A new analytical solution for the load-deflection of square membranes

Author

Maier-Schneider, Dieter ; Maibach, J. ; Obermeier, Ernst

Author_Institution

Dept. of Electr. Eng., Tech. Univ. Berlin, Germany

Volume

4

Issue

4

fYear

1995

fDate

12/1/1995 12:00:00 AM

Firstpage

238

Lastpage

241

Abstract

Accurate models are essential for the determination of the elastic properties of thin films from load-deflection experiments. Although finite element method (FEM) models have the potential to be very accurate, analytical models are desirable because of their simplicity. In this paper we present a new analytical solution for the load-deflection of membranes. Our solution yields the same relationship between the load and the deflection as the known analytical solution. However, the values of two constants are up to 35% higher and correspond well with the results from FEM analysis. In addition, the new solution yields analytical forms of the bending lines, which agree well with experimental measurements carried out with silicon nitride membranes

Keywords

bending; membranes; micromechanical devices; silicon compounds; Si₃N₄; bending lines; elastic properties; load deflection; square membranes; suspended thin films; Analytical models; Biomembranes; Capacitive sensors; Finite element methods; Potential energy; Pressure measurement; Residual stresses; Shape measurement; Tensile strain; Transistors;

fLanguage

English

Journal_Title

Microelectromechanical Systems, Journal of

Publisher

ieee

ISSN

1057-7157

Type

jour

DOI

10.1109/84.475551

Filename

475551