In material characterization, identifying defective areas on a material surface is fundamental. The conventional approach involves measuring the relevant physical properties point-by-point at the predetermined mesh grid points on the surface and determining the area at which the property does not reach the desired level. To identify defective areas more efficiently, we propose adaptive mapping methods in which measurement resources are used preferentially to detect the boundaries of defective areas. We interpret this problem as an active-learning (AL) of the level set estimation (LSE) problem. The goal of AL-based LSE is to determine the level set of the physical property function defined on the surface with as small number of measurements as possible. Furthermore, to handle the situations in which materials with similar specifications are repeatedly produced, we introduce a transfer learning approach so that the information of previously produced materials can be effectively utilized. As a proof-of-concept, we applied the proposed methods to the red-zone estimation problem of silicon wafers and demonstrated that we could identify the defective areas with significantly lower measurement costs than those of conventional methods.

翻译：在材料表征中，识别材料表面的缺陷区域是基础性工作。传统方法是在表面预设网格点上逐点测量相关物理特性，并确定特性未达到期望水平的区域。为更高效地识别缺陷区域，我们提出自适应映射方法，优先将测量资源用于检测缺陷区域的边界。我们将该问题解释为水平集估计问题的主动学习。基于主动学习的水平集估计目标是以尽可能少的测量次数确定表面物理特性函数的水平集。此外，为处理规格相近材料重复生产的情况，我们引入迁移学习方法，使先前生产材料的信息能被有效利用。作为概念验证，我们将所提方法应用于硅晶圆红区估计问题，并证明相较于传统方法，我们能以显著更低的测量成本识别缺陷区域。