detail in the following sections.

In figure 3.2 a drawing of the vacuum chambers is presented. In chamber (I) the pulsed arc cluster ion source (PACIS) is situated. Here, helium at high pressure is used as a process gas and therefore vacuum pumps with a high throughput are needed to keep the pressure as low as possible. Since ions in the gas phase have a mean free path which is strongly dependent on the pressure, great care has to be taken to keep the pressure at very low levels until the clusters reach the interaction zone, where they are investigated.

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Figure 3.1: The schematic drawing of the experiment setup is presented. Clusters are generated via a pulsed arc cluster ion source (PACIS) (I). Separation of the clusters is achieved by a time-of-flight mass spectrometer and improved by employing a reflectron (II, III and V). In the interaction zone (IV) the clusters are irradiated by two pulses of the femtosecond laser system. The kinetic energy of the electrons is analyzed using a magnetic-bottle-type time-of-flight spectrometer. (Adapted from [38].)

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3.1 Experimental Setup

Figure 3.2: A sketch of the vacuum chambers is shown in (a) and (b): source chamber (I), differential pumping stage (II), lens chamber (III), time-of- flight spectrometer with reflectron (IV) and interaction zone and energy spectrometer (IV).

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of the setup, facilitating easy and regular maintenance of the PACIS.

After the differential pumping stage the clusters are accelerated and collimated in the lens chamber (III). There, a pulsed electrostatic field is used to accelerate the clusters and continuous electrostatic fields are used to collimate and guide the clusters through the rest of the experimental setup. Many cluster sizes are produced in the cluster source. In order to investigate particular cluster sizes a mass spectrometer has to applied to achieve mass selection. Here a time-of-flight mass spectrometer is used. After all clusters are accelerated with the same energy, they drift through a field free region (IV). As different cluster sizes have different masses they travel at different velocities and are therefore separated in time when reaching the detector.

For increasing the mass resolution a reflectron is employed (see subsection 3.3.1 for details).

A well established method to investigate clusters in the gas phase is photoelectron spectroscopy (PES). In this method a bunch of clusters of the same size is irradiated by a single-energy photon source, which is usually a laser, in order to ionize the clusters. The electrons which are extracted from the clusters are collected and their kinetic energy is determined. Here, a femtosecond laser is employed to produce two laser-pulses, where one of the pulses is used to excite the cluster and the other is used to extract photoelectrons from the cluster. This method is called time-resolved photoelectron spectroscopy (TRPES) and provides access to the dynamics in clusters after photoexcitation. In order to measure the kinetic energy of the electrons, a magnetic-bottle-type time-of-flight spectrometer is applied. This spectrometer allows for the collection of nearly all produced electrons. This is important since two-photon signals are generally quite weak and are therefore difficult to observe. The interaction zone, where the clusters interact with the laser light, and the PES spectrometer is situated in chamber V.

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3.2 PACIS Cluster Source

Clusters are usually produced in the gas phase by condensation during an adiabatic expansion into vacuum. For materials which are solid under ambient conditions different methods have to be applied to evaporate atoms of the material into the gas phase, including the use of an oven [69], vaporization with a laser [70, 71] and sputtering of the material [72, 73]. These atoms are subsequently carried by a buffer gas and are expanded into vacuum, where they cool down and coalesce to form clusters.

In this work, the pulsed arc cluster ion source (PACIS) has been chosen. The two main reasons are its high cluster intensity and the low price compared to a laser-vaporization source [39]. Additionally, the extensive knowledge regarding this methods accumulated in the current research group of the author, provided an op- timized experimental setup.

Figure 3.3 shows the PACIS cluster source, where the dimensions and employed materials have changed considerably since the first experiments [72, 73].

Figure 3.3: Schematic drawing of the pulsed arc cluster ion source (PACIS).

(Adapted from [38].)

The heart of the PACIS consists of a cube, constructed from an insulating material, that can either be made of silicon oxide (quartz glass) or boron nitride.

Here, silicon oxide glass is used since boron nitride causes impurities in the cluster mass spectrum. The glass cube has four boreholes which intersect at the center

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First helium gas is introduced into the arc area, then two electric pulses are sent to the two electrodes. The first pulse is a short high-voltage pulse with the purpose of starting the arc. The second voltage pulse, the burning pulse, is of lower voltage but higher current to allow a sufficiently high rate of sputtering. In the arc, helium is ionized and accelerated towards the material of interest. The process of evaporation of this material can be regarded as a conjunction of two processes. Atoms get sputtered by high energetic helium ions and the heat deposited in the surface leads to thermal evaporation. Since a lot of heat is generated in the arc, the glass cube is housed in water-cooled copper. The helium also carries the sputtered atoms out of the arc region inside the glass cube. At the exit, a long copper tube is mounted, which is called extender. The extender is used to cool down the clusters efficiently with the helium atoms. This is necessary because cooling during expansion into vacuum is not sufficient to ignite cluster formation. The extender is water cooled, which cools down the helium atoms that pick up heat from the atoms and clusters due to collisions. In three body collisions two atoms can lose their binding energy to a third body (mostly helium), which enables them to coalesce. This can happen several times to the same cluster, allowing it to grow in size. After leaving the extender the cluster beam is a pulse of many different cluster sizes. The distribution of the cluster sizes can be influenced by the following source parameters:

• extender geometry:

The diameter and length of the extender influences the amount of collisions that occur between the helium and atoms/clusters. If there are more collisions, the probability to form heavier clusters is higher.

