effects can lead to electronic, optical, magnetic, chemical, and other properties ..... After the aggregation, the clusters expand through a nozzle into the next ...... Radiat. Eff. Def. Sol. 130â131: 225â233. Zhurkin, E.E. and Kolesnikov, A.S. 2003.
Clusters and Fullerenes
Klaus D. Sattler
Boca Raton London New York
CRC Press is an imprint of the Taylor & Francis Group, an informa business
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19 Energetic Cluster–Surface Collisions 19.1 Introduction ...........................................................................................................................19-1 19.2 Brief History of Cluster Beam Development .....................................................................19-2 19.3 Formation of Cluster Beams ................................................................................................19-2 Fundamental Aspects of Cluster Nucleation and Growth • Cluster Sources • Mass Selection of Clusters
19.4 Energetic Cluster–Surface Interaction ...............................................................................19-5 Cluster Deposition • Energetic Deposition and Pinning of Clusters • Implantation of Clusters • Surface Erosion on Cluster Impact
Vladimir Popok University of Gothenburg
19.5 Summary ...............................................................................................................................19-13 Acknowledgment............................................................................................................................. 19-14 References......................................................................................................................................... 19-14
Atomic (or molecular) clusters are aggregates of atoms (or molecules). Their sizes vary from two or three up to tens or hundreds of thousands constituents. Medium- and large-sized clusters have diameters on the scale of nanometers, and are often called nanoparticles (NPs) or nanocrystals (depending on their structure). Clusters show properties intermediate between those of individual atoms (or molecules), with discrete energy states, and bulk matter characterized by continua or bands of states. One can say that clusters represent a distinct form of matter: a “bridge” between atoms and molecules on the one hand and solids on the other. Clusters can be formed by most of the elements in the periodic table. They can be of different types, compositions, and structures. A wide variety of clusters has been produced and investigated from precursors including metals, semiconductors, ionic solids, noble gases, and molecules. More detailed information about the classification of clusters, their bonding types, structures, and properties in the gas phase goes beyond the scope of this chapter and can be found elsewhere (Haberland 1994, Martin 1996, Johnston 2002, Alonso 2005, Baletto and Ferrado 2005). Interest in clusters comes from various fields. Clusters are used as models to investigate the fundamental physical aspects of the above-mentioned transition from atomic scale to bulk material. They can also be used as a bridge across the disciplines of physics and chemistry to understand the nonmonotonic variations of properties and unusual phenomena of nanoscale objects (Jena and Castleman 2006). Clusters on surfaces define a new class
of systems highly relevant for practical applications. Finite size effects can lead to electronic, optical, magnetic, chemical, and other properties that are quite different from those of molecules or condensed matter and that are of great interest for practical applications in areas such as catalysis; electronics and nanotechnologies; bio-compatible, magnetic, and optical materials, etc. (Kreibig and Vollmer 1995, Meiwes-Broer 2000, Binns 2001, Palmer et al. 2003, Binns et al. 2005, Roduner 2006, Wegner et al. 2006, Woodruff 2007). Utilizing cluster beam technology (Milani and Iannotta 1999, Popok and Campbell 2006), one can control the cluster or nanoparticle (NP) size, its impact energy with surface and, to a certain extent, the spatial distribution of the deposited NPs on a surface, for example, by preliminary processing or functionalization (Bardotti et al. 2002, Corso et al. 2004, Queitsch et al. 2007). With clusters consisting of thousands of atoms, it is possible to transport and locally deposit a large amount of material, providing an advanced method for the growth of thin fi lms that can either be porous or very compact and smooth depending on the energy regime used for cluster impact (Haberland et al. 1993, 1995, Paillard et al. 1995, Milani et al. 1997, Qiang et al. 1998). So-called cluster-assisted deposition, when the depositing material is bombarded by lowenergy clusters, allows to control the structure and composition of the grown layers, for instance, to fabricate the thin and hard diamond-like carbon fi lms (Kitagawa et al. 2003). Low-energy cluster implantation is found to be an efficient tool for ultrashallow junction formation and infusion doping of shallow layers (Yamada et al. 1997, Cvikl et al. 1998, Borland et al. 2004). Energetic cluster beams can also be used as very efficient tools 19-1
Handbook of Nanophysics: Clusters and Fullerenes
for the processing of surfaces (dry etching and cleaning) or improving their surface topology (smoothing) (Gspann 1997, Yamada et al. 2001, Yamada and Toyoda 2007). The current state of the art in the field of energetic cluster– surface interactions is presented below. However, before concentrating on the fundamental physics of cluster–solid collisions and practical applications of cluster beams for the modification of surfaces and the building of nanostructures, brief surveys of the physical principles of cluster formation and the history of cluster beams are given.
