Abstract
This paper presents an overview of the modeling and model based control of the microvia fill process. A detailed, general-purpose microvia fill model that utilizes the arbitrary Lagrange–Eulerian method for shape change modeling is presented first. Modeling results are presented and compared with the measured data. Then a simplified model of the process is presented followed by a model based control algorithm being developed based on the simplified stochastic model with typical uncertainties induced by unmodelled phenomena and measurement error. The developed control algorithm is analyzed in terms of possible control errors and applied to control the firstly presented microvia fill process model.
Similar content being viewed by others
References
T.P. Moffat, D. Wheeler, W.H. Huber, D. Josell, Electrochem. Solid-State Lett. 4, C26–C29 (2001)
T.P. Moffat, D. Wheeler, D. Josell, Electrochem. Soc. Interface 13, 46–52 (2004)
T.P. Moffat, D. Wheeler, S.K. Kim, D. Josell, J. Electrochem. Soc. 153, C127–C132 (2006)
D. Josell, T.P. Moffat, D. Wheeler, J. Electrochem. Soc. 154, D208–D214 (2007)
D. Wheeler, D. Josell, T.P. Moffat, J. Electrochem. Soc. 150, C302–C310 (2003)
W.-P. Dow, H.-S. Huang, Z. Lin, Electrochem. Solid-State Lett. 6, C134–C136 (2003)
W.-P. Dow, H.-S. Huang, J. Electrochem. Soc. 152, C67–C88 (2005)
W.-P. Dow, M.-Y. Yen, S.-Z. Liao, Y.-D. Chiu, H.-S. Huang, Electrochim. Acta 53, 8228–8237 (2008)
P.C. Andricacos, C. Uzoh, J.O. Dukovic, J. Horkans, H. Deligianni, IBM J. Res. Dev. 42, 567–574 (1998)
P.M. Vereecken, R.A. Binstead, H. Deligiani, P.C. Andricacos, IBM J. Res. Dev. 49, 3–18 (2005)
A.C. West, J. Electrochem. Soc. 147, 227–232 (2000)
A.C. West, S. Mayer, J. Reid, Electrochem. Solid-State Lett. 4, C50–C53 (2001)
Y. Cao, P. Taephaisitphongse, R. Chalupa, A.C. West, J. Electrochem. Soc. 148, C466–C472 (2001)
M. Lefebvre, G. Allardyce, M. Seita, H. Tsuchida, M. Kusaka, S. Hayashi, Circuit World 29, 9–14 (2003)
J.F. Coombs Jr, Printed Circuits Handbook (eBook), 6th edn. (McGraw-Hill, New York, 2008)
J. Donea, A. Huerta, Finite Element Methods for Flow Problems (Wiley, New York, 2003)
A. Pohjoranta, R. Tenno, J. Electrochem. Soc. 154, D502–D509 (2007)
T.P. Moffat, D. Wheeler, S.K. Kim, D. Josell, Electrochim. Acta 53, 145–154 (2007)
Y. Kaneko, Y. Hiwatari, K. Ohara, Mol. Simul. 30, 895–899 (2004)
T.J. Pricer, M.J. Kushner, R.C. Alkire, J. Electrochem. Soc. 149, C406–C412 (2002)
X. Li, T.O. Drews, E. Rusli, F. Xue, Y. He, R. Braatz, R. Alkire, J. Electrochem. Soc. 154, D230–D240 (2007)
A. Pohjoranta, R. Tenno, Eng. Comput. 27, 165–175 (2011)
R. Tenno, A. Pohjoranta, J. Electrochem. Soc. 155, D383–D388 (2008)
R. Tenno, A. Pohjoranta, Int. J. Control 82, 883–893 (2009)
R. Tenno, Int. J. Control 85, 1807–1826 (2012)
I. Karatzas, S. Shreve, Brownian Motion and Stochastic Calculus, 2nd edn. (Springer, Berlin, 1991)
R. Tenno, Evolution of the regulation errors in the diffusion layer in electrodeposition process control. IFAC J. Proc. Control 24 (2014, in press)
R. Tenno, A. Pohjoranta, Simul. study IFAC J. Proc. Control 22, 228–235 (2012)
R. Tenno, IFAC J. Proc. Control 24, 82–92 (2014)
J.L. Lions, Optimal Control of Systems Covered by Partial Differential Equations (Springer, Berlin, 1971)
G. Da Prato, J. Zabczyk, Stochastic Equations in Infinite Dimensions (Cambridge University Press, Cambridge, 1992)
G. Da Prato, Kolmogorov Equation for Stochastic PDEs (Springer, Berlin, 2004)
Acknowledgments
Timo Närhi of Meadville Aspocomp Intl. Ltd. is thanked for his comments on PCB manufacturing today.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pohjoranta, A., Tenno, R. Microvia fill process model and control. J Math Chem 52, 1414–1440 (2014). https://doi.org/10.1007/s10910-014-0320-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-014-0320-6