IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v58y2013icp407-419.html
   My bibliography  Save this article

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

Author

Listed:
  • Borgoni, Riccardo
  • Radaelli, Luigi
  • Tritto, Valeria
  • Zappa, Diego

Abstract

Deposition of silicon dioxide (SiO2) is a critical step of integrated circuit manufacturing; hence it is monitored during the manufacturing process at a grid of points defined on the wafer area. Since collecting thickness measurements is expensive, it is a compelling issue to investigate how a sub grid can be identified. A strategy based on spatial prediction and simulating annealing is proposed to tackle the problem which proved to be effective when applied to a real process. A diagnostic device for monitoring the deposition process is also discussed which can be usefully adopted in the day-to-day activity by practitioners acting in process control of a microelectronics fab.

Suggested Citation

  • Borgoni, Riccardo & Radaelli, Luigi & Tritto, Valeria & Zappa, Diego, 2013. "Optimal reduction of a spatial monitoring grid: Proposals and applications in process control," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 407-419.
    • Handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:407-419
    DOI: 10.1016/j.csda.2012.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312003106
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.08.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter Diggle & Søren Lophaven, 2006. "Bayesian Geostatistical Design," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(1), pages 53-64, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. K. Shuvo Bakar & Nicholas Biddle & Philip Kokic & Huidong Jin, 2020. "A Bayesian spatial categorical model for prediction to overlapping geographical areas in sample surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 535-563, February.
    2. Victor De Oliveira & Zifei Han, 2022. "On Information About Covariance Parameters in Gaussian Matérn Random Fields," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(4), pages 690-712, December.
    3. Erum Zahid & Ijaz Hussain & Gunter Spöck & Muhammad Faisal & Javid Shabbir & Nasser M. AbdEl-Salam & Tajammal Hussain, 2016. "Spatial Prediction and Optimized Sampling Design for Sodium Concentration in Groundwater," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-16, September.
    4. Hartman, Linda & Hossjer, Ola, 2008. "Fast kriging of large data sets with Gaussian Markov random fields," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2331-2349, January.
    5. Eidsvik, Jo & Finley, Andrew O. & Banerjee, Sudipto & Rue, Håvard, 2012. "Approximate Bayesian inference for large spatial datasets using predictive process models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1362-1380.
    6. Letícia Ellen Dal Canton & Luciana Pagliosa Carvalho Guedes & Miguel Angel Uribe-Opazo, 2021. "Reduction of Sample Size in the Soil Physical-Chemical Attributes Using the Multivariate Effective Sample Size," Journal of Agricultural Studies, Macrothink Institute, vol. 9(1), pages 357-376, June.
    7. Jacopo Paglia & Jo Eidsvik & Juha Karvanen, 2022. "Efficient spatial designs using Hausdorff distances and Bayesian optimization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1060-1084, September.
    8. Finley, Andrew O. & Sang, Huiyan & Banerjee, Sudipto & Gelfand, Alan E., 2009. "Improving the performance of predictive process modeling for large datasets," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2873-2884, June.
    9. Sudipto Banerjee & Alan E. Gelfand & Andrew O. Finley & Huiyan Sang, 2008. "Gaussian predictive process models for large spatial data sets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 825-848, September.
    10. Qian Ren & Sudipto Banerjee, 2013. "Hierarchical Factor Models for Large Spatially Misaligned Data: A Low-Rank Predictive Process Approach," Biometrics, The International Biometric Society, vol. 69(1), pages 19-30, March.
    11. Arbia, Giuseppe & Lafratta, Giovanni & Simeoni, Carla, 2007. "Spatial sampling plans to monitor the 3-D spatial distribution of extremes in soil pollution surveys," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 4069-4082, May.
    12. Elizabeth G. Ryan & Christopher C. Drovandi & James M. McGree & Anthony N. Pettitt, 2016. "A Review of Modern Computational Algorithms for Bayesian Optimal Design," International Statistical Review, International Statistical Institute, vol. 84(1), pages 128-154, April.
    13. Jo Eidsvik & Sara Martino & Håvard Rue, 2009. "Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 1-22, March.
    14. Wang, Craig & Furrer, Reinhard, 2021. "Combining heterogeneous spatial datasets with process-based spatial fusion models: A unifying framework," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    15. Elizabeth Eisenhauer & Ephraim Hanks, 2020. "A lattice and random intermediate point sampling design for animal movement," Environmetrics, John Wiley & Sons, Ltd., vol. 31(6), September.
    16. Shengde Liang & Sudipto Banerjee & Bradley P. Carlin, 2009. "Bayesian Wombling for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 65(4), pages 1243-1253, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:58:y:2013:i:c:p:407-419. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.