Polinómios de Appell multidimensionais e sua representação matricial

Nesta dissertação é apresentada uma abordagem a polinómios de Appell multidimensionais dando-se especial relevância à estrutura da sua função geradora. Esta estrutura, conjugada com uma escolha adequada de ordenação dos monómios que figuram nos polinómios, confere um carácter unificador à abordagem e possibilita uma representação matricial de polinómios de Appell por meio de matrizes particionadas em blocos. Tais matrizes são construídas a partir de uma matriz de estrutura simples, designada matriz de criação, subdiagonal e cujas entradas não nulas são os sucessivos números naturais. A exponencial desta matriz é a conhecida matriz de Pascal, triangular inferior, onde figuram os números binomiais que fazem parte integrante dos coeficientes dos polinómios de Appell. Finalmente, aplica-se a abordagem apresentada a polinómios de Appell definidos no contexto da Análise de Clifford.

Development of a single photon counting computed tomography system using MPGDs

The development of computed tomography systems with energy resolving detectors is a current challenge in medical physics and biomedical engineering. A computed tomography system of this kind allows getting complementary informations relatively to conventional systems, that can help the medical diagnosis, being of great interest in medicine. The work described in this thesis is related to the development of a computed tomography system using micropattern gaseous detectors, which allow storing, simultaneously, information about the interaction position and the energy of each single photon that interacts with the detector. This kind of detectors has other advantages concerning the cost and characteristics of operation when compared with solid state detectors. Tomographic acquisitions were performed using a MicroHole & Strip Plate based detector, which allowed reconstructing cross-sectional images using energy windows, applying the energy weighting technique and performing multi-slice and tri-dimensional reconstructions. The contrast-to-noise ratio was improved by 31% by applying the energy weighting technique, comparing with the corresponding image obtained with the current medical systems. A prototype of a computed tomography with flexibility to change the detector was developed, making it possible to apply different detectors based on Thick-COBRA. Several images acquired with these detectors are presented and demonstrate their applicability in X-ray imaging. When operating in NeCH4, the detector allowed a charge gain of 8 104, an energy resolution of 20% (full width at half maximum at 8 keV), a count rate of 1 106 Hz/mm2, a very stable operation (gain fluctuations below 5%) and a spacial resolution of 1.2 mm for an energy photon of 3.6 keV. Operating the detector in pure Kr allowed increasing the detection efficiency and achieving a charge gain of 2 104, an energy resolution of 32% (full width at half maximum at 22 keV), a count rate of 1 105 Hz/mm2, very stable operation and a spatial resolution of 500 m. The software already existing in the group was improved and tools to correct geometric misalignments of the system were also developed. The reconstructions obtained after geometrical correction are free of artefacts due to the referred misalignments.

