Real-Time Monitoring and Prediction of Defects in 2D Materials Synthesis Using Kalman Filtering

2D materials, epitomized by graphene, are at the forefront of materials science due to their novel electronic, optical, and mechanical properties. However, the inherent imperfections or defects that emerge during their fabrication can significantly modulate these properties, thus affecting their utility in technological applications. This research introduces a sophisticated methodology using the Kalman filter to continuously monitor and estimate the imperfections in 2D materials during their synthesis. By simulating the growth of these materials and introducing controlled defects, we integrate noisy measurements—akin to real-world fabrication uncertainties—into our model. Our results demonstrate that the Kalman filter, traditionally employed in navigation and control systems, can effectively track, and predict the density and propagation of imperfections, offering a significant advantage over traditional monitoring methods. The findings not only open avenues for enhancing the quality and consistency of 2D material fabrication but also underscore the versatility of the Kalman filter in novel applications outside its conventional domains.