Investigation of Transmon Qubit Designs - A Study of Plasma Frequency Predictability

This master thesis was dedicated to design, fabricate, and characterize subsystems of superconducting transmon qubits. Especially, focus was on investigating the predictability of the plasma frequency of the transmon, from which its operational properties are govern. In turn, the plasma frequency is governed by the normal state resistance of the two Josephson junctions along with its total capacitance. In previous experiments, this frequency predictability relied entirely upon successful simulations of the system. However, even small simulation errors prove to generate severe consequences for the system and a better, more systematic control is desired. In order to identify and minimize this uncertainty, subsystems of the transmon were isolated and investigated. Test structures were fabricated and used to measure the normal state resistance of tunnel junctions with different areas and oxidation parameters using a four-point probe setup. A regime within which the reproducibility is increased was statistically identified. The shunt capacitance, i.e. the largest contribution to the total capacitance, of transmons was extracted by coupling identical capacitors to resonators. The coupling capacitance of a resonator is related to its external quality factor which was measured from analyzing the reflected microwave signal at cryogenic temperatures. The smallest standard deviation of normal state resistances for 110 junction pairs was measured for junctions with an area 2.37 um^2 to be 1.48%, corresponding to an uncertainty contribution of 2 MHz for a designed plasma frequency of 6 GHz. Six resonators were measured throughout the shunt capacitance experiment and a linear t was used to compare the results with a written model based on conformal mapping.