A Fracture Mechanics Model for the Repair of Microcantilevers by Laser Induced Stress Waves

A fracture mechanics model was developed, and experimentally verified, to model stress wave repair of stiction-failed microcantilevers. This model allows us to predict accurately the number of laser pulses, at a specific fluence and wavelength, required to fully repair stiction-failed microcantilevers. The proposed fracture mechanics model includes the strain energy stored in a stiction-failed microcantilever and the strain energy supplied by laser induced stress-waves propagating in the material. The ‘unstuck’ portion of the microcantilever is modeled as a crack so that crack growth reduces the stiction-failed length of the microcantilever. A full range of experiments have been performed to validate the model. Experiments using laser fluences ranging from 0.5 kJ/m – 45 kJ/m at two different wavelengths have been performed. The experiments are in good agreement with the model predictions. Additionally we have identified practical ranges for irradiation, including a lower bound fluence below which repair is impractical, and an upper bound above which damage to the substrate and microcantilevers occurs. INTRODUCTION Construction of MEMS devices are typically limited by fabrication issues [1], primarily because microscale structures are extremely compliant and susceptible to failure by secondary forces. Failure by adhesion to neighboring structures or the substrate is commonly referred to as stiction. If stiction failures can be prevented or repaired, device yields would increase dramatically. As a result, a great deal of effort is focused on research into stiction prevention/repair. Stiction-failed microstructures have been repaired using many different methods, including: laser induced thermomechanical repair [2]; ultrasonic actuation[3]; pulsed Lorentz forces[4]; direct application of force[5]; and, most recently, stress wave debonding[6]. In the stress-wave repair method, laser irradiation of the substrate initiates a compressive stress wave that propagates through the material. These compressive stress waves pass through the substrate, across the stiction-failed interface and reflect from the top free surface of the cantilever. Upon reflection, the compressive stress waves become tensile and propagate back through the structure passing across the stiction-failed interface and, potentially, rupturing the secondary bonds at that interface. In this article we discuss a fracture mechanics model that we have developed [7] along with new experimental results. We show that our experimental results agree well with the previously developed theory and also present engineering guidelines for laser repair of stiction failed MEMS microcantilevers. These guidelines include the wavelength, fluence, number of pulses, etc. needed to repair stiction failed microcantilevers. THEORY Stiction failed beams are categorized as having either an sshaped failure or arc-shaped failure, Figure 1. The ‘un-stuck’ portion of the beam is modeled as a crack of length s, with the crack tip located at the point where the un-stuck portion of the beam meets the substrate (see Figure 1).