Download this article
 Download this article For screen
For printing
Recent Issues

Volume 20, 1 issue

Volume 19, 5 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 1559-3959 (online)
ISSN 1559-3959 (print)
 
Author index
To appear
 
Other MSP journals
A mechanical model for direct wafer bonding by strain energy under normal pressure

Shirong Cai, Yunyun Sun, Shijing Wu and Henry Tan

Vol. 20 (2025), No. 1, 1–14
Abstract

Direct wafer bonding is widely applied in the fabrication of microelectromechanical systems. In this study, a mathematical model is proposed to analyze the interface contact behavior during direct wafer bonding. The model describes the wafer bonding process before the bonding pressure is released and takes into account the curvature of the both wafers. The wafer bonding process is analyzed for different wafer curvatures and thicknesses, and the bonding results are predicted. Results show that the critical contact radius, deflections and strain energy increase nonlinearly with the increase of bonding pressure. It is also observed that the smaller the curvature and thickness of the wafer, the easier it is to bond successfully. Due to the assumption that κ1 > κ2, the curvature and thickness of the lower wafer have less influence on the bonding result than the upper wafer, but still cannot be neglected. Finally, the correctness of the proposed model is verified by finite element simulation. This study can provide a reference for the design of bonding pressure and initial geometry of wafers in industrial applications.

Keywords
direct wafer bonding, mathematical model, contact mechanics, strain energy
Milestones
Received: 17 April 2024
Revised: 11 November 2024
Accepted: 20 December 2024
Published: 20 January 2025
Authors
Shirong Cai
School of Power and Mechanical Engineering
Wuhan University
Wuhan City, 430072
China
Yunyun Sun
School of Power and Mechanical Engineering
Wuhan University
Wuhan City, 430072
China
Shijing Wu
School of Power and Mechanical Engineering
Wuhan University
Wuhan City, 430072
China
Henry Tan
School of Engineering
University of Aberdeen
Aberdeen, AB243UE
United Kingdom