# Enhancing Precision in SQUID Sensors: Analyzing Washer Geometry Dependence at the Microscale
## 6 Conclusions  
This study uses the Python package for modeling and optimizing SQUID devices, streamlining design processes. We investigated how washer geometries (circular, octagonal, and square) affect SQUID performance, focusing on washer inductance, shielding currents, and the noise spectrum. Shielding current simulations indicated that the octagonal geometry distributes the current more evenly, minimizing high-current density regions that contribute to vortex movement and 1/f noise; this uniform current distribution leads to a reduction in 1/f noise. The noise spectrum analysis showed that circular and octagonal washers produce lower noise levels across a range of frequencies. The results show circular and octagonal washers enhance sensitivity and reduce noise better than traditional square washers. These discoveries hold great potential for breakthroughs in a number of fields, such as increased sensitivity to tiny magnetic fields that can speed up data processing and, in the case of medical instrumentation applications, significantly improve the spatial resolution of devices. With the growing demand for detecting extremely weak magnetic fields, SQUIDs, with a sensitivity at the \(fT/\sqrt{\mathrm{Hz}}\) level and noise at the \(\mu\Phi_{0}/\sqrt{\mathrm{Hz}}\) level, play a crucial role in enabling high-resolution magnetic field sensing [37]. Our research lays the groundwork for achieving femtotesla sensitivity and beyond in SQUID sensors through meticulous optimization, representing a significant leap in weak magnetic field detection. However, integrating these optimized washer designs into diverse SQUID applications and scaling up for mass production while maintaining precision remain the primary challenges for future endeavors.  
Conceptualization, Y.Z. and X.Q.; methodology, X.Q. and G.L.; software, X.Q. and Q.L.; validation, Y.Z. and C.W.; formal analysis, Y.Z. and X.Q.; investigation, X.Q. and C.W.; resources, Y.Z. and X.Q.; data curation, Y.Z., X.Q. and J.Y.; writing--original draft preparation, Y.Z. and X.Q.; writing--review and editing, Y.Z.; visualization, X.Q.; supervision, Y.Z. and W.L.; project administration, Y.Z. and W.L.; funding acquisition, Y.Z. and W.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Foundation of State Key Laboratory of Dynamic Measurement Technology (2023-SYSJ-05), the National Natural Science Foundation of China (62201523), the Fundamental Research Program of Shanxi Province (20210302124329), and the Innovative Research Group Project of the National Science Foundation of China (51821003).  
Not applicable.  
The original contributions presented in the study are included in the article, and further inquiries can be directed to the corresponding author.  
We extend our heartfelt thanks to [PERSON] of the Department of Physics, Stanford University, for the generous support and invaluable assistance provided throughout our research.  
The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of the data; in the writing of the manuscript; or in the decision to publish the results.