Frequenzabhängigkeit eines Primärnormals für Kapazität im Audiofrequenzbereich

The Thompson–Lampard theorem is a theorem of electrostatics which describes a so-called cross capacitance independent of its cross sectional dimensions. It is therefore best suited to be used as a capacitance standard for the absolute determination of the unit of capacitance, the farad. As this cross capacitance is defined for DC but must be operated at AC, a frequency correction must be applied the uncertainty of which is one of the largest contributions to the uncertainty budget. The frequency correction can be calculated with a sufficient accuracy using an equivalent circuit model which describes the behaviour of the calculable cross capacitor at AC. Calculable cross capacitors are mostly operated at a frequency of 1592 Hz ( = 104 rad/s) which is convenient for the link between the farad and the ohm. The determination of the frequency behavior of the PTB calculable cross capacitor in the audio frequency range is carried out by applying an equivalent circuit model which considers the influence of distributed admittances and impedances within the calculable cross capacitor. It has been derived taking into account the main currents flowing inside the calculable cross capacitor and the voltage drops caused by these currents. Most of the circuit parameters of the model were directly measured in the actual configuration of the electrode system with a commercial auto-balancing bridge in a frequency range between 1 kHz and 10 kHz. Owing to the uncertainty of the bridge which is 0.1 % for capacitance measurements and 2 % for inductance measurements, the calculated uncertainty of the frequency correction amounts to a few parts in 108. The capacitances on the calculable cross capacitor were found to be frequency independent, but self-inductances and mutual inductances of the electrodes are frequency dependent and linearly proportional to the inverse square root of the frequency in the examined frequency range. The frequency dependence of the calculable cross capacitor has been calculated based on the measured circuit parameters. It has been found that the frequency dependence of the cross capacitance is proportional to the square of the frequency, and that the influence of mutual inductances of opposite electrodes dominate the behavior at higher frequencies. At a frequency of 1592 Hz, the correction of the PTB calculable cross capacitor with a value of 1 pF amounts to 9.2×10-8 pF with an expanded uncertainty (k=2) of 3.1×10-8 pF.Das Thompson-Lampard Theorem ist ein Theorem der Elektrostatik, das eine sogenannte Kreuzkapazität beschreibt, die unabhängig von den Querschnittsabmessungen ist. Sie ist daher bestens als Kapazitätsnormal für die Darstellung der Kapazitätseinheit Farad geeignet. Da die Kreuzkapazität für den statischen Fall definiert ist, jedoch bei Wechselstrom betrieben wird, muss eine Frequenzkorrektur angebracht werden, deren Unsicherheit einen wesentlichen Beitrag zum Unsicherheitsbudget des Kondensators leistet. Die Frequenzkorrektur kann mit ausreichender Genauigkeit unter Verwendung eines Wechselstrom-Ersatzschaltbildes für den Kreuzkondensator berechnet werden. Kreuzkondensatoren werden im Allgemeinen bei einer Frequenz von 1592 Hz, entsprechend einer Kreisfrequenz von 10 rad/s, betrieben, die für die Ableitung der Widerstandseinheit Ohm aus der Kapazitätseinheit Farad am geeignetsten ist. Das Frequenzverhalten des PTB Kreuzkondensators im Tonfrequenzbereich wurde unter Anwendung eines Ersatzschaltbildes bestimmt, das den Einfluss der verteilten Impedanzen und Admittanzen im Kondensator berücksichtigt. Es wurde unter Beachtung der wesentlichen Ströme im Kondensator sowie ihrer Spannungsabfälle an den Impedanzen abgeleitet. Die Mehrzahl der Ersatzschaltbild-Parameter wurde direkt in der originalen Konfiguration des Elektrodensystems mit einer kommerziellen selbst abgleichenden Messbrücke in einem Frequenzbereich von 1 kHz bis 10 kHz bestimmt. Mit der Messunsicherheit der Messbrücke, die 0,1 % für Kapazitätsmessungen und 2% für Induktivitätsmessungen beträgt, ergibt sich für die Frequenzkorrektur eine Unsicherheit von einigen 10-8. Die Kapazitäten des Kreuzkondensators sind im untersuchten Bereich frequenzunabhängig, während die Selbst- und Gegeninduktivitäten sich linear mit der inversen Quadratwurzel der Frequenz ändern. Die Frequenzabhängigkeit des Kreuzkondensators wurde auf der Grundlage der gemessenen Ersatzschaltbild-Parameter berechnet. Sie ist proportional zum Quadrat der Frequenz. Den stärksten Einfluss auf das Frequenzverhalten bei höheren Frequenzen haben die Gegeninduktivitäten gegenüberliegender Elektroden. Bei einer Frequenz von 1592 Hz beträgt die Frequenzkorrektur des PTB Kreuzkondensators bei einer Kapazität von 1 pF 9.2×10-8 pF mit einer erweiterten Unsicherheit (k=2) von 3.1×10-8 pF

