Strain gradient crystal plasticity theoryfor modeling of metal thin film behaviorI. Ertürk, J.A.W. van Dommelen and M.G.D. Geers

Mechanics of Materials

/department of mechanical engineering

IntroductionRF-MEMS switches are tunable parallel plate capacitorsto be used in next generation wireless technologies.Their moveable electrodes are made of a free-standingthin metal film, which can show irreversible and timedependent reversible deformation, Figure. 1.

Figure. 1: An RF-MEMS device before (a) and after (b) prolonged actuation times.

Thin film behaviorScale dependent behaviorAs dimensions of materials become comparable withtheir intrinsic length scales, their mechanical behaviordeviates from those in bulk form, see Figure. 2a.

Figure. 2: a) Moment-strain curves of Ni films of different thicknesses, [1]. b) Stress-strain curves from bulge test experiments on Al film, [2].

Time dependent behaviorTwo different time dependent phenomena are observedin thin metal films:• Creep: irreversible deformations under constant loads.• Anelasticity: Recovery of deformation over time afterunloading, which is not common for bulk metals (seeFigure 2b).

ObjectiveThis study aims at:• The extension of a present strain gradient crystalplasticity theory (SGCP) [3] to account for the timedependent mechanical behavior of thin films.• The implementation of it for the solution of a multi-domain boundary value problem (MBVP), see Figure 3a.

Fig. 3: a) Schematic representation of the MBVP. b) Numerical model ofan RF-MEMS device.

Method• Current flow rule of SGCP is to be enhanced for theincorporation of real time dependent behavior:

• A numerical model of an RF-MEMS device is built byusing:

− SGCP for mechanical domain.− Reynolds squeeze film theory and theory ofrarefied gases for the fluid domain [4].− Electro-mechanical transducer [5] for electrostaticsdomain, see Figure. 3b.

DiscussionBy extending SGCP, the effect of length scales on thetime dependent mechanical response of thin films, whichis crucial for the trustful estimation of life time of RF-MEMS switches, can be captured. Use of this extendedtheory together with the other domains provides anengineering tool for the optimized design of RF-MEMSdevices.

References[1] J.S. Stölken, A.G. Evans: Acta Mater. 46 (1998) 5109[2] S. Hyun et al.: Appl. Phy. Lett. 87 (2005) 061902-1[3] İ. Ertürk et al.: J. Mech. Phys. Sol. 57 (2009) 1801[4] F. Sharipov (1999) J. Vac. Sci. Technol. A17(5) 3062[5] M. Gyimesi, D. Ostergaard: Proceedings of MSMC’99

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