Superconducting quantum interference device (SQUID) arrays have been widely investigated to extend the functionality of a single SQUID. Despite the existence of models for SQUID arrays at low-temperatures, these models fail to correctly predict the response of arrays operating at higher temperatures.

Here we will discuss a new model capable of simulating the response of 2D SQUID arrays operating at high-temperatures [1] and we will prove its validity by comparing our model with experimental data of YBCO SQUID arrays [1, 2]. We will show the capabilities of this model by independently studying several array parameters. In particular, we will compare the voltage to magnetic field response of 1D and 2D SQUID arrays showing its dependence on the number of Josephson junctions connected in parallel and in series [1, 3]. Then we will analyse these results for arrays with different SQUID loop sizes [4]. These results will show that the coupling radius [4, 5], limits the magnetic field response to increase beyond a certain number of junctions in parallel.
In summary, with this work we aim to demonstrate the importance of considering the effects of thermal noise as well as using a complete theoretical description of 2D arrays to accurately model these devices.

[1] M.A. Galí Labarias, K-H. Müller and E.E. Mitchell, Phys. Rev. Applied, 17, 064009 (2022)
[2] K-H. Müller and E.E. Mitchell, Phys. Rev. B 103, 054509 (2021)
[3] E.E. Mitchell et al., Superconductor Science and Technology,  32, 124002 (2019).
[4] M.A. Galí Labarias, K-H. Müller and E.E. Mitchell, IEEE Trans., Appl. Supercond. 32, 1600205 (2022)
[5] V. Kornev et al., IEEE Trans. Appl. Supercond. 21 (3) pp. 394-398 (2011)