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Register a new userCryogenic Calibration Setup for Broadband Complex Impedance Measurements
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Reflection measurements give access to the complex impedance of a material on a wide frequency range. This is of interest to study the dynamical properties of various materials, for instance disordered superconductors. However reflection measurements made at cryogenic temperature suffer from the difficulty to reliably subtract the circuit contribution. Here we report on the design and first tests of a setup able to precisely calibrate in situ the sample reflection, at 4.2 K and up to 2 GHz, by switching and measuring, during the same cool down, the sample and three calibration standards.
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The characteristic frequencies of a system provide important information on the phenomena that govern its physical properties. In this framework, there has recently been renewed interest in cryogenic microwave characterization for condensed matter systems since it allows to probe energy scales of the order of a few $mu$eV. However, broadband measurements of the absolute value of a sample response in this frequency range are extremely sensitive to its environment and require a careful calibration. In this paper, we present an textit{in situ} calibration method for cryogenic broadband microwave reflectometry experiments that is both simple to implement and through which the effect of the sample electromagnetic environment can be minimized. The calibration references are here provided by the sample itself, at three reference temperatures where its impedance is assumed or measured, and not by external standards as is usual. We compare the frequency-dependent complex impedance (0.1--2 GHz) of an a-Nb$_{15}$Si$_{85}$ superconducting thin film obtained through this Sample-Based Calibration (SBC) and through an Open-Short-Load Standard Calibration (SC) when working at very low temperature (0.02--4 K) and show that the SBC allows us to obtain the absolute response of the sample. This method brings the calibration planes as close as possible to the sample, so that the environment electrodynamic response does not affect the measurement, provided it is temperature independent. This results in a heightened sensitivity, for a given experimental set--up.
We developed an impedance bridge that operates at cryogenic temperatures (down to 60 mK) and in perpendicular magnetic fields up to at least 12 T. This is achieved by mounting a GaAs HEMT amplifier perpendicular to a printed circuit board containing the device under test and thereby parallel to the magnetic field. The measured amplitude and phase of the output signal allows for the separation of the total impedance into an absolute capacitance and a resistance. Through a detailed noise characterization, we find that the best resolution is obtained when operating the HEMT amplifier at the highest gain. We obtained a resolution in the absolute capacitance of 6.4~aF$/sqrt{textrm{Hz}}$ at 77 K on a comb-drive actuator, while maintaining a small excitation amplitude of 15~$k_text{B} T/e$. We show the magnetic field functionality of our impedance bridge by measuring the quantum Hall plateaus of a top-gated hBN/graphene/hBN heterostructure at 60~mK with a probe signal of 12.8~$k_text{B} T/e$.
This thesis is organized as follows: Chapter 1 introduces the background, motivation, objectives, and contributions of this thesis. Chapter 2 presents a review of existing online impedance extraction approaches. Chapter 3 proposes the improved measurement setup of the inductive coupling approach and introduces the theory behind time-variant online impedance extraction. Chapter 4 develops a three-term calibration technique for the proposed measurement setup to deembed the effect of the probe-to-probe coupling between the inductive probes with the objective to improve the accuracy of online impedance extraction. Chapter 5 discusses the additional measurement setup consideration in industrial applications where significant electrical noise and power surges are present. Chapter 6 discusses and demonstrates the application of the inductive coupling approach in online detection of the incipient stator faults in the inverter-fed induction motor. Chapter 7 further extends the application of this approach for non-intrusive extraction of the voltage-dependent capacitances of the silicon carbide (SiC) power metal-oxide-semiconductor field-effect transistor (MOSFET). Finally, Chapter 8 concludes this thesis and proposes future works that are worth exploring.
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