Development and characterisation of traceable force measurement for nanotechnology

Traceable low force metrology should be an essential tool for nanotechnology. Traceable measurement of micro- and nanonewton forces would allow independent measurement and comparison on material properties, MEMS behaviour and nanodimensional measurement uncertainties. Yet the current traceability infrastructure in the UK is incomplete. This thesis describes the incremental development of the low force facility at the National Physical Laboratory (NPL). The novel contribution of this thesis has three components. First, specific modifications to the NPL Low Force Balance were undertaken. This involved developing novel or highly modified solutions to address key issues, as well as undertaking detailed comparions with external ans internal traceability references. Second, a triskelion force sensor flexure was proposed and mathematically modelled using both analytical and finite element techniques, and compared to experimentally measured spring constant estimates. The models compared satisfactorily, though fabrication defects in developed prototype artefacts limited the experimental confirmation of the models. Third, a piezoelectric sensor approach for quasistatic force measurement was proposed, experimentally evaluated and rejected. Finally, an improved design for a low force transfer artefact system is presented, harnessing the findings of the reported investigations. The proposed design combines proven strain-sensing technology with the advantageous triskelion flexure, incorporating an external stage and packaging aspects to achieve the requirements for a traceable low force transfer artefact

Superinductance and fluctuating two-level systems: Loss and noise in disordered and non-disordered superconducting quantum devices

In this thesis, we first demonstrate that a disordered superconductor with high kinetic inductance can realise a microwave low-loss, non-dissipative circuit element with impedance greater than the quantum resistance. This element, known as a superinductor, can suppress the fluctuations of charge in a quantum circuit.For this purpose, we fabricated and characterised 20 nm thick, 40 nm wide niobium-nitride nanowires and determined the impedance to 6.795 kΩ. We demonstrate internal quality factors Qi = 2.5e4 in nanowire resonators at single photon excitation, which is significantly higher than values reported in devices with similar materials and geometries. Moreover, we show that the dominant dissipation in our nanowires is not an intrinsic property of the disordered films, but can instead be fully understood within the framework of two-level systems.To further characterise these losses, we then explore the geometrical scaling, toward nanowire dimensions, of dielectric losses in superconducting microwave resonators fabricated with the same techniques and from the same NbN thin-film as the nanowire superinductors. For this purpose, we perform an experimental and numerical study of dielectric loss at low temperatures. Using 3D finite-element simulation of the Maxwell--London equations, we compute the geometric filling factors of the lossy regions in our resonator structures and fit the experimental data to determine the intrinsic loss tangents of its interfaces and dielectrics. Finally, we study the effect of two-level systems on the performance of various superconducting quantum circuits. For this purpose, we measure coherence-time fluctuations in qubits and frequency fluctuations in resonators. In all devices, through statistical analysis, we identify the signature of individual Lorentzian fluctuators in the noise. We find that fluctuations in qubit relaxation are local to the qubit and are caused by instabilities of near-resonant two-level-systems. Furthermore, when examining the low-frequency noise of three different types of superconducting resonator - one NbN nanowire, one Al coplanar waveguide, and one Al 3D cavity - we observe a similar power-law dependence of the Lorentzian switching time and amplitude on the circulating power in the resonators, suggesting a common noise mechanism in the three different types of devices

