Strength Reliability of Micro Polycrystalline Silicon Structure

In order to evaluate strength reliability of micron size polycrystalline silicon (poly-Si) structure, bending tests of cantilever beam and Weibull analysis are performed. Recently, the importance of microelectromechanical systems (MEMS) in society is increasing, and the number of production is also increasing. The MEMS devices, which contain mechanical movement, have to maintain their reliability in face of external shock, thermal stress and residual stress from manufacturing processes. In greeting the mass production era of the MEMS, in case the material strength design of MEMS is performed, required strength data is not average value but the variation, especially minimum value of the material. Micron size poly-Si structure is widely employed in the MEMS such as microsensor, switching device and so on. Then, in order to evaluate strength reliability of micron size poly-Si structure, tests and analysis are performed. The specimen is made by chemical vapor deposition (CVD) process and thickness is 3.5, 6.4 and 8.3 micrometer and the specimen has notch. The test specimen used for the test changed characteristics of (1) film thickness (2) stress concentration, and investigation about the influence each effects of the variation in a bending strength are discussed.


Introduction
Polycrystalline silicon (poly-Si) structure is widely employed in the microelectromechanical systems (MEMS) [1,2]. MEMS devices, which contain mechanical movement, have to maintain their reliability in face of external shock, thermal stress and residual stress from manufacturing processes, and fracture will begin mainly in stress concentration area. Therefore, it is necessary to build up reliability design criterion of the poly-Si structure that has stress concentration [3][4][5][6][7][8][9]. On the other hand, in mass production of MEMS products, it is also important to control the quality considering the reliability of poly-Si structure, which has scattered strength. Thus, we have to clarify the stress concentration effect on strength and the scatter of the strength of the poly-Si structure. In order to clarify these subjects, bending tests using micro scale cantilever beams with or without notch of several sizes.

Test Method and Results
Specimen and test method. The specimens are illustrated in Fig. 1, and the photographs of specimens are shown in Fig. 2. Shapes and dimensions of the specimens are shown in Table 1. For bending tests, two type specimens; Type-A and B are prepared. In the Type-A specimen, the notch of several sizes (1~5µm) is introduced in the root section of microcantilever beam. In the Type-B, by the microscopic observation, the fillet of 1µm radius is recognized indeed in the root section of microcantilever beam. And the thickness of the specimen is 3.5, 6.4 and 8.3µm.
The poly-Si is chemical vapor deposited (CVD) on single crystal silicon wafer surface, and the specimens are made from surface micromachining process.
A dynamic ultra micro hardness tester (Shimadzu Co. DUH-W201) is used for the bending tests. The bending tests are carried out at room temperature under the atmospheric environment.   Figure 9 indicates the examples of FEM models of the specimens (Type-A, L15R1). For the Type-B specimen, the notch of 1µm radius is taken into the model based on the microscopic observations mentioned above. The element sizes of the models are about 1µm in the overall region and are about 0.1µm in the stress concentration area near the notch root. The analyses are carried out under the load condition such as the displacement of loading point is equal to 1µm. Figure 4 shows examples of the relationship between the load and displacement of the bending tests. In this figure, it is known that the polycrystalline silicon deformed elastically until final catastrophic failure in room temperature, showing a brittle nature. Figure 5 shows an expression of the test results by use of maximum peak stress σ max in the notch root obtained by FEM analysis. In this figure, the plots of solid mark means the data of fracture specimens and the open mark means the data of non-fracture specimens due to the contact of free edge to the substrate surface before break. In Figure 7, a tendency can be seen that the plots by the  σ max move down with the increase in notch radius because of the effect of the difference on the stress distribution pattern.    Figure 6 shows the Weibull plots of bending strength for poly-Si. The non-fracture data are treated statistically [10]. By Weibull analysis, Shape parameter (α) and Scale parameter (β) of poly-Si are calculated. Figure 7 shows the α and β. By this figure scale parameters are depend on the stress concentration factor and the value is 2.5 to 5. Shape parameters are 5 to 14. The dependency of the specimen type needs further discussion.

Conclusion
In order to evaluate strength reliability of micron size polycrystalline silicon (poly-Si) structure, bending tests of cantilever beam and Weibull analysis are performed. The test specimen used for the test changed characteristics of (1) film thickness (2) stress concentration. The test results are concluded as follows.
(a) Scale parameter (β) of the bending strength of the poly-Si is 2.5 to 5 and depends on the stress concentration factor. (b) Shape parameter (α) of the bending strength of the poly-Si is 5 to 14 and the dependency of the specimen type needs further discussion.