The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Wafer bin map failure pattern recognition using hierarchical clustering

계층적 군집분석을 이용한 반도체 웨이퍼의 불량 및 불량 패턴 탐지

  • 정주원 (고려대학교 데이터 통계학과) ;
  • 정윤서 (고려대학교 데이터 통계학과)
  • Received : 2022.02.22
  • Accepted : 2022.03.20
  • Published : 2022.06.30
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Abstract

The semiconductor fabrication process is complex and time-consuming. There are sometimes errors in the process, which results in defective die on the wafer bin map (WBM). We can detect the faulty WBM by finding some patterns caused by dies. When one manually seeks the failure on WBM, it takes a long time due to the enormous number of WBMs. We suggest a two-step approach to discover the probable pattern on the WBMs in this paper. The first step is to separate the normal WBMs from the defective WBMs. We adapt a hierarchical clustering for de-noising, which nicely performs this work by wisely tuning the number of minimum points and the cutting height. Once declared as a faulty WBM, then it moves to the next step. In the second step, we classify the patterns among the defective WBMs. For this purpose, we extract features from the WBM. Then machine learning algorithm classifies the pattern. We use a real WBM data set (WM-811K) released by Taiwan semiconductor manufacturing company.

반도체는 제조 공정이 복잡하고 길어 결함이 발생될 때 빠른 탐지와 조치가 이뤄져야 결함으로 인한 손실을 최소화할 수 있다. 테스트 공정을 거쳐 구성된 웨이퍼 빈 맵(WBM)의 체계적인 패턴을 탐지하고 분류함으로써 문제의 원인을 유추할 수 있다. 이 작업은 수작업으로 이뤄지기 때문에 대량의 웨이퍼를 단 시간에 처리하는 데 한계가 있다. 본 논문은 웨이퍼 빈 맵의 정상 여부를 구분하기 위해 계층적 군집 분석을 활용한 새로운 결함 패턴 탐지 방법을 제시한다. 제시하는 방법은 여러 장점이 있다. 군집의 수를 알 필요가 없으며 군집분석의 조율 모수가 적고 직관적이다. 동일한 크기의 웨이퍼와 다이(die)에서는 동일한 조율 모수를 가지므로 대량의 웨이퍼도 빠르게 결함을 탐지할 수 있다. 소량의 결함 데이터만 있어도 그리고 데이터의 결함비율을 가정하지 않더라도 기계학습 모형을 훈련할 수 있다. 제조 특성상 결함 데이터는 구하기 어렵고 결함의 비율이 수시로 바뀔 수 있기 때문에 필요하다. 또한 신규 패턴 발생시에도 안정적으로 탐지한다. 대만 반도체 기업에서 공개한 실제 웨이퍼 빈 맵 데이터(WM-811K)로 실험하였다. 계층적 군집 분석을 이용한 결함 패턴탐지는 불량의 재현율이 96.31%로 기존의 공간 필터(spatial filter)보다 우수함을 보여준다. 결함 분류는 혼합 유형에 장점이 있는 계층적 군집 분석을 그대로 사용한다. 직선형과 곡선형의 긁힘(scratch) 결함의 특징에 각각 주성분 분석의 고유값과 2차 다항식의 결정계수를 이용하고 랜덤 포레스트 분류기를 이용한다.

Keywords

Acknowledgement

이 논문은 2021년도 정부(과학기술정보통신부)의 재원으로 한국연구재단의 지원을 받아 수행된 연구임 (2021R1F1A1062347). 또한 고려대학교의 지원을 받아 수행된 연구임 (K2122591).

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