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TECHNICAL PAPERS

[+] Author and Article Information
Rongjing Zhang, Guruswami Ravichandran, Kaushik Bhattacharya

Division of Engineering and Applied Science,  California Institute of Technology, Pasadena, CA 91125

Doron Shilo

Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, Haifa 32000, Israel

J. Appl. Mech 73(5), 730-736 (Nov 16, 2005) (7 pages) doi:10.1115/1.2166652 History: Received July 05, 2005; Revised November 16, 2005

## Abstract

The design of reliable micro electro-mechanical systems (MEMS) requires understanding of material properties of devices, especially for free-standing thin structures such as membranes, bridges, and cantilevers. The desired characterization system for obtaining mechanical properties of active materials often requires load control. However, there is no such device among the currently available tools for mechanical characterization of thin films. In this paper, a new technique, which is load-controlled and especially suitable for testing highly fragile free-standing structures, is presented. The instrument developed for this purpose has the capability of measuring both the static and dynamic mechanical response and can be used for electro∕magneto∕thermo mechanical characterization of actuators or active materials. The capabilities of the technique are demonstrated by studying the behavior of $75nm$ thick amorphous silicon nitride $(Si3N4)$ membranes. Loading up to very large deflections shows excellent repeatability and complete elastic behavior without significant cracking or mechanical damage. These results indicate the stability of the developed instrument and its ability to avoid local or temporal stress concentration during the entire experimental process. Finite element simulations are used to extract the material properties such as Young’s modulus and residual stress of the membranes. These values for $Si3N4$ are in close agreement with values obtained using a different technique, as well as those found in the literature. Potential applications of this technique in studying functional thin film materials, such as shape memory alloys, are also discussed.

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## Figures

Figure 1

(a) Schematic illustration of the experimental setup; (b) Photograph of the experimental apparatus

Figure 2

Schematics of the loading system, (a) at the point where the tip first comes into contact with the sample; (b) at some arbitrary moment during the experiment. d0 is the initial distance between the upper and lower magnets at the moment as shown in (a); d is the distance between the magnets at some arbitrary loading; z0 is the initial reading of the upper magnets position; z is the absolute position at some arbitrary loading moment.

Figure 3

The applied force, F in mN, as a function of the change in the position (displacement) of the upper magnet, Δz in mm for the identical z0 as in the experiments. This response curve was obtained by applying force on a load cell.

Figure 4

The tip displacement, u, as a function of the position of the upper magnet, z. The slope of the curve changes abruptly at the point where the tip first comes into contact with the sample. The maximum value of Δu is less than 50μm, for a change in position of the upper magnet which is on the order of 10mm, 3 orders of magnitude larger than Δu. As a consequence, the load is completely determined by z and the setup is working in load-control mode.

Figure 5

Figure 6

A series of optical images of a Si3N4 membrane under different loads (corresponding load (F) and displacement (d) are indicated). These images were captured by a CCD camera mounted on the microscope above the membrane. In each image, the gray square is the Si3N4 membrane (window); the circular region is the ruby ball tip; the small dark region in the center which expands when loading increases is the contact area.

Figure 7

A wafer consisting of 6×6 devices (insert) was tested at various locations. The mechanical responses of five membranes located at different regions of the same wafer are highly repeatable.

Figure 8

Schematic diagram of a ridged spherical loading tip deforming a free-standing membrane. The relevant geometric variables are labeled.

Figure 9

Load-deflection (F‐d) curve obtained from the finite element simulation and is used to obtain the shape factors in Eq. 2. The solid curve is the fit and the solid dots are the finite element analysis data.

Figure 10

Least square fitting of force-displacement (F‐d) curve of the experimental data for extracting material properties using Eqs. 4,5

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