Diagnostic microstructures for the measurement of intrinsic strain in thin films

Abstract

Freestanding flexible microstructures fabricated from deposited thin films become mechanically unstable when internal stresses exceed critical values. A series of structures with varying geometries is used to determine the critical geometry at which buckling occurs. Observation with an optical microscope quickly reveals qualitative and quantitative information about the internal strain in the film. Strain values between +or-1.5% can be measured for a 2.0 mu m thick film using doubly-supported beams for compressive strain fields, and ring and beam structures for tensile strain fields. Parametric formulae are developed for diagnostic structure response with selected verification by finite element computations.

<title>Interferometric measurement for improved understanding of boundary effects in micromachined beams</title>

“…Recall from Equations (1) and (2) that the model indicates that everything about the pad is known if the equivalent length L~p and cross-sectional moment of inertia Z~Pare known. If Lo and Lb are defined as the equivalent support post cantilever lengths found using the (3'sand /5's,respectively, then and (4) (5) which are derived from Equations (1) and (2). If model 1 is correct, then these two equivalent lengths should be equal.…”

“…For example, cantilever beams have been used to measure curvature resulting from a strain gradient [1][2][3] as well as Young's modulus [3]. A number of researchers have also used fixed-fixed beams to measure residual stress [1][2][3][4][5][6][7]. Most of these researchers have concluded that boundary conditions at the beam ends significantly affect the accuracy of the measurements.…”

Using ElectroMechanical Buckling for Measuring Residual Stress

“…The total potential may be written in the following normalized form For any given ~ and Ẽ , the deflection of the beam at the critical buckling state can be derived by extracting the constant parameters from (11) and substituting them into the general solution (8). This calculation yields the mode of the deflection at the onset of buckling g x f,…”

“…In some of these structures the buckling phenomenon is utilized to measure residual stress. Notable among these passive test structures are clamped-clamped beams and Gukel rings [11]. Compressive residual stress can cause buckling in clamped-clamped beams.…”

“…However, this method is incapable of measuring tensile residual stress. To this end, Gukel rings were proposed [11].…”