• carrier gas:

The amount of helium gas introduced into the cluster source is controlled by the pressure on the pulsed valve and the time the valve is kept open. More gas yields more collisions inside the extender and therefore heavier clusters are produced.

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3.3 Time-Of-Flight Mass Spectrometer

• power of the electrical arc:

By adjusting the voltage and the length of the electrical discharge, the amount of evaporated material can be controlled and therefore the amount of all produced clusters can be influenced.

• time delays:

The time delays between the helium pulse and the electric discharge pulse can be tuned, changing the amount of helium available for cluster formation.

• distance between the electrodes:

By controlling the distance between the electrodes, the arc volume can be adjusted, which influences the helium density and therefore the operation of the source. This distance also has to be adjusted during operation due to the fact that it increases when material is sputtered away. Additionally, material can accumulate on the copper anode, which can reduce the distance between the electrodes.

Adjusting all these parameters is important to maintain a good performance of the cluster source. During operation some of the parameters can change continuously, thus requiring thorough attention in order to keep the cluster current as constant as possible. This constant attendance is mandatory for experiments where many measurement runs on specific cluster sizes are compared, considering that a fluctuating cluster current can influence the electron signal strongly.

Attached to the extender is a second valve, which enables the introduction of another gas into the extender. This gas can react with the clusters to produce clusters with molecules adsorbed. This part of the experimental setup has been essential for producing the clusters which are investigated in chapter 5.

3.3 Time-Of-Flight Mass Spectrometer

As the cluster source provides a pulse of different cluster sizes, the individual masses have to be separated in order to perform experiments on a single cluster size. Here, a time-of-flight spectrometer is applied, which facilitates the separation of different cluster sizes in time. This method has the advantage that with a single run a mass spectrum of the whole cluster pulse, produced by the PACIS via one electrical discharge, can be generated.

The idea of the time-of-flight mass spectrometer is that all cluster sizes are accelerated by the same electric field. After acceleration heavier clusters have ac- quired a smaller velocity than smaller clusters. Therefore, after a certain field free

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the calibration of the experimental time axis at the cluster detector, by measuring clusters of known mass. However, this is a simple picture and in reality several other factors have to be taken into account when designing a time-of-flight mass spectrometer. For instance, the length of the acceleration field area is crucial for the dimension and resolution of the spectrometer. The resolution of a mass spectrometer expresses the limitation which mass differences can still be distinguished. When considering only one cluster size, not all of them are at the same spot within the acceleration area when the field is turned on. That in turn means that not all of them acquire the same velocity after traversing the acceleration area and will therefore not arrive at the same time at the detector. Thus the voltage peak for this cluster can be considerably broad. Two broad peaks close to each other can not be distinguished as soon as they overlap too much. The resolution m/dm (where m is the mass and dm the smallest mass difference that can be distinguished) of a mass spectrometer describes what masses can be separated by the spectrometer, e.g., a resolution of 100 means that the masses 100 and 101 can still be separated. As the mass stands in the definition of the resolution, it varies over the mass range. For example, mass 300 can not be distinguished from 301, when a resolution of 100 is assumed, only mass 303 is distinguishable.

In general, the resolution depends linearly on the acceleration voltage and the length of the field free zone. But as the voltage and length can not be increased indefinitely other methods to increase the resolution have to be applied. Reducing the length of the acceleration field could improve the resolution but at the same time the intensity of the clusters reaching the detector would also decrease. One trick is to use a specific length of the field free area where slow and fast clusters arrive at the same time. For a one-stage acceleration setup the length would be 2L, when L is the length of the acceleration field. As a small L leads to a small cluster signal this is no solution for the problem. A way out of this dilemma is applying two acceleration fields. This allows the adjustment of the distance from the acceleration area until the focus, where fast clusters overtake slower ones. The variables to change the

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3.3 Time-Of-Flight Mass Spectrometer length of the spectrometer are the length of the acceleration fields and the value of the two acceleration voltages. This type of mass spectrometer was first proposed by Wiley and Mclaren [74]. In the experimental setup used in this work a reflectron is applied to improve the resolution of the spectrometer, which is a variation of a two stage setup and will be explained in more detail in the following subsection.