Ferroelectric : CNTs structures fabrication for advanced functional nano devices

This work is about the combination of functional ferroelectric oxides with Multiwall Carbon Nanotubes for microelectronic applications, as for example potential 3 Dimensional (3D) Non Volatile Ferroelectric Random Access Memories (NVFeRAM). Miniaturized electronics are ubiquitous now. The drive to downsize electronics has been spurred by needs of more performance into smaller packages at lower costs. But the trend of electronics miniaturization challenges board assembly materials, processes, and reliability. Semiconductor device and integrated circuit technology, coupled with its associated electronic packaging, forms the backbone of high-performance miniaturized electronic systems. However, as size decreases and functionalization increases in the modern electronics further size reduction is getting difficult; below a size limit the signal reliability and device performance deteriorate. Hence miniaturization of siliconbased electronics has limitations. On this background the Road Map for Semiconductor Industry (ITRS) suggests since 2011 alternative technologies, designated as More than Moore; being one of them based on carbon (carbon nanotubes (CNTs) and graphene) [1]. CNTs with their unique performance and three dimensionality at the nano-scale have been regarded as promising elements for miniaturized electronics [2]. CNTs are tubular in geometry and possess a unique set of properties, including ballistic electron transportation and a huge current caring capacity, which make them of great interest for future microelectronics [2]. Indeed CNTs might have a key role in the miniaturization of Non Volatile Ferroelectric Random Access Memories (NVFeRAM). Moving from a traditional two dimensional (2D) design (as is the case of thin films) to a 3D structure (based on a tridimensional arrangement of unidimensional structures) will result in the high reliability and sensing of the signals due to the large contribution from the bottom electrode. One way to achieve this 3D design is by using CNTs. Ferroelectrics (FE) are spontaneously polarized and can have high dielectric constants and interesting pyroelectric, piezoelectric, and electrooptic properties, being a key application of FE electronic memories. However, combining CNTs with FE functional oxides is challenging. It starts with materials compatibility, since crystallization temperature of FE and oxidation temperature of CNTs may overlap. In this case low temperature processing of FE is fundamental. Within this context in this work a systematic study on the fabrication of CNTs - FE structures using low cost low temperature methods was carried out. The FE under study are comprised of lead zirconate titanate (Pb1-xZrxTiO3, PZT), barium titanate (BaTiO3, BT) and bismuth ferrite (BiFeO3, BFO). The various aspects related to the fabrication, such as effect on thermal stability of MWCNTs, FE phase formation in presence of MWCNTs and interfaces between the CNTs/FE are addressed in this work. The ferroelectric response locally measured by Piezoresponse Force Microscopy (PFM) clearly evidenced that even at low processing temperatures FE on CNTs retain its ferroelectric nature. The work started by verifying the thermal decomposition behavior under different conditions of the multiwall CNTs (MWCNTs) used in this work. It was verified that purified MWCNTs are stable up to 420 ºC in air, as no weight loss occurs under non isothermal conditions, but morphology changes were observed for isothermal conditions at 400 ºC by Raman spectroscopy and Transmission Electron Microscopy (TEM). In oxygen-rich atmosphere MWCNTs started to oxidized at 200 ºC. However in argon-rich one and under a high heating rate MWCNTs remain stable up to 1300 ºC with a minimum sublimation. The activation energy for the decomposition of MWCNTs in air was calculated to lie between 80 and 108 kJ/mol. These results are relevant for the fabrication of MWCNTs – FE structures. Indeed we demonstrate that PZT can be deposited by sol gel at low temperatures on MWCNTs. And particularly interesting we prove that MWCNTs decrease the temperature and time for formation of PZT by ~100 ºC commensurate with a decrease in activation energy from 68±15 kJ/mol to 27±2 kJ/mol. As a consequence, monophasic PZT was obtained at 575 ºC for MWCNTs - PZT whereas for pure PZT traces of pyrochlore were still present at 650 ºC, where PZT phase formed due to homogeneous nucleation. The piezoelectric nature of MWCNTs - PZT synthesised at 500 ºC for 1 h was proved by PFM. In the continuation of this work we developed a low cost methodology of coating MWCNTs using a hybrid sol-gel / hydrothermal method. In this case the FE used as a proof of concept was BT. BT is a well-known lead free perovskite used in many microelectronic applications. However, synthesis by solid state reaction is typically performed around 1100 to 1300 ºC what jeopardizes the combination with MWCNTs. We also illustrate the ineffectiveness of conventional hydrothermal synthesis in this process due the formation of carbonates, namely BaCO3. The grown MWCNTs - BT structures are ferroelectric and exhibit an electromechanical response (15 pm/V). These results have broad implications since this strategy can also be extended to other compounds of materials with high crystallization temperatures. In addition the coverage of MWCNTs with FE can be optimized, in this case with non covalent functionalization of the tubes, namely with sodium dodecyl sulfate (SDS). MWCNTs were used as templates to grow, in this case single phase multiferroic BFO nanorods. This work shows that the use of nitric solvent results in severe damages of the MWCNTs layers that results in the early oxidation of the tubes during the annealing treatment. It was also observed that the use of nitric solvent results in the partial filling of MWCNTs with BFO due to the low surface tension (<119 mN/m) of the nitric solution. The opening of the caps and filling of the tubes occurs simultaneously during the refluxing step. Furthermore we verified that MWCNTs have a critical role in the fabrication of monophasic BFO; i.e. the oxidation of CNTs during the annealing process causes an oxygen deficient atmosphere that restrains the formation of Bi2O3 and monophasic BFO can be obtained. The morphology of the obtained BFO nano structures indicates that MWCNTs act as template to grow 1D structure of BFO. Magnetic measurements on these BFO nanostructures revealed a week ferromagnetic hysteresis loop with a coercive field of 956 Oe at 5 K. We also exploited the possible use of vertically-aligned multiwall carbon nanotubes (VA-MWCNTs) as bottom electrodes for microelectronics, for example for memory applications. As a proof of concept BiFeO3 (BFO) films were in-situ deposited on the surface of VA-MWCNTs by RF (Radio Frequency) magnetron sputtering. For in situ deposition temperature of 400 ºC and deposition time up to 2 h, BFO films cover the VA-MWCNTs and no damage occurs either in the film or MWCNTs. In spite of the macroscopic lossy polarization behaviour, the ferroelectric nature, domain structure and switching of these conformal BFO films was verified by PFM. A week ferromagnetic ordering loop was proved for BFO films on VA-MWCNTs having a coercive field of 700 Oe. Our systematic work is a significant step forward in the development of 3D memory cells; it clearly demonstrates that CNTs can be combined with FE oxides and can be used, for example, as the next 3D generation of FERAMs, not excluding however other different applications in microelectronics.