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Simulating wafer bow for integrated capacitors using a multiscale approach

Simulation der Waferverbiegung von integrierten Kondensatoren über einen Multiskalenansatz. Simulation der Scheibenverbiegung für integrierte Kondensatoren mit einem Multiskalen-Ansatz
: Wright, Alan; Krach, Florian; Thielen, Nils; Grünler, Saeideh; Erlbacher, Tobias; Pichler, Peter

Postprint urn:nbn:de:0011-n-4105118 (4.0 MByte PDF)
MD5 Fingerprint: fe00a1e2182e7a087b5fa06a80cd0404
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Erstellt am: 18.8.2016

Institute of Electrical and Electronics Engineers -IEEE-:
17th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems, EuroSimE 2016 : Montpellier, 18-20 April 2016
Piscataway, NJ: IEEE, 2016
ISBN: 978-1-5090-2106-2
International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems (EuroSimE) <17, 2016, Montpellier>
European Commission EC
FP7-ICT; 619246; ATHENIS 3D
Automotive Tested High Voltage and Embedded Non-Volatile Integrated System on Chip platformemploying 3D Integration
Konferenzbeitrag, Elektronische Publikation
Fraunhofer IISB ()
wafer bow; integrated capacitor; Multiscale Simulation; microelectronics; microsystems; thermal expansion; coefficients of thermal expansions; conductive layer; effective stiffness tensors; homogeneous materials; integrated capacitors; intrinsic strain; multi-scale approaches; volume change

To simulate the bow of wafers with integrated capacitors in the form of pit arrays, various approaches were pursued. After unfruitful attempts to reliably obtain the wafer bow directly from simulating part of the wafer, a multi-scale approach was used. In this approach, the layer with the integrated capacitors was replaced by a homogeneous material having the same properties. Small-scale simulations of representative parts of the layer were performed to determine its effective stiffness tensor. Inclusion of the intrinsic strains of the grown and deposited dielectric and conductive layers enabled the volume change to be calculated of the layer with the integrated capacitors upon fabrication. Finally, the structure obtained was used in a full-wafer-scale model to simulate the bow of the wafers. Even for uncalibrated values for the coefficients of thermal expansion, most simulations agreed well with measurements.