“nanoscience era” stimulated a significant increase of interest in research on both free clusters in the gas phase and deposited (supported) clusters. At the same time, a systematic experimental work corroborated by molecular dynamics (MD) simulations has started to obtain a clear picture of the physical background of energetic cluster–surface interactions. The milestones in this research field are reviewed below.
19.3 Formation of Cluster Beams 19.3.1
Brief History of Cluster Beam Development
The first mention of cluster beam production and investigation occurred in the 1950s (Becker et al. 1956). The possibility to separate small clusters of hydrogen, nitrogen, and argon from noncondensed residual gas and transfer them into a high vacuum was shown. At the same time, it was demonstrated with CO2 and H2 that cluster beams can be ionized by electron bombardment enabling mass spectra to be obtained (Henkes 1961, 1962). These experiments were followed by investigations of the cluster size distribution in a beam of (CO2)n+, depending on conditions of the cluster source (Bauchert and Hagena 1965) and by the development of methods to evaluate cluster sizes, for example, by scattering of a potassium atomic beam passing through a nitrogen cluster beam (Burghoff and Gspann 1967). In the 1970s, the cluster technique underwent further development and improvement in order to get more stable and controllable beams (Hagena and Obert 1972) as well as expanding the spectrum of species used to produce clusters. In particular, gas aggregation (vaporization) sources for the production of metal and semiconductor clusters were developed (Hogg and Silbernagel 1974, Takagi et al. 1976, Kimoto and Nishida 1977). However, the first published results on the deposition of Si, Au, and Cu suffer from a lack of confirmation concerning the cluster-to-monomer ratio in the beams (Takagi et al. 1976). About the same time, the first cluster implantation experiments were performed, and the stopping of swift proton clusters in carbon and gold foils was studied (Brandt et al. 1974). Further development of the technique in the 1980s provided more controllable parameters of the beams and showed the applicability of ionized clusters for the synthesis of thin metal films and heterostructures (Yamada and Takagi 1981, Yamada et al. 1986). A source utilizing laser ablation was invented that allowed to extend cluster production over practically any solid material including those with high melting points (Smalley 1983). Development of this source and the study of carbon clusters led to the discovery of fullerenes in 1985 (Kroto et al. 1985). In the 1990s, new methods of cluster formation utilizing arc discharge, sprays, ion, and magnetron sputtering were introduced together with further development of techniques for cluster beam control, manipulation, and characterization (de Heer 1993, Haberland 1994, Milani and Iannotta 1999). Progress in cluster beam techniques together with the beginning of the
Fundamental Aspects of Cluster Nucleation and Growth
The probability of spontaneous cluster formation under equilibrium conditions is extremely low. Cluster production requires a thermodynamic nonequilibrium that can be implemented by means of a cluster source that can be of different types (see below). In all cluster sources, cluster generation consists of the following stages: vaporization (the production of atoms or molecules in the gas phase); nucleation (the initial condensation of atoms or molecules to form a cluster nucleus); growth (the addition of more atoms or molecules to the nucleus); coalescence (the merging of small clusters to form larger ones);and evaporation (the loss of one or more atoms) (Kappes and Leutwyler 1988, de Heer 1993). If the local thermal energy or temperature of the gas consisting of the monomer species is less than the binding energy of the dimer, then a three-atom collision can lead to stable dimer formation. Three atoms are necessary for the fulfi llment of energy and momentum conservation: A + A + A → A2 + A ,
where the third atom (A on the right-hand side of the equation) removes the excess energy. To make the nucleation step more efficient, an inert carrier (cooling) gas is often injected into the nucleation chamber of a cluster source. Once the dimer is formed it acts as a condensation nucleus for further cluster growth. Early growth occurs by incorporation of atoms (or molecules) one at a time. Subsequently, collisions between smaller clusters can lead to coalescence and the formation of larger clusters. In the cluster growth region, the clusters are generally hot, because their growth is an exothermic process, i.e., the internal energy increases due to the heat of condensation of the added atoms. Since the clusters are hot, there is competition between growth and decay. For practical reasons, i.e., the formation of a stable cluster beam, it is often necessary to lower the temperature of the clusters. A few mechanisms can be realized. Cooling under adiabatic expansion. This mechanism works simultaneously with the cluster formation in the case of supersonic nozzle sources (see next section). A gas under high stagnation pressure is expanded into a vacuum chamber through a nozzle: an abrupt decrease of pressure leads to a drastic temperature decrease in the beam causing supersaturation and, finally, cluster formation (Haberland 1994).
