Master thesis defense by August Lademark Heegaard

Modeling and Analysis of Josephson Junction Variability for Qubit Fabrication

This thesis investigates the reproducibility and spatial uniformity of Josephson junction (JJ) fabrication for superconducting qubit applications. A novel image analysis pipeline was developed to extract JJ areas from scanning electron microscope (SEM) images with high precision. The refined algorithm significantly improves the correlation with measured conductance (R^2 =0.97) compared to traditional rectangular estimation methods. 

Conductance measurements across nine chips and four junction designs reveal within-chip variations of 2.3–7.6% and chip-to-chip variations up to 25.1%. Smaller junctions exhibit greater relative variation, and both area and conductance show strong spatial dependence across the chip surface. Monte Carlo simulations based on measured JJ variation predict frequency uncertainties in flux-tunable qubits of up to 14%, far exceeding thresholds required for scalable quantum architectures.

Analysis of fabrication parameters identifies oxidation pressure as the dominant factor influencing JJ conductance, while electrode height showed no measurable effect underscoring that only the overlap area of the electrodes is important. 

To investigate the origin of the spatial patterns found, a geometric simulation model of the deposition process was developed. Incorporating finite source size, shadowing from the resist mask, and chip rotation, the model captures 52.9% of the observed spatial variation in JJ area on average, indicating that evaporation source geometry is a major contributor to within-chip variability.

These findings underscore the importance of improving oxidation control and actively monitoring evaporation conditions. The methods and analyses presented here provide a framework for data-driven process optimization for reproducible JJ fabrication at scale. These results provide guidance for improving junction uniformity to support scalable quantum hardware development.