Cleanroom contamination and its impact on the performance of devices are beginning to be investigated due to the increasing sensitivity of the semiconductor manufacturing process to airborne molecular contamination (AMC). A clean bench was equipped with different filter modules and then most AMC in the cleanroom and in the clean bench was detected through air-sampling and wafer-sampling experiments. Additionally, the effect of AMC on device performance was examined by electrical characterization. A combination of the NEUROFINE PTFE filter and chemical filters was found to control metal, organic, and inorganic contamination. We believe that the new combination of filters can be used to improve the manufacturing environment of devices, which are being continuously shrunk to the nanometer scale.

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Airborne molecular contamination (AMC) is becoming increasingly important as devices are scaled down to the nanometer generation. Optimum ultra low penetration air (ULPA) filter technology can eliminate AMC. In a cleanroom, however, the acid vapor generated from the cleaning process may degrade the ULPA filter, releasing AMC to the air and the surface of wafers, degrading the electrical characteristics of devices. This work proposes the new PTFE ULPA filter, which is resistant to acid vapor corrosion, to solve this problem. Experimental results demonstrate that the PTFE ULPA filter can effectively eliminate the AMC and provide a very clean cleanroom environment.

In this paper, we provide a mathematical and statistical methodology using heteroscedastic estimation to achieve the aim of building a more precise mathematical model for complex financial data. Considering a general regression model with explanatory variables (the expected value model form) and the error term (including heteroscedasticity), the optimal expected value and heteroscedastic model forms are investigated by linear, nonlinear, curvilinear, and composition function forms, using the minimum mean-squared error criterion to show the precision of the methodology. After combining the two optimal models, the fitted values of the financial data are more precise than the linear regression model in the literature and also show the fitted model forms in the example of Taiwan stock price index futures that has three cases: (1) before COVID-19, (2) during COVID-19, and (3) the entire observation time period. The fitted mathematical models can apparently show how COVID-19 affects the return rates of Taiwan stock price index futures. Furthermore, the fitted heteroscedastic models also show how COVID-19 influences the fluctuations of the return rates of Taiwan stock price index futures. This methodology will contribute to the probability of building algorithms for computing and predicting financial data based on mathematical model form outcomes and assist model comparisons after adding new data to a database.