Energy resolving power of transition-edge X-ray microcalorimeters

This thesis describes the development and device physics of an X-ray microcalorimeter. This is a device for measuring the energy of X-rays. The microcalorimeter measures the temperature increase that is the result of the absorption of an X-ray photon. Combined into an array, the microcalorimeter can be used as an imaging spectrometer. The availability of an imaging X-ray spectrometer with a high energy resolving power will have a significant impact in astronomy and material analysis. In astronomy, X-ray spectra provide information about high-energy processes taking place in the universe. In material analysis, the structure and composition of materials can be determined. The work described here is guided by therequirements of an instrument for XEUS, a future space-based astrophysical observatory. The microcalorimeter is based on a superconducting-to-normal phase transition edge thermometer (TES). This is a superconductor that is voltage-biased in the very narrow transition from superconducting to resistive behaviour. In the transition, the electrical resistance is very sensitive to changes in the temperature, making the TES a good temperature to resistance transducer. The resistive element is easily incorporated in an electrical read-out circuit. The energy resolving power of the microcalorimeter is limited by noise. In this thesis, this noise is studied in detail, both in experimental sensors as well as through simulations. The sensors are fabricated using existing Si3N4 micromachining and thin-film photolithographical techniques. Several sensors with small square absorbers were manufactured and tested. With an operating temperature of 0.1 K, their energy resolution was about 4.5 eV for X-ray photons of 5.9 keV. This is equivalent to a resolving power of 1300. This energy resolution is satisfactory, but not as good as predicted by theory. This discrepancy was investigated and forms the heart of this thesis. The difference between theory and measurement was explained by a combination of two effects: Firstly, because the TES and absorber are seperate parts in the sensor, there can be an exchange of energy between the two. This results in an internal noise component which deteriorates the energy resolution. By changing the sensor geometry, we were able to influence and reduce the spectral density of this noise component. Using a numerical noise simulation, several geometries were evaluated. Secondly, the predicted resolution is based on a small-signal model, which assumes limited excursions over the transition of the TES. For actual X-ray pulses that use a significant part of the dynamic range of the TES, this model was found to be incorrect. The large excursions cause the pulse shape to deviate from the ideal shape as assumed by the small-signal model. Because of this, the small-signal model predicts a better resolution than could actually be measured. Using measured pulse shapes, a more accurate prediction was made, which is in agreement with the measurements. A simple large-signal model was constructed to simulate pulse shapes based on the sensor parameters. With this model, the energy resolution can be described as a function of the size of the excursion over the transition (equivalent to different X-ray photon energy or device heat capacity). The model can be used for performance prediction at arbitrary X-ray energies and for improved sensor optimisation