3.3.1 Reflectron

The basic purpose of a reflectron is to focus the distribution of velocities of one cluster size in time onto the detection spot. The clusters are accelerated by an electric field and are then decelerated and subsequently reflected by another electric field. The resolution is improved by giving the faster clusters of the same size a time delay as compared to the slower ones. Figure 3.4 illustrates the working principle.

The fast clusters penetrate further into the reflectron’s electric field and therefore travel a longer distance compared to slow clusters. Thus the longer path traveled by the faster clusters compensates for their higher velocity, allowing them to arrive at the detector simultaneously with the slower ones.

Figure 3.4: The basic idea behind the reflectron is illustrated. Fast clusters penetrate further into the reflectron and thus spend more time in the reflectron.

This way slow and fast clusters are focused in time onto the detector.

(Taken from [38].)

The reflectron consist of many identical metallic rings, connected via resistors.

The first and the last ring are connected to two voltages, that create a homogeneously and slowly increasing electric field within the rings. The voltage on the first ring decelerates the clusters to a moderate velocity. After this first ring, they enter the homogenous and slowly changing linear field. In this field the faster clusters

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Figure 3.5: Measurements of small gold clusters before (a) and after (b,c) installing the reflectron. (Adapted from [38].)

3.3.2 Ion Guide

As charged clusters tend to repel each other, they have to be focused in order to travel through the experimental setup. Furthermore the mechanical alignment of the different parts of the experimental setup can not be achieved perfectly. Thus the clusters have to be deflected towards the correct direction in order to travel through the apparatus, fit through the interaction zone (about 2 mm in diameter), and hit the detector. This guidance is achieved by applying electrostatic lenses and

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3.3 Time-Of-Flight Mass Spectrometer steerers. A typical realization is displayed in figure 3.6. Using electrostatic fields to manipulate the paths of the clusters has the advantage that the effect of the field only depends on the cluster’s kinetic energy and is therefore independent of its mass.

Figure 3.6: Schematic drawing of an electrostatic lens and an X-Y steerer, which is employed in the experimental setup. The applied voltages are: ground potential (V₀), lens voltage (V_lens) and the steerer plus and minus voltages for x and y (V_sx/sy^+/−).

Electrostatic Steerer

The steerer is built like a simple capacitor with two plates. At the two plates the same voltage with opposite sign is applied (V_sx/sy^+/−). Before and after the plates a cylindrical electrode is situated. These electrodes are kept at ground potential (V₀) to ensure that the clusters have the same kinetic energy before and after traversing the steerer. The field between the plates is quasi linear. When a cluster travels through the field it is deflected into another direction. As the field is linear, clusters that do not travel through the center of the steerer get deflected into the same direction as the cluster that is traveling through the center.

Electrostatic Lens

The electrostatic lens consists of three cylindrical electrodes. The outer electrodes are kept at ground potential (V₀), which ensures that the clusters have the same kinetic energy before and after passing the lens. The electrode in the middle is set to a certain voltage (V_lens). The potential lines of the resulting electric field look similar to an optical lens and have similar effects on a cluster beam. Clusters which travel through the center of the lens are not deflected. However, the ones farther

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details on how to interpret a spectrum of kinetic energy are presented in section 2.2.

The standard method to measure the kinetic energy of electrons is to use electric or magnetic fields, where the hemispherical analyzer is the most commonly used spectrometer, employing electric fields. This type of spectrometer has the main disadvantage that only a few percent of the omnidirectional emitted electrons are collected.

The goal of this thesis is to measure two-photon electron signals from clusters using two femtosecond laser pulses. In this technique the intensity of the laser pulse has to be kept at moderate levels to minimize two-photon signals from one pulse only, thus the signals are often very faint. A magnetic-bottle-type time-of-flight spectrometer is employed, which permits to collect practically all emitted electrons.

This is achieved by applying a strong divergent magnetic field. As the Lorentz force for charged particles is perpendicular to the direction of motion, the kinetic energy is maintained throughout the magnetic field. This spectrometer was first employed by Kruit and Read [75] to analyze electrons and shortly thereafter by Chesnovsky et al. ([67]), and Ganteför et al. [76] to analyze photoelectrons generated from clusters in the gas phase.

The working principle of this electron spectrometer is basically the same as for the mass spectrometer. The electrons require a certain amount of time to travel through the electric field free area depending on the kinetic energy according to the relation tα^√_E¹

kin (see equation 3.1). The time axis of the spectrometer can be calibrated to kinetic energy by measuring electronic states with known binding energy. Charged particles are traveling in spirals around magnetic field lines due to the Lorentz force. When a particle enters a region where the magnetic field strength becomes stronger, the field lines are not parallel anymore. This results in a net force against the direction of motion. Depending on the velocity of the particle and the magnetic field strength this force can turn around the travel direction. Such a strong divergent field is called a magnetic mirror as charged particles which travel towards the strong field region are reflected. A combination of two magnetic mirrors is called

Time-resolved photoelectron spectroscopy of mass-selected metal-water clusters