Browsing by Author "Wendel, Lars"

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Dielectric measurements at GHz frequencies
(2019) Wendel, Lars
Amongst the many dielectric materials that are topic of present research, two examples might be mentioned: SrTiO3 and nano-confined water molecules in single crystals. In SrTiO3 a quantum paraelectric or incipient ferroelectric behavior can be observed [1]. For low temperatures SrTiO3 is in a paraelectric phase, and the dielectric constant as a function of temperature follows a Curie-Weiss behavior. However, a real phase transition is not fully reached, indicated by the absence of a divergence in the permittivity at lowest observable temperatures. Quantum fluctuations then start to come into play and stabilize the frequency of the soft mode which leads to a saturation of the permittivity [2]. The dielectric constant of SrTiO3 is strongly anisotropic and depends vastly on temperature and frequency range and can go up to around 20000 [3, 4]. To confine water molecules in single crystals and observe the (quantum) paraelectric behavior, suitable hosts are needed. Possible candidates are single crystals of beryl or cordierite belonging to the gemstone family, where the water molecules are confined in structural channels [5, 6]. These large open channels run parallel to the crystal c-axis. In beryl the channels consist of six SiO4 tetrahedral rings, while in cordierite they consist of four SiO4 and two AlO4 tetrahedral rings. The water molecules are trapped in the center of the channels during the growth process and can occur in two distinct orientations: Either the electric dipole is perpendicular (type I) or parallel (type II) to the c-axis. For type I paraelectric behavior of the water molecules can be observed. This is due to the prevented hydrogen bonding, while the dipole-dipole interactions are kept which results in incipient ferroelectricity. The dielectric permittivity follows a Curie-Weiss behavior and saturates for low temperatures due to quantum fluctuations [6]. Whereas the permittivity of SrTiO3 ranges up to very large values, the dielectric constant of confined water molecules only goes up to around 20. Measurements were performed up to THz frequencies, where especially the cordierite system lacks information about the microwave regime. The different frequency regimes require separate approaches to probe the sample under study [7–9]. Different high frequency dielectric measurement techniques can access the desired dielectric properties in the GHz range of the bulk material. The methods can be roughly classified in four categories: Transmission and reflection line techniques, free-space methods, open-ended coaxial-probe techniques and resonant techniques [10–14]. Each technique has advantages and limitations regarding sample material and shape and which frequencies are possible to probe. Generally, the measurement methods can be classified if discrete frequencies are measured or the measurement is of broadband type. In broadband approaches the electromagnetic wave passes the material and allows to access frequencies continuously over a wide range. An example is the transmission line method where frequencies from the MHz up to the GHz range can be accessed [15]. However, this method lacks heavily in accuracy due to the non-resonant fixture type. Furthermore, unwanted parasitic losses occur in the microwave regime, strongly 11. Motivation influencing the measurement. Since the accuracy is of major interest, resonant techniques are suited for bulk dielectric measurements [16–18]. The obtained results are of highest accuracy compared to the other mentioned techniques. However, one big disadvantages is the accessibility of only a single frequency. The different resonant approaches are directly fabricated for the sample under test and are therefore able to probe only a single frequency in the spectrum. Especially regarding frequency-dependent dielectric properties this is an enormous weakness. Microwave waveguide resonator utilize the cavity perturbation theory and are able to probe numerous discrete frequencies [19]. Most of all, planar microwave resonators provide a wide field of potential researches [20–24]. It is possible to probe higher harmonics of a fundamental resonance frequency and perform measurements at cryogenic temperatures, while remaining at highly accurate results. A further upside is the simple fabrication of the the planar resonators as well as an fast and straightforward sample preparation of the studied materials. However, planar waveguide resonators are used for studies on dielectric thin films [25], whereas probing bulk dielectrics with this method is a recent research area. In this thesis a new resonant approach for bulk dielectric samples is developed in the microwave regime up to 20 GHz. With simulations utilized, different possible approaches are firstly studied regarding their suitability and functionality. This is investigated with focusing on the challenges which occur by going from thin films under study to bulk dielectrics. The respective approaches are then tested within experiments to check the simulated predictions. Finally, a new method is established by measuring known dielectrics and comparing the results to the literature. This thesis begins with a short guide into fundamental theoretical principles required for characterizing resonators and the analysis of microwave resonator experiments. Afterwards, the state of art of high frequency dielectric measurements is presented including several exemplary methods. Following, simulation and experimental basics and the consistency between them are elucidated. The first approach where the bulk dielectric sample acts as perturbation to the waveguide is then discussed for two different planar resonator structures. The new method with the resonator directly shaped on the sample under study is subsequently analyzed and discussed in detail including model requirements, simulations and experiments on TiO2, MgO and LaAlO3. This work finishes with an outlook for possible future experiments for the established resonant approach.