Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

A maximal operator, Carleson's embedding, and tent spaces for vector-valued functions

This thesis is concerned with the area of vector-valued Harmonic Analysis, where the central theme is to determine how results from classical Harmonic Analysis generalize to functions with values in an infinite dimensional Banach space. The work consists of three articles and an introduction. The first article studies the Rademacher maximal function that was originally defined by T. Hytönen, A. McIntosh and P. Portal in 2008 in order to prove a vector-valued version of Carleson's embedding theorem. The boundedness of the corresponding maximal operator on Lebesgue-(Bochner) -spaces defines the RMF-property of the range space. It is shown that the RMF-property is equivalent to a weak type inequality, which does not depend for instance on the integrability exponent, hence providing more flexibility for the RMF-property. The second article, which is written in collaboration with T. Hytönen, studies a vector-valued Carleson's embedding theorem with respect to filtrations. An earlier proof of the dyadic version assumed that the range space satisfies a certain geometric type condition, which this article shows to be also necessary. The third article deals with a vector-valued generalizations of tent spaces, originally defined by R. R. Coifman, Y. Meyer and E. M. Stein in the 80's, and concerns especially the ones related to square functions. A natural assumption on the range space is then the UMD-property. The main result is an atomic decomposition for tent spaces with integrability exponent one. In order to suit the stochastic integrals appearing in the vector-valued formulation, the proof is based on a geometric lemma for cones and differs essentially from the classical proof. Vector-valued tent spaces have also found applications in functional calculi for bisectorial operators. In the introduction these three themes come together when studying paraproduct operators for vector-valued functions. The Rademacher maximal function and Carleson's embedding theorem were applied already by Hytönen, McIntosh and Portal in order to prove boundedness for the dyadic paraproduct operator on Lebesgue-Bochner -spaces assuming that the range space satisfies both UMD- and RMF-properties. Whether UMD implies RMF is thus an interesting question. Tent spaces, on the other hand, provide a method to study continuous time paraproduct operators, although the RMF-property is not yet understood in the framework of tent spaces.

Exploring Problem Decomposition in Conceptual Design

Design embraces several disciplines dedicated to the production of artifacts and services. These disciplines are quite independent and only recently has psychological interest focused on them. Nowadays, the psychological theories of design, also called design cognition literature, describe the design process from the information processing viewpoint. These models co-exist with the normative standards of how designs should be crafted. In many places there are concrete discrepancies between these two in a way that resembles the differences between the actual and ideal decision-making. This study aimed to explore the possible difference related to problem decomposition. Decomposition is a standard component of human problem-solving models and is also included in the normative models of design. The idea of decomposition is to focus on a single aspect of the problem at a time. Despite its significance, the nature of decomposition in conceptual design is poorly understood and has only been preliminary investigated. This study addressed the status of decomposition in conceptual design of products using protocol analysis. Previous empirical investigations have argued that there are implicit and explicit decomposition, but have not provided a theoretical basis for these two. Therefore, the current research began by reviewing the problem solving and design literature and then composing a cognitive model of the solution search of conceptual design. The result is a synthetic view which describes recognition and decomposition as the basic schemata for conceptual design. A psychological experiment was conducted to explore decomposition. In the test, sixteen (N=16) senior students of mechanical engineering created concepts for two alternative tasks. The concurrent think-aloud method and protocol analysis were used to study decomposition. The results showed that despite the emphasis on decomposition in the formal education, only few designers (N=3) used decomposition explicitly and spontaneously in the presented tasks, although the designers in general applied a top-down control strategy. Instead, inferring from the use of structured strategies, the designers always relied on implicit decomposition. These results confirm the initial observations found in the literature, but they also suggest that decomposition should be investigated further. In the future, the benefits and possibilities of explicit decomposition should be considered along with the cognitive mechanisms behind decomposition. After that, the current results could be reinterpreted.

