PhD Defence Joanna Liberadzka

heat transfer across dielectric-metallic interfaces and thin layers at low and ultra-low temperatures

Joanna Liberadzka is a PhD student in the research group Energy, Materials & Systems (EMS). Her supervisor is H.J.M. ter Brake from the Faculty of Science and Technology.

The AEgIS project is one of the experiments based in the Antimatter Factory of the European Organisation for Nuclear Research (CERN). Its goal is the first direct measurement of the Earth's gravitational acceleration on antimatter within 1 % precision. In the framework of this project, a thermalisation strategy for a set of ultra-cold electrodes forming a Penning trap for antimatter has been investigated. The electrodes need to fulfil a series of requirements. Some of them must be divided into 4 sectors and the electrical insulation between the sectors and the neighbouring electrodes must withstand up to 1 kV potential difference. Each electrode will be made of a single sapphire crystal and the four sectors will be sputtered with gold to provide a sufficient electrical insulation and at the same time proper thermal anchoring.

Two sandwich setups reflecting two possible ways of anchoring the electrodes on a mixing chamber of a dilution refrigerator have been analysed. The first sandwich consisted of copper, indium and sapphire, and the second of copper, indium, gold, titanium and sapphire. Sapphire was always in the form of a flat polished disk of 1 mm thickness, and the metallic thin layers had following thicknesses: Ti 45 nm, Au 520 nm and In 125 µm.

The thermal resistivity of both setups with and without an external magnetic field was measured. The total thermal resistivity of the first setup with indium in the normal conducting state takes a value from 17 cm2K4/W to 44 cm2K4/W in the temperature range from 30 mK to 375 mK. With indium in the superconducting state, the total thermal resistivity is much higher and takes a value from 100 cm2K4/W at 50 mK to 163 cm2K4/W at 340 mK. The investigation of the first sandwich has confirmed the validity of the parallel plates assumption at the sapphire disk, and demonstrated the importance of the oxide layers on the interface thermal resistance. The important conclusion has been drawn that with indium in the normal conducting state the compression force can be removed without changing the total thermal resistivity of the sandwich. It allowed a significant modification of the clamping structure and the shape of the electrode.

The total thermal resistivity of the second setup with thin layers of gold and titanium takes a value from 28 cm2K4/W at 38 mK to 77 cm2K4/W at 407 mK with titanium and indium in the normal conducting state. This result shows that sputtering of titanium and the mechanism of its adhesion to sapphire can have a significant influence on the interface thermal resistivity. The same setup with superconducting layers of titanium and indium has the highest thermal resistivity of all the measured configurations, which takes a value from 187 cm2K4/W at 63 mK to 480 cm2K4/W at 400 mK. It shows a huge influence of the thin layers on the total thermal resistivity of the sandwich.

The low temperature and ultra-low temperature thermal diffusivity of the sandwich has also been measured. The results are consistent with respect to the built model over the whole temperature range, opening a possibility of a correct evaluation of the ultra-low temperature behaviour of the setup by measuring its low temperature properties. Such a conclusion is very important not only for the application in the AEgIS project, but also in any other system where the difficult to evaluate ultra-low temperature thermal performance plays a main role.

 The new electrode has been designed taking into account findings from the ultra-low temperature measurements and conclusions drawn from the stress analysis. The electrode has been manufactured according to rigorous procedure to make sure it fulfils all of the demanding constraints. A new way of clamping the electrode has been designed. It provides a more uniform pressure distribution on the bottom surface of the electrode and increases the chances for a formation of a robust indium bond. The thermal performance of the electrode has been tested in steady state and transient conditions and it proved to be over five times higher than the performance of the old design. The newly designed electrode fulfils all requirements and has a sufficient thermal performance for the application in the AEgIS experiment.