# Dissertation: Dissertation: 2.9. Studies of Two-Dimensional and Three-Dimensional Phononic Crystal Structures (Tian)

2.9.2016 12:00 — 15:00

Location: Ylistonrinne, FYS1

M.Sc. **Yaolan Tian** defends her doctoral dissertation in Physics ”Studies of Two-Dimensional and Three-Dimensional Phononic Crystal Structures”. Opponent Professor **Karl Joulain** (Université de Poitiers, France) and custos Professor **Ilari Maasilta** (University of Jyväskylä).

This thesis focuses on studying phononic crystal structures. It is aimed at fabrication and measurement of thermal properties of two-dimensional (2D) periodic microstructures and three-dimensional (3D) nanostructures.

A process of fabricating two-dimensional hole array phononic (2D PnC) structures is described. Three simple 2D square arrays of holes of periods 4, 8, 16 µm were fabricated, with a filling factor of the holes of 0.7. Thermal conductance was measured on all three different periodic structures, and compared with membranes at temperatures from 50 mK to 1.2 K using SINIS thermometry. All PnC structures gave a much lower thermal conductance than the membrane. The thermal conductance of the 8 µm periodic structure was the lowest, which indicates that there is a period between 4 and 16 µm giving a minimum thermal conductance for 300 nm thick SiNx. Besides, different types of SINIS junction pairs were fabricated on membrane and the thermal conductance was measured. The results show it is important to keep SINIS the same when comparing thermal conductance of different PnC structures of different periods.

3D PnC domains were self-assembled by simply dipping into polystyrene (PS) nano-spheres solution. Statistics of 3D colloidal crystal domain sizes were collected by varying the dipping withdrawal speed, the concentration of PS nano-sphere colloidal solution, and the dipping angle on plain chips. It turned out that lower speed, higher concentration and vertical dipping produces larger and thicker 3D PnC domains. Samples with etched in-situ silicon boxes and polymer boxes fabricated by three-dimensional lithography were vertically dipped. Depth and size of the boxes directly affect the self-assembly of PS nano-spheres. Even though PS domains were treated to survive from unavoidable lithography process, it is still challenging to fabricate a thermal conductance measurement device on top of 3D PnC structures.**Further information:**

Yaolan Tian, yaolan.y.tian@jyu.fi, puh. +358 45 176 3864

Communications intern Petra Toivanen, tiedotus@jyu.fi

Tian completed her Bachelor Degree of Science in 2010 at Beijing normal university. She started her PhD study in 2010 at the University of Jyväskylä.

Published in series: Department of Physics, University of Jyväskylä Research Report number 10/2016, Jyväskylä 2016, ISSN 0075-465X, ISBN 978-951-39-6701-7, ISBN 978-951-39-6702-4 (pdf).

Abstract

This thesis focuses on studying phononic crystal structures. More specifically, it is aimed at fabrication and measurement of thermal properties of two-dimensional (2D) periodic microstructures and three-dimensional (3D) nanostructures. There is great interest in understanding, manipulating and considering application perspective of minimizing of thermal transport in periodic structures. Periodic structures have been studied more on their optical properties, but this thesis places emphasis on their application of manipulating heat. A process of fabricating two-dimensional hole array phononic (2D PnC) structures is described here. It consists of membrane preparation, superconductor-insulatornormal metal-insulator-superconductor (SINIS) tunnel junction fabrication and etching of 2D PnC structures. Simple square array geometries of periods 4, 8, 16 µm were fabricated, keeping filling factor of holes as 0.7. Thermal conductance of phononic structures with the three different periods were measured and compared with uncut membranes at temperatures from 50 mK to 1.2 K. All PnC structures gave a lower thermal conductance than membrane. In addition, thermal conductance was measured on membranes by different types of SINIS junction pairs. The variables were the geometry, the normal metal material and the normal metal length, which all affected the measured result. It is thus important to keep the SINIS heaters and thermometers the same when studying thermal conductance and its dependence on the period of the PnC structure. Additionally, sometimes superconductor-normal metal-superconductor (SNS) junction pairs were accidentally made. Thermal conductance measured using a SNS structure as a heater and SINIS structure as a thermometer is also shown. We also address the fabrication of 3D colloidal polystyrene(PS) nano-sphere PnC structures on plain chips and the statistics of the deposition process, selfassembly by vertical dipping. Combinations of dipping angle of 45 and 90, withdrawal speed of 0.01 mm/min to 0.05 mm/min and nano-sphere colloidal solution concentration of 0.02%, 0.2%, 2%, 5% and 10% were studied. Colloidal 3D PnC structure of face-centered cubic (fcc) crystal domains were self-assembled. Silicon chips with etched microscale boxes were fabricated and dipped vertically into 10% concentration PS colloidal solution at withdrawal at speed of 0.01 mm/min to 0.04mm/min. Lower speed, higher concentration and 90_ vertical dipping produce larger 3D PnC domain sizes on average. It was found that one big domain could fill a 20 µm deep confined box no larger than 200 µm length. However, there were always cracks between the domains and the edges of the box. Therefore, a polymer box was developed and used instead as a confinement box. It was fabricated by three dimensional lithography (3DL), using two types of resist: IPL 780 and IPDIP. Glass substrates with 10 µm high IPL780 resist polymer boxes of hollow area of 100 µm by 100 µm were dipped into a solution of 0.5%, 1% and 2% concentration of 260 nm diameter polystyrene nano-spheres at withdrawal speed of 0.01 and 0.02 mm/min. Only the sample with 1% concentration at withdrawal speed of 0.01 mm/min gave good results. There were no PS nano-sphere self-assembled on top of IPL780 box. However, there were several domains inside one box. So, a 20 µm high polymer box of 50 µm by 50 µm area was fabricated on silicon chips. They were dipped into a PS nano-sphere solution of 1%, 2 % and 5 % concentration at the speed of 0.01mm/min. Finally, a method was also developed to protect PS colloidal PnC structures from deformation and dissolution. As expected, there was only one domain inside the box formed from the concentration of 1%. Unexpected, there were PS nano-spheres also on top of the sides of IPDIP boxes. PnC structures were treated by e-beam irradiation and protected by a capping layer of AlOx. Aluminum wires were successfully deposited on top of the PnC structures, which is promising for mounting thermal conductance measurement devices on top.