The 25th Annual Precise Time and Time Interval (PTTI) Applications and Planning Meeting

Papers in the following categories are presented: recent developments in rubidium, cesium, and hydrogen-based frequency standards, and in cryogenic and trapped-ion technology; international and transnational applications of precise time and time interval (PTTI) technology with emphasis on satellite laser tracking networks, GLONASS timing, intercomparison of national time scales and international telecommunication; applications of PTTI technology to the telecommunications, power distribution, platform positioning, and geophysical survey industries; application of PTTI technology to evolving military communications and navigation systems; and dissemination of precise time and frequency by means of GPS, GLONASS, MILSTAR, LORAN, and synchronous communications satellites

A design and evaluation of a miniaturised position-sensitive energetic particle detector for small satellites

This thesis is concerned with the design and evaluation of an in-situ energetic particle detector for space weather measurements consisting of a position-sensitive solid state detector and a coded aperture mask. The combination of the two presents a novel technique that provides far higher resolution angular information of supra-thermal particles in low-flux environments in two dimensions than previously possible, over a wide field of view. After consideration of the historical and current status of in-situ plasma instruments and coded aperture techniques, a proposed design was modelled with the Geant4 toolkit. A proof-of-concept instrument has been designed and assembled and then tested in the laboratory with three electron sources and the results have been analysed. While the available hardware limited the amount of characterisation possible, the instrument made impressive strides in understanding the setup itself and demonstrated its potential within the tested energy ranges. Further to this, a simulation of such an instrument or its descendants in a space plasma environment was completed and an outlook on the use of the concept in space was discussed. In some configurations this will allow simultaneous energy and high-resolution angular measurements of energetic particle fluxes on small satellites. If such an instrument were flown on a swarm mission, the possibilities for multi-point directional measurements of energetic particles would be hugely increased, especially at low altitudes

Design, fabrication, characterization and reliability study of CMOS-MEMS Lorentz-Force magnetometers

Tesi en modalitat de compendi de publicacionsToday, the most common form of mass-production semiconductor device fabrication is Complementary Metal-Oxide Semiconductor (CMOS) technology. The dedicated Integrated Circuit (IC) interfaces of commercial sensors are manufactured using this technology. The sensing elements are generally implemented using Micro-Electro-Mechanical-Systems (MEMS), which need to be manufactured using specialized micro-machining processes. Finally, the CMOS circuitry and the MEMS should ideally be combined in a single package. For some applications, integration of CMOS electronics and MEMS devices on a single chip (CMOS-MEMS) has the potential of reducing fabrication costs, size, parasitics and power consumption, compared to other integration approaches. Remarkably, a CMOS-MEMS device may be built with the back-end-of-line (BEOL) layers of the CMOS process. But, despite its advantages, this particular approach has proven to be very challenging given the current lack of commercial products in the market. The main objective of this Thesis is to prove that a high-performance MEMS, sealed and packaged in a standard package, may be accurately modeled and manufactured using the BEOL layers of a CMOS process in a reliable way. To attain this, the first highly reliable novel CMOS-MEMS Lorentz Force Magnetometer (LFM) was successfully designed, modeled, manufactured, characterized and subjected to several reliability tests, obtaining a comparable or superior performance to the typical solid-state magnetometers used in current smartphones. A novel technique to avoid magnetic offsets, the main drawback of LFMs, was presented and its performance confirmed experimentally. Initially, the issues encountered in the manufacturing process of MEMS using the BEOL layers of the CMOS process were discouraging. Vapor HF release of MEMS structures using the BEOL of CMOS wafers resulted in undesirable damaging effects that may lead to the conclusion that this manufacturing approach is not feasible. However, design techniques and workarounds for dealing with the observed issues were devised, tested and implemented in the design of the LFM presented in this Thesis, showing a clear path to successfully fabricate different MEMS devices using the BEOL.Hoy en día, la forma más común de producción en masa es una tecnología llamada Complementary Metal-Oxide Semiconductor (CMOS). La interfaz de los circuitos integrados (IC) de sensores comerciales se fabrica usando, precisamente, esta tecnología. Actualmente es común que los sensores se implementen usando Sistemas Micro-Electro-Mecánicos (MEMS), que necesitan ser fabricados usando procesos especiales de micro-mecanizado. En un último paso, la circuitería CMOS y el MEMS se combinan en un único elemento, llamado package. En algunas aplicaciones, la integración de la electrónica CMOS y los dispositivos MEMS en un único chip (CMOS-MEMS) alberga el potencial de reducir los costes de fabricación, el tamaño, los parásitos y el consumo, al compararla con otras formas de integración. Resulta notable que un dispositivo CMOS-MEMS pueda ser construido con las capas del back-end-of-line (BEOL) de un proceso CMOS. Pero, a pesar de sus ventajas, este enfoque ha demostrado ser un gran desafío como demuestra la falta de productos comerciales en el mercado. El objetivo principal de esta Tesis es probar que un MEMS de altas prestaciones, sellado y empaquetado en un encapsulado estándar, puede ser correctamente modelado y fabricado de una manera fiable usando las capas del BEOL de un proceso CMOS. Para probar esto mismo, el primer magnetómetro CMOS-MEMS de fuerza de Lorentz (LFM) fue exitosamente diseñado, modelado, fabricado, caracterizado y sometido a varias pruebas de fiabilidad, obteniendo un rendimiento comparable o superior al de los típicos magnetómetros de estado sólido, los cuales son usados en móviles actuales. Cabe destacar que en esta Tesis se presenta una novedosa técnica con la que se evitan offsets magnéticos, el mayor inconveniente de los magnetómetros de fuerza Lorentz. Su efectividad fue confirmada experimentalmente. En los inicios, los problemas asociados al proceso de fabricación de MEMS usando las capas BEOL de obleas CMOS resultaba desalentador. Liberar estructuras MEMS hechas con obleas CMOS con vapor de HF producía efectos no deseados que bien podrían llevar a la conclusión de que este enfoque de fabricación no es viable. Sin embargo, se idearon y probaron técnicas de diseño especiales y soluciones ad-hoc para contrarrestar estos efectos no deseados. Se implementaron en el diseño del magnetómetro de Lorentz presentado en esta Tesis, arrojando excelentes resultados, lo cual despeja el camino hacia la fabricación de diferentes dispositivos MEMS usando las capas BEOL.Postprint (published version

Particle Physics Reference Library

This second open access volume of the handbook series deals with detectors, large experimental facilities and data handling, both for accelerator and non-accelerator based experiments. It also covers applications in medicine and life sciences. A joint CERN-Springer initiative, the “Particle Physics Reference Library” provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A,B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access

Characterisation of the KATRIN tritium source and evaluation of systematic effects

The Karlsruhe Tritium Neutrino (KATRIN) Experiment aims to measure the effective electron antineutrino mass with a sensitivity of 200 meV (90 % C. L.) by analysing the kinematic endpoint of the tritium beta-electron spectrum. In this thesis, the systematic effects of KATRIN are evaluated. Since most of them are linked to the tritium source, the source cryostat performance is fully characterised in this work. With a dedicated measurement campaign performed with krypton-83m, energy scale-related systematic effects are investigated and the great capabilities of KATRIN in high-resolution spectroscopy of keV-scale electrons are demonstrated