A technique for measuring the distance between the micro-device and substrate is developed. An electron beam scan of a scanning electron microscope used for this method. A micro-device is placed over the substrate and obstructs the back-scattered electrons from the substrate. Therefore, the shadow image of the micro-device is observed in the SEM image. The distance between the micro-device and the substrate can be calculated using the width of the shadow, dimension of the detectors for the back-scattered electrons and the dimension of the micro-devices. This method makes it possible not only to measure the distance between the micro-device and the substrate and also detect the form of the specimen surface. In addition, observation of the micro-devices and measuring the distance between the micro-device and the substrate can perform at the same time. As a demonstration, the distance between the micro-bar and the substrate and the shape of the micro-hardness tester's indent mark is measured.
Accurate determination of the as-built geometry of micro-electro-mechanical systems (MEMS)is important given the magnitude of the geometric uncertainty relative to the dimensions of these devices. A method for determining geometric process errors in MEMS fabrication from measurements of the resonant frequencies of simple structures is presented. This method provides a way to determine the process offset (the difference between the design width of a structural element and the as-built width) and, in the ideal case, the average angle of the side-walls of the films involved. An important feature of the approach presented is that by using frequency ratios, neither the elastic modulus nor the mass density of the film need be known a priori. This paper also introduces a robust design technique for MEMS subject to the inherent geometric and material uncertainties discussed previously. Although a range of design tools have been developed for MEMS, little has been done to account for the uncertainties associated with MEMS fabrication. The robust design problem we pose is to minimize the expected variance between the specified target system performance and the actual performance that a particular realization would be expected to exhibit. This robust design problem can be written as a constrained minimization. We consider a subset of these problems and develop an algorithm to minimize rational polynomial functions subject to polynomial inequality constraints. The details of the algorithm are presented and we verify its performance by examining the design of lateral resonators with specified resonant frequency. This example shows that the robust design nominally meets the target performance and is significantly less sensitive to geometric uncertainties than typical designs.
A wide range of techniques have been developed recently for testing the mechanical properties of materials used in MEMS. Many of these techniques focus on uniaxial tension testing, while others address bending or torsional modes of deformation. This paper compares the two primary modes of testing - uniaxial tension and bending - in terms of the associated forces, deflections and sensitivities to uncertainty in geometry and loading. When determining elastic modulus, the bending test is shown to be more sensitive to uncertainties in beam cross section than is the tension test. On the other hand, in connection with strength characterization it is shown that small deviations form ideal uniaxial loading, either in terms of an offset from the neutral axis or an angular misalignment from the axis, can result in a large decrease in the apparent strength. Bending test for strength determination do not suffer such dramatic effects due to the misalignment of the applied loading.
The fracture of brittle MEMS materials is often characterized by ultimate strength measures such as the maximum stress or strain in an element at failure. It has been known for many decades that a better way to characterize the strength of a brittle material on the macro-scale is to make use of statistical measures. This is due to the nature of brittle materials in which failure occurs when a critically sized flaw exists in the region that is under tensile stress. The distribution of flaws is often random, so the strength of a brittle material can only be properly characterized by statistical measures. Working with MEMS devices, where the site scale is small, it becomes even more important to use a statistical approach. Doing so can explain two observed effects. First, there is an apparent size effect on the strength of the material. The larger the structure that is under a given stress, the larger the region where a critically sized flaw may exist, resulting a higher probability of failure. Second, two identical beams with different stress states, loaded to the same maximum stress can have dramatically different average strengths. In this paper, Weibull statistics are used to characterize the strength of one MEMS material-- polycrystalline silicon. The relevant statistical measures are obtained from the fracture of a large number of cantilever beams. It is shown that, for this material, the average failure strength of a beam loaded in uniaxial tension should be on the order of 40% lower than the average strength of identical beams loaded in cantilever bending.
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