Development of Transition Edge Sensor Distributed Read-Out Imaging Devices for Applications in X-ray Astronomy Thesis submitted for the degree of Doctor of Philosophy at the University of Leicester By Stephen James Smith Space Projects and Instrumentation Group Department of Physics and Astronomy University of Leicester 24th April 2006 Development of Transition Edge Sensor Distributed Read-Out Imaging Devices for Applications in X-ray Astronomy Stephen James Smith Abstract This thesis is concerned with the development of, position-sensitive, Transition Edge Sensors (TESs) operating at cryogenic temperatures (~ 0.1 K). The Distributed Read-Out Imaging Device (DROID) uses TES read-out at both ends of a linear X-ray absorber, to derive, through heat diffusion, both spectral and spatial information. Potentially, DROIDs offer a simpler technological alternative to the development of large area pixel arrays for future X- ray space observatories. We have established a finite-element model to numerically calculate the response of the DROID to an X-ray photon. The model estimates the noise spectral density at the detector outputs, including the frequency dependent correlations between the two TESs. This model is used to implement pre-existing signal processing algorithms, based on the digital optimal filter, to calculate the position and energy resolution along the length of experimental DROID designs. We show that these algorithms do not lead to optimum performance under all conditions and derive the true optimal filters, based on least-squares minimisation of the total noise power in the DROID. By numerical simulation, we show that improvements in the energy and in particular, in the position resolution, are theoretically possible. We investigate the trade-offs resulting from changing key detector design parameters, such as the thermal conductances of the different detector elements. These simulations enable the DROID design to be optimised for specific detector applications. The design and experimental characterisation of prototype DROIDs are described. The first X-ray results from a prototype DROID, using single TES read-out, are reported. The data shows different populations of signal corresponding to X-ray absorption in different parts of the DROID. These results demonstrate proof of concept, confirming spatial sensitivity along the length of the DROID absorber, though the actual spectral and spatial resolutions are limited by the availability of only a single read-out channel. ii Declaration I hereby declare that no part of this thesis has been previously submitted to this or any other University as part of the requirement for a higher degree. The work described herein was conducted solely by the undersigned except for those colleagues and other workers acknowledged in the text. Stephen James Smith 24th April 2006 iii Publications Some of the results in this thesis are reported in the following publications: Smith S. J., Whitford, C., Fraser G. W., Holland A. D., Goldie D., Ashton T. J. R., Limpenny R. J., Stevenson T., First results from a 1-D imaging spectrometer using Ir TESs, Nucl. Instr. and Meth. A 520 (2004) 449. Smith S. J., Whitford, C. H., Fraser G. W., Optimised filtering for improved energy and position resolution in position-sensitive TES based X-ray detectors, Nucl. Instr. and Meth. A 556 (2006) 237. Smith S. J., Whitford, C. H., Fraser G. W., Signal processing for distributed readout using TESs, Nucl. Instr. and Meth. A 559 (2006) 782. Smith S. J., Whitford C. H., Fraser G. W., Goldie D. J., Characterisation and modelling of transition edge sensor distributed read-out imaging devices, Nucl. Instr. and Meth. A 559 (2006) 500. Smith S. J., Watterson J. I. W., Ambrosi R. M., A position-sensitive cryogenic detector for fast neutron spectroscopy using a silicon absorber, submitted to Nucl. Instr. and Meth. A 2006. iv Acknowledgements I would like to acknowledge the following people, without whom, this thesis would not have been possible. In general, I must thank all of the staff and fellow PhD students in the Space Research Centre for the assistance and the friendship provided over the past three years, which has made it so worthwhile and enjoyable. Special thanks go to my supervisor Prof. George Fraser for his support in the preparation of this thesis. Special thanks must also go to the cryo-team, including Rob Limpenny, Terry Ashton, Tim Stevenson and Chris Whitford, for their expert technical support throughout my PhD. In particular, to Rob and Terry for their time and effort both in and out of the lab. Of particular use were the frequent Friday lunch time discussions, especially in the early stages of my PhD, which have provided me with much support. I would also like to thank Dr. David Goldie of the Cavendish Laboratory, University of Cambridge, for many useful technical discussions, as well as assistance with the experimental programme and provision of read-out electronics. Finally, I would like to thank Prof. Alan Wells for securing the departmental studentship to allow me to carry out this PhD. v Contents Abstract..................................................................................................................................... ii Declaration .............................................................................................................................. iii Publications ............................................................................................................................. iv Acknowledgements ...................................................................................................................v Contents ................................................................................................................................... vi Chapter 1: Introduction and Background.............................................................................1 1.1. The X-ray Universe ................................................................................................................1 1.2. The XEUS Mission and Instrument Requirements.................................................................2 1.3. Thesis Structure ......................................................................................................................4 Chapter 2: Transition Edge Sensor Theory ..........................................................................6 2.1. Microcalorimeters as X-ray Detectors....................................................................................6 2.1.1. Calorimeter Basics .........................................................................................................6 2.1.2. Semiconductor Thermistors ...........................................................................................9 2.1.3. Transition Edge Sensors...............................................................................................10 2.1.4. Metallic Magnetic Calorimeters...................................................................................13 2.2. Detailed Examination of TES Theory ..................................................................................15 2.2.1. The Effect of Negative ETF on Decay Time and Energy Integral...............................15 2.2.2. Effect of Current Dependence and Non-Perfect Voltage Bias.....................................19 2.2.3. Noise and Energy Resolution.......................................................................................23 2.3. Summary...............................................................................................................................28 Chapter 3: The DROID Detector – Modelling the Position Response and Noise Characteristics ........................................................................................................................29 3.1. Position-Sensitive TES Detectors.........................................................................................29 3.1.1. Pixel Arrays .................................................................................................................29 3.1.2. DROID Concept...........................................................................................................31 3.2. Modelling Techniques for Position-Sensitive Cryogenic Detectors.....................................33 3.3. Modelling the DROID Position Response............................................................................34 vi 3.4. Investigating the DROID Noise Response ...........................................................................42 3.5. Summary...............................................................................................................................50 Chapter 4: Calculating the DROID Energy and Position Resolution...............................51 4.1. Optimal Filtering and Energy Resolution.............................................................................51 4.1.1. Single TES Optimal Filtering and Energy Resolution.................................................52 4.1.2. DROID Energy Resolution ..........................................................................................55 4.2. Position Resolution using the Normalised Energy Ratio......................................................57 4.3. Optimised Filtering for Position and Energy Determination................................................59 4.4. Numerical Simulations of Energy and Position Resolution .................................................65 4.4.1. Energy