Dimension effect on mechanical behavior of silicon micro-cantilever beams
Introduction
In recent years, micro-electro-mechanical system (MEMS) structures have emerged for a wide range of applications including micro-motors, accelerometers, and biomedical devices. However, one of the major barriers in the large-scale commercialization of MEMS is the development of a detailed study of failure mechanisms under various kinds of loadings [1]. Although many MEMS devices are fabricated from silicon based materials, these micro scale silicon structures may not behave similar to bulk silicon structures. Unlike bulk mechanical properties of silicon, which have received considerable attention in the literature, there have only been limited studies of mechanical properties of silicon at the micro-scale.
It is easier to test MEMS materials in bending because many microdevices that move do so parallel to the substrate [2]. Jadaan et al. [3] provided a good summary of the strength of both single crystal silicon (SCS) and polysilicon. Almost half of the SCS specimens were tested by bending in the beam configuration, and the strength ranged from 0.31 to 17.5 GPa; while the strength for polysilicon is in a narrower range of 0.57–4.9 GPa. The results showed that both testing methods and brittleness of the silicon lead to the variation of strength. Wilson et al. [4] found that there is variation of bending strength of the SCS micro cantilever beam tested from front surface (3.3 GPa) and from back surface (1.0 GPa) due to anisotropic etching on the back surface. Detailed studies of the influence of chemical solution in wet etching on tensile strength of SCS were done by Taechung [5]. The SCS specimen with highest strength 1.24 GPa is etched by EDP, while the lowest strength 0.63 GPa is etched by KOH. The SCS micro cantilever beam is further set up such that the loading can be applied on the side surface [6]. The beam with fracture along (1 1 0) surface shows higher strength than the one with fracture along (1 1 1) surface. Jadaan et al. [7] indicated that the SCS elastic modulus was independent of size, while the bending strength displayed significant sensitivity to size.
Recently, Chen and Ou [8] proposed a model which can predict the strength of the same material tested by another type of structure associated with a different size, geometry, and loading situation based on a known testing result. The Weibull statistics was adopted in their work for the development of the strength conversion flow. Based on previous studies, the issue needed to be addressed here is that micro-fabricated materials have properties that are highly dependent on the fabrication route used to create them and the scale of the structures that they constitute. However, the development of both standardized test methods and material property data bases has lagged behind that of the design and simulation tools, limiting their utility. Even though moduli tests on polysilicon deposited by identical process have been done, the discrepancy in moduli values has been reported probably only due to differences in experimental technique and associated measurement error at the MEMS scale. The first step towards the solution of this dilemma is to develop standard test methods with which to characterize the mechanical properties of micro-fabricated material produced by the same processes and at the same scales as the intended application.
Therefore, a simple but useful testing methodology on MEMS structures is provided in this work. The center of the methodology is applying mechanical loads via testing micro-probe on the specimens with various dimensions by a highly precise micro-force testing apparatus. This method allows testing various specimens in a larger range of forces and displacements. The bulk micro-machining technique is adopted to fabricate the micro-cantilever beam on a silicon wafer. The mechanical loading is applied on the beam by direct contact between the probe and the free end of the beam. The proposed testing methodology can probably be expected to develop as one of the standard test methods, and not only would extend applications of SCS in MEMS devices based on the better understanding of its mechanical properties, but also strengthen design and simulation tools in MEMS.
Section snippets
Micro-cantilever beams
The material used for micro-cantilever beams is 4 in. single crystal silicon (Si) p type (1 0 0) wafer. The direction of orientation flat is [1 1 0]. The mask is arranged such that the length direction of the beam is along [1 1 0] orientation. The schematic diagram for the beam is shown in Fig. 1a. The length of the beam is designed as 400 μm, 500 μm, 600 μm, and 700 μm; the width is 100 μm; and the thickness is designed as 50 μm and 60 μm. The variation of all dimensions of the beams is found to be 1 – 2 μm.
Stress–strain relationship
Fig. 3 shows flexural stress–strain relationships of beams with same width 100 μm, thickness 50 μm, lengths of 400 μm (Fig. 3a), and 700 μm (Fig. 3b); and thickness 60 μm, lengths of 400 μm (Fig. 3c), and 700 μm (Fig. 3d). Stresses and strains are derived from the forces and displacements as shown in Table 2 measured by micro-force testing machine. For 50 μm thick beams with various lengths, maximum forces decrease with increasing length and range from 0.189 N to 0.094 N, and maximum displacements range
Conclusions
The most significant advances in MEMS may occur by developing technologies to produce smaller devices with similar unit costs to those for existing microelectronics. To achieve this goal, the development of standard characterization techniques, particularly with regard to the mechanical properties, is very important if the full potential for paralleling the simulation-based design methodology achieved for IC devices is to be realized for MEMS. With a micro-probe, special designed fixtures, and
Acknowledgment
Authors are grateful for financial support from National Science Council in Taiwan on this work under contract NSC 94-2212-E-035-005.
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