Energetic Cluster–Surface Collisions
Collisional cooling. Collisions with other atoms in the beam remove the excess energy from the clusters as kinetic energy: A n (E1 ) + B(ε1 ) → A n (E2 < E1 ) + B(ε 2 > ε1 )
where B may be a single atom of element A constituting the cluster or an inert cold carrier gas, which is more common. E is the internal energy of the cluster species and ε is the kinetic energy of atom B. This cooling mechanism is only significant in the initial expansion and condensation regions. Evaporative cooling. Clusters can lower their internal energy by evaporation, losing one or more atoms in an endothermal desorption process. The internal energy is channeled statistically into the appropriate cluster vibration mode, in order to overcome the activation barrier for bond breaking. After evaporation, excess energy is imparted as kinetic energy to the escaping atom and the daughter cluster: An (E1 ) → An −1(E2 < E1 ) + A(ε1 ) → An − 2 (E3 < E2 ) + A(ε 2 ) → (19.3) This is the main cooling mechanism once free flight of the cluster has been achieved and there are no further collisions. Radiative cooling. Clusters can also lower their internal energy by emitting radiation: An (E1 ) → An (E2 < E1 ) + hv
However, radiative cooling is an inefficient cooling mechanism, which is slow compared to the time scale of typical cluster experiments (μs). Electron emission can be an additional channel for cluster cooling.
19.3.2 Cluster Sources As mentioned above, cluster nucleation requires a thermodynamic nonequilibrium condition that can be realized by means of special equipment—a cluster source. There are a number of approaches for cluster beam formation, see for example (Kappes and Leutwyler 1988, Hagena 1992, de Heer 1993, Haberland 1994, Milani and Iannotta 1999, Pauly 2000, Wegner et al. 2006). Although a classification of the methods to produce clusters is somewhat arbitrary today, because often combinations of two or more methods are used, here the most common approaches are briefly reviewed, namely, gas aggregation, supersonic jet, surface erosion, and sprays. 220.127.116.11 Effusive and Gas Aggregation Sources A Knudsen cell, which is based on the thermal vaporization of liquids or solids in an oven, is one of the simplest ways to produce small clusters. Since the vapor is kept in equilibrium in the oven there is a low probability for clusters to nucleate. The beam of atoms and clusters is formed by eff usion from the oven
through a nozzle into a low-pressure chamber. The intensity of the beam falls exponentially with cluster size increase. Hence, a Knudsen cell can produce a low flux continuous beam of small (few atoms in size) clusters. In most cases, however, larger clusters and higher beam intensities are required for research-oriented or practical applications. The gas aggregation method, in which a solid or liquid is evaporated into a carrier gas and the atoms and molecules are collisionally cooled forming clusters, is a more advanced approach (Sattler et al. 1980). A smoking fire or cloud and fog formation in nature are good examples of gas aggregation, therefore, this type of source is also called a “smoking source.” After the aggregation, the clusters expand through a nozzle into the next vacuum chamber forming a subsonic beam. Gas-aggregation cluster sources produce continuous beams of elements with not very high melting points (