Determination of maximum allowable strain for polysilicon micro-devices
Introduction
The design of devices that are reliable under load requires knowledge of the mechanical properties of the material. However, the design of micro-mechanical devices is hampered because the mechanical properties of many materials used in micro-electro-mechanical systems (MEMS) designs are not well understood at the micro level. Most MEMS are made using fabrication methods very similar to those used to make integrated circuits. The electrical properties of the materials used in these processes are very well understood, but the mechanical properties are not as well known. Polycrystalline silicon (polysilicon) is a common MEMS material for which reliable mechanical properties data is not available, especially for devices that have dimensions on the order of microns. Properties such as Youngs modulus and strength are complicated by the fact that the device sizes often approach the grain size of the material. Because there are few grains in the particular member, there are not enough for the random orientation of multiple grains to cause the material to be isotropic. The testing of the mechanical properties of polycrystalline silicon then results in data with a large standard deviation.
This paper proposes a method for using strength test data that accounts for the uncertainties in mechanical properties and presents data from tests of polysilicon that may be used in the future design of polysilicon MEMS.
Section snippets
Background
Much more work has been done in recent years to better understand the mechanical properties of polysilicon. The properties of polysilicon have been tested a number of ways, including the deflection of beams using devices such as nanoindenters 1, 2 surface profilers [3]and torsion devices [4]. Sharpe et al. [5] tested 48 beams and found that the average Youngs modulus was 169±6.2 GPa. They also summarized the values for Youngs modulus reported in various studies ranging from 123–175 GPa.
Approach
To avoid failure, the maximum stress of a component should be kept below the stress at which failure occurs (the material strength). A common approach in design is to maintain the maximum stress, σmax, below the maximum allowable stress, σallowable, orwhere the maximum allowable stress is safely below the material strength. If Youngs modulus (E) is a constant (i.e. if the stress–strain curve is linear and σ = Eε) then an equivalent but less commonly used expression of Eq. (1)may
Test procedure
The theoretical approach described above was used to approximate the nominal strain at failure for flexible devices made of polysilicon using the MUMPs process [10]. Two separate studies were performed. In the first study (Test 1), several types of flexible devices were tested to failure, including flexible beams, compliant parallel-guiding mechanisms [11] and compliant straight-line mechanisms [12]. In Test 2, cantilevered beams were tested. The experimental designs for Tests 1 and 2 are
Results
The following two sections report the results of Tests 1 and 2. A later section contains a summary of the data and discusses its usefulness in design.
Discussion of error
Seeing the significant scatter in the strain data, one must address whether the scatter is due to micro phenomena or to the error inherent in the testing techniques and analysis. The errors introduced in fabrication, loading and data analysis were examined. Because the beam load was applied by a manually operated probe tip, the loading was not always perfectly directed. In Test 1, any force applied at a distance from the center of the rigid coupler link resulted in an additional moment on the
Implications for design
Combining the results of the two tests, the average nominal strain is 0.0181 and the average standard deviation is 0.0042 as shown in Table 7. These results may be used in a number of different ways in the design of MEMS devices. The mean nominal strain at failure may be used in design in a manner similar to how the fracture strength would be used. One approach is to ensure that the nominal strain is less than the mean nominal strain at fracture minus three standard deviations, or:
Conclusion
The nominal strain at failure for polysilicon has been investigated. The approach used includes deflecting a component to failure, measuring the deflection and calculating the corresponding nominal strain. The mean nominal strain for the 161 polysilicon devices tested was 0.0181, with a standard deviation of 0.0042. The scatter in the data is most likely due to the small number of grains in a given test specimen. The uncertainty in material properties increases as the number of grains decreases
Acknowledgements
The authors express their appreciation to Linton Salmon and the staff of the Integrated Microelectronics Laboratory for their assistance in this work. The help of Daniel Gunyan, Dani Johnson, Brian Christensen and Darrