Optimal reduction of a spatial monitoring grid: Proposals and applications in process control

Borgoni, Riccardo; Radaelli, Luigi; Tritto, Valeria; Zappa, Diego

doi:10.1016/j.csda.2012.08.007

Cited by 9 publications

(10 citation statements)

References 22 publications

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“…Along this paper, a specific data set is used, compare with the related paper . The data are masked for confidentiality reasons: we cannot identify the source nor give any further detail on the technology.…”

Section: The Modelmentioning

confidence: 99%

“…We will consider a case study based on industrial data, kindly communicated to us by the organizers of the workshop Statistical methods applied in microelectronics , 13 June 2011, Università Cattolica del Sacro Cuore, Milano, concerning the measurements of the thickness of the SiO 2 deposition during the silicon wafer's diffusion process, see . The control quality operators, which make the data available, use a peculiar experimental design on the circular surface of each wafer.…”

Section: Introductionmentioning

confidence: 99%

“…In absence of a specific physical model of the diffusion process, one phenomenological option would be to consider a regression model, for example, see . Here, we follow mainly , where the authors explore various fractions of the full design and use the ordinary Kriging model, a natural candidate for the interpolation algorithm and for predicting the thickness values at untried points.…”

Section: Introductionmentioning

confidence: 99%

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Kriging prediction from a circular grid: application to wafer diffusion

Pistone

Vicario

2013

Appl Stoch Models Bus & Ind

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In the production process of silicon wafers, which are crystalline slices used as substrate of electronic micro-circuits, the thickness of the SiO 2 deposition on their top is a main characteristic to be controlled during the process. The experimental design that is commonly used to monitor the thickness to the target value consists of a regular array of points lying on concentric circles, the silicon wafer itself being a disk. To speed up the control process, the engineers aim to use just only a limited subset of such points. To reconstruct the values on untried locations of the silicon wafer, the Kriging interpolation has been proposed because of its recognized ability in providing fairly good predictions. In this paper, we consider two methodological issues related to universal Kriging models. First, we discuss the modeling of the covariance structure among the measured points; in fact, spatial data usually show a strong correlation when they come from spatially near observed points. Second, we put forward an algebraic method to assess the identifiability of trend models, based both on the full experimental design and on special fractions of it. Our findings are illustrated by a data set from an industrial application.

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Section: The Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kriging prediction from a circular grid: application to wafer diffusion

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2013

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“…Although issues related to quality control of semiconductor process have been mostly considered by physics engineering and chemistry literature so far, articles emphasizing the use of statistical methods in this field have recently appeared ( amongst others).…”

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Statistics for microelectronics

Borgoni

Deldossi

Radaelli

et al. 2013

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This paper introduces a special issue entirely devoted to the topic 'Statistics for Microelectronics'. The relevance of the theme for this journal is due to both the primary role that microelectronics has in many business activities of the modern society and to the complexity of the production process of integrated circuits that are obtained by several different steps performed on a wafer (i.e., a thin silicon slice of a few inches of diameter). Advanced statistical methods are necessary to monitor and improve this process because the yield of this industrial manufacturing is typically tiny and requires a very high precision. After a brief review of the semiconductor manufacturing process, we point out how statistical methodologies can contribute to this. Finally, we introduce the papers that discuss some key aspects of this subject. Copyright © 2013 John Wiley & Sons, Ltd.Keywords: semiconductor manufacturing; integrated circuit; process control Microelectronics industry faces a relevant role in modern society. Microchips, which control electronic devices, enable systems and products that we use to work, communicate, travel, entertain, harness energy, treat illness, and make scientific discoveries. They are present in several different kinds of objects, ranging from computers, tablets and smartphones to cars and planes, household appliances, and military systems.Also, the huge advances in medical devices are being driven by most recent developments in semiconductors that permit to reduce size, cost, and power consumption of medical electronic devices, yet boasting significant improvement in overall performance. A variety of not invasive, portable, and wearable devices are now usable to monitor the condition of a patient, such as the contact lens sensor for continuous monitoring of intra-ocular pressure. Moreover, several implantable and invasive medical devices are available as well, such as insulin pump for drug delivery and defibrillators.Over the last 50 years, the semiconductors content in electronic equipment has grown up significantly, raising from 2% in 1965 to 23% in 2012, when the total worldwide semiconductor revenue reached $299.9 bn.

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“…Borgoni et al [2] proposed a simulated annealing and spatial prediction strategy to optimise the selection of a reduced set of sites from a larger candidate grid for a silicon oxide deposition process.…”

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confidence: 99%