Method to Build a Predictive Control Model for a Semiconductor Wafer Process Based on Historical Data of Many Products in Small Quantities : Statistical Predictive Model for Engineering Service using MCMC Method

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  • 多品種小量生産履歴データに基づく半導体ウェハ加工プロセス予測制御モデルの構築手法 : MCMC法による統計的予測モデル構築のエンジニアリングサービス実現(事例研究,<特集>サービス工学)
  • 多品種小量生産履歴データに基づく半導体ウェハ加工プロセス予測制御モデルの構築手法 : MCMC法による統計的予測モデル構築のエンジニアリングサービス実現
  • タヒンシュ ショウリョウ セイサン リレキ データ ニ モトズク ハンドウタイ ウェハ カコウ プロセス ヨソク セイギョ モデル ノ コウチク シュホウ : MCMCホウ ニ ヨル トウケイテキ ヨソク モデル コウチク ノ エンジニアリングサービス ジツゲン

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Abstract

This paper proposes a generic methodology for engineering service to build a statistical predictive model based on historical data of many products in small quantities. The methodology is evaluated via simulations for polishing rate prediction in a semiconductor chemical mechanical polishing (CMP) process. The process control model enables process engineers to control the polished amOunt, while the equipment monitoring model enables equipment maintenance engineers to replace consumed materials at the appropriate point. The model can quickly predict the polishing rate based on equipment-derived data to ensure prompt handling of high-speed process drift. However, the polishing rate varies randomly in the production of many products in small quantities. To separate the equipment drift in the polishing rate from the seemingly random effects of product switching, we developed a new predictive model and method for building this model. In the methodology, multilevel model configuration is employed to allow the polishing rate prediction model to be adjusted to individual variability of products. Parameters of the complicated predictive model including those for individual variability of products are identified using a procedure including Markov chain Monte Carlo (MCMC) sampling from probability variables defined in a hierarchical Bayesian model. Simulation results show that the proposed methodology could identify the model parameters for individual variability of products with a high degree of accuracy despite the skewed distribution of data of many products in small quantities. Furthermore, root-mean-square deviations of the control of polished amount are suppressed by 20% using the predictive model. The results show that the methodology is suitable for use in engineering service.

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