Abstract Body

I. Introduction
We have previously developed a Monte Carlo simulation for the crystal growth of REBCO thin films and investigated the self-organization of BaMO₃ (BMO, M=Zr, Sn, Hf…) in REBCO thin films doped with BMO [1]. However, this simulation has the issue that the grain size of REBCO is smaller than that observed in actual experimental results. In this study, we aimed to improve the accuracy of the REBCO crystal growth simulation by using Bayesian optimization to compare experimental and simulation results and investigate for simulation parameters that can reproduce experimental results.

II. Simulation
The simulation in this study is a crystal growth simulation using the Monte Carlo method, and the simulation code developed in reference [1] was used. The number and size of the islands of REBCO thin film crystals vary depending on the binding energy between REBCO molecules (E_AA), the binding energy between REBCO and the substrate (E_AS), and the evaporation energy from the substrate (E_des). In this study, E_des was fixed at 10000 K, and Bayesian optimization was used to optimize E_AA and E_AS in the range of 0 to 10000 K. The objective variable in Bayesian optimization was the crystal island density (σ) of REBCO, and an evaluation function f that becomes maximize when the experimental results [2] and the simulation results coincide was defined as follows.

Here, x = log10 𝜎, and 𝑥_𝑒𝑥 corresponds to the experimental YBCO island density 𝜎_𝑒𝑥. 𝑓(𝑥) is a Gaussian distribution centered at 𝑥_𝑒𝑥, with a full width at half maximum of ｗ.

III. Results and discussion
Fig. 1 shows the results of Bayesian optimization when E_AA and E_AS are varied in the range of 0 to 10000 K. From the figure, the parameters with the maximum evaluation function at present are around E_AA = 500 K and E_AS = 4000 K. Fig. 2 shows the evolution of the evaluation function value over 40 iterations of the Bayesian optimization. The results indicate that the evaluation function increased until the 21st iteration but plateaued thereafter. This suggests that varying only E_AA and E_AS was insufficient to achieve a satisfactory fit to the experimental data, as the maximum attainable value of the evaluation function (f=0.091) was significantly lower than the objective value of 1.

To further explore the parameter space and potentially improve the fit to the experimental data, we will present results from a Bayesian optimization study where all three parameters, E_AA, E_AS, and E_des, are varied.

References

[1] Y. Ichino, et al., JJAP 56 (2017) 015601, IEEE TAS 27 (2017) 7500304, IEEE TAS 31 (2021) 7500204.
[2] B. Dam, J.H. Rector, J.M. Huijbregtse, R. Griessen, Physica C 305 (1998) 1-10.

Acknowledgment

This research was supported by JST-CREST (JPMJCR2336). The AFM measurements were performed using an instrument provided by the Yoshida Laboratory, Department of Electrical Engineering, Nagoya University.

Figure 1. Distribution of evaluation function values for 40 different combinations of EAAand EAS, ranging from 0 to 10000 K.
Figure 2. Evaluation function values as a function of the number of Bayesian optimization iterations.

Keywords: Bayesian optimization, Monte Carlo simulation, REBCO thin film, crystal growth