Temperature sensitivity of soil organic matter decomposition in boreal soils

The temperature sensitivity of decomposition of different soil organic matter (SOM) fractions was studied with laboratory incubations using 13C and 14C isotopes to differentiate between SOM of different age. The quality of SOM and the functionality and composition of microbial communities in soils formed under different climatic conditions were also studied. Transferring of organic layers from a colder to a warmer climate was used to assess how changing climate, litter input and soil biology will affect soil respiration and its temperature sensitivity. Together, these studies gave a consistent picture on how warming climate will affect the decomposition of different SOM fractions in Finnish forest soils: the most labile C was least temperature sensitive, indicating that it is utilized irrespective of temperature. The decomposition of intermediate C, with mean residence times from some years to decades, was found to be highly temperature sensitive. Even older, centennially cycling C was again less temperature sensitive, indicating that different stabilizing mechanisms were limiting its decomposition even at higher temperatures. Because the highly temperature sensitive, decadally cycling C, forms a major part of SOM stock in the organic layers of the studied forest soils, these results mean that these soils could lose more carbon during the coming years and decades than estimated earlier. SOM decomposition in boreal forest soils is likely to increase more in response to climate warming, compared to temperate or tropical soils, also because the Q10 is temperature dependent. In the northern soils the warming will occur at a lower temperature range, where Q10 is higher, and a similar increase in temperature causes a higher relative increase in respiration rates. The Q10 at low temperatures was found to be inversely related to SOM quality. At higher temperatures respiration was increasingly limited by low substrate availability.

Radical Enhanced Atomic Layer Deposition of Metals and Oxides

Atomic Layer Deposition (ALD) is a chemical, gas-phase thin film deposition method. It is known for its ability for accurate and precise thickness control, and uniform and conformal film growth. One area where ALD has not yet excelled is film deposition at low temperatures. Also deposition of metals, besides the noble metals, has proven to be quite challenging. To alleviate these limitations, more aggressive reactants are required. One such group of reactants are radicals, which may be formed by dissociating gases. Dissociation is most conveniently done with a plasma source. For example, dissociating molecular oxygen or hydrogen, oxygen or hydrogen radicals are generated. The use of radicals in ALD may surmount some of the above limitations: oxide film deposition at low temperatures may become feasible if oxygen radicals are used as they are highly reactive. Also, as hydrogen radicals are very effective reducing agents, they may be used to deposit metals. In this work, a plasma source was incorporated in an existing ALD reactor for radical generation, and the reactor was used to study five different Radical Enhanced ALD processes. The modifications to the existing reactor and the different possibilities during the modification process are discussed. The studied materials include two metals, copper and silver, and three oxides, aluminium oxide, titanium dioxide and tantalum oxide. The materials were characterized and their properties were compared to other variations of the same process, utilizing the same metal precursor, to understand what kind of effect the non-metal precursor has on the film properties and growth characteristics. Both metals were deposited successfully, and silver for the first time by ALD. The films had low resistivity and grew conformally in the ALD mode, demonstrating that the REALD of metals is true ALD. The oxide films had exceptionally high growth rates, and aluminium oxide grew at room temperature with low cycle times and resulted in good quality films. Both aluminium oxide and titanium dioxide were deposited on natural fibres without damaging the fibre. Tantalum oxide was also deposited successfully, with good electrical properties, but at slightly higher temperature than the other two oxides, due to the evaporation temperature required by the metal precursor. Overall, the ability of REALD to deposit metallic and oxide films with high quality at low temperatures was demonstrated.

Atomic Layer Deposition of Electroluminescent ZnS, SrS, and BaS Thin Films

The light emitted by flat panel displays (FPD) can be generated in many different ways, such as for example alternating current thin film electroluminescence (ACTFEL), liquid crystal display (LCD), light emitting diode (LED), or plasma display panel (PDP) technologies. In this work, the focus was on ACTFEL devices and the goal was to develop new thin film processes for light emitting materials in ACTFEL devices. The films were deposited with the atomic layer deposition (ALD) method, which has been utilized in the manufacturing of ACTFEL displays since the mid-1980s. The ALD method is based on surface-controlled self-terminated reactions and a maximum of one layer of the desired material can be prepared during one deposition cycle. Therefore, the film thickness can be controlled simply by adjusting the number of deposition cycles. In addition, both large areas and deep trench structures can be covered uniformly. During this work, new ALD processes were developed for the following thin film materials: BaS, CuxS, MnS, PbS, SrS, SrSe, SrTe, SrS1-xSex, ZnS, and ZnS1-xSex. In addition, several ACTFEL devices were prepared where the light emitting material was BaS, SrS, SrS1-xSex, ZnS, or ZnS1-xSex thin film that was doped with Ce, Cu, Eu, Mn, or Pb. The sulfoselenide films were made by substituting the elemental selenium for sulfur on the substrate surface during film deposition. In this way, it was possible to replace a maximum of 90% of the sulfur with selenium, and the XRD analyses indicated that the films were solid solutions. The polycrystalline BaS, SrS, and ZnS thin films were deposited at 180-400, 120-460, and 280-500 °C, respectively, and the processes had a wide temperature range where the growth rate of the films was independent of the deposition temperature. The electroluminescence studies showed that the doped sulfoselenide films resulted in low emission intensity. However, the emission intensities and emission colors of the doped SrS, BaS, and ZnS films were comparable with those found in earlier studies. It was also shown that the electro-optical properties of the different ZnS:Mn devices were different as a consequence of different ZnS:Mn processes. Finally, it was concluded that because the higher deposition temperature seemed to result in a higher emission intensity, the thermal stability of the reactants has a significant role when the light emitting materials of ACTFEL devices are deposited with the ALD method.

Atomic Layer Deposition for optical applications: metal fluoride thin films and novel devices

Thin films of various metal fluorides are suited for optical coatings from infrared (IR) to ultraviolet (UV) range due to their excellent light transmission. In this work, novel metal fluoride processes have been developed for atomic layer deposition (ALD), which is a gas phase thin film deposition method based on alternate saturative surface reactions. Surface controlled self-limiting film growth results in conformal and uniform films. Other strengths of ALD are precise film thickness control, repeatability and dense and pinhole free films. All these make the ALD technique an ideal choice also for depositing metal fluoride thin films. Metal fluoride ALD processes have been largely missing, which is mostly due to a lack of a good fluorine precursor. In this thesis, TiF4 precursor was used for the first time as the fluorine source in ALD for depositing CaF2, MgF2, LaF3 and YF3 thin films. TaF5 was studied as an alternative novel fluorine precursor only for MgF2 thin films. Metal-thd (thd = 2,2,6,6-tetramethyl-3,5-heptanedionato) compounds were applied as the metal precursors. The films were grown at 175 450 °C and they were characterized by various methods. The metal fluoride films grown at higher temperatures had generally lower impurity contents with higher UV light transmittances, but increased roughness caused more scattering losses. The highest transmittances and low refractive indices below 1.4 (at 580 nm) were obtained with MgF2 samples. MgF2 grown from TaF5 precursor showed even better UV light transmittance than MgF2 grown from TiF4. Thus, TaF5 can be considered as a high quality fluorine precursor for depositing metal fluoride thin films. Finally, MgF2 films were applied in fabrication of high reflecting mirrors together with Ta2O5 films for visible region and with LaF3 films for UV region. Another part of the thesis consists of applying already existing ALD processes for novel optical devices. In addition to the high reflecting mirrors, a thin ALD Al2O3 film on top of a silver coating was proven to protect the silver mirror coating from tarnishing. Iridium grid filter prototype for rejecting IR light and Ir-coated micro channel plates for focusing x-rays were successfully fabricated. Finally, Ir-coated Fresnel zone plates were shown to provide the best spatial resolution up to date in scanning x-ray microscopy.

Atomic Layer Deposition and Photocatalytic Properties of Titanium Dioxide Thin Films

Photocatalytic TiO2 thin films can be highly useful in many environments and applications. They can be used as self-cleaning coatings on top of glass, tiles and steel to reduce the amount of fouling on these surfaces. Photocatalytic TiO2 surfaces have antimicrobial properties making them potentially useful in hospitals, bathrooms and many other places where microbes may cause problems. TiO2 photocatalysts can also be used to clean contaminated water and air. Photocatalytic oxidation and reduction reactions proceed on TiO2 surfaces under irradiation of UV light meaning that sunlight and even normal indoor lighting can be utilized. In order to improve the photocatalytic properties of TiO2 materials even further, various modification methods have been explored. Doping with elements such as nitrogen, sulfur and fluorine, and preparation of different kinds of composites are typical approaches that have been employed. Photocatalytic TiO2 nanotubes and other nanostructures are gaining interest as well. Atomic Layer Deposition (ALD) is a chemical gas phase thin film deposition method with strong roots in Finland. This unique modification of the common Chemical Vapor Deposition (CVD) method is based on alternate supply of precursor vapors to the substrate which forces the film growth reactions to proceed only on the surface in a highly controlled manner. ALD gives easy and accurate film thickness control, excellent large area uniformity and unparalleled conformality on complex shaped substrates. These characteristics have recently led to several breakthroughs in microelectronics, nanotechnology and many other areas. In this work, the utilization of ALD to prepare photocatalytic TiO2 thin films was studied in detail. Undoped as well as nitrogen, sulfur and fluorine doped TiO2 thin films were prepared and thoroughly characterized. ALD prepared undoped TiO2 films were shown to exhibit good photocatalytic activities. Of the studied dopants, sulfur and fluorine were identified as much better choices than nitrogen. Nanostructured TiO2 photocatalysts were prepared through template directed deposition on various complex shaped substrates by exploiting the good qualities of ALD. A clear enhancement in the photocatalytic activity was achieved with these nanostructures. Several new ALD processes were also developed in this work. TiO2 processes based on two new titanium precursors, Ti(OMe)4 and TiF4, were shown to exhibit saturative ALD-type of growth when water was used as the other precursor. In addition, TiS2 thin films were prepared for the first time by ALD using TiCl4 and H2S as precursors. Ti1-xNbxOy and Ti1-xTaxOy transparent conducting oxide films were prepared successfully by ALD and post-deposition annealing. Highly unusual, explosive crystallization behaviour occurred in these mixed oxides which resulted in anatase crystals with lateral dimensions over 1000 times the film thickness.

Atomic Layer Deposition of Multicomponent Oxide Materials

Atomic layer deposition (ALD) is a method for thin film deposition which has been extensively studied for binary oxide thin film growth. Studies on multicomponent oxide growth by ALD remain relatively few owing to the increased number of factors that come into play when more than one metal is employed. More metal precursors are required, and the surface may change significantly during successive stages of the growth. Multicomponent oxide thin films can be prepared in a well-controlled way as long as the same principle that makes binary oxide ALD work so well is followed for each constituent element: in short, the film growth has to be self-limiting. ALD of various multicomponent oxides was studied. SrTiO3, BaTiO3, Ba(1-x)SrxTiO3 (BST), SrTa2O6, Bi4Ti3O12, BiTaO4 and SrBi2Ta2O9 (SBT) thin films were prepared, many of them for the first time by ALD. Chemistries of the binary oxides are shown to influence the processing of their multicomponent counterparts. The compatibility of precursor volatilities, thermal stabilities and reactivities is essential for multicomponent oxide ALD, but it should be noted that the main reactive species, the growing film itself, must also be compatible with self-limiting growth chemistry. In the cases of BaO and Bi2O3 the growth of the binary oxide was very difficult, but the presence of Ti or Ta in the growing film made self-limiting growth possible. The application of the deposited films as dielectric and ferroelectric materials was studied. Post-deposition annealing treatments in different atmospheres were used to achieve the desired crystalline phase or, more generally, to improve electrical properties. Electrode materials strongly influenced the leakage current densities in the prepared metal insulator metal (MIM) capacitors. Film permittivities above 100 and leakage current densities below 110-7 A/cm2 were achieved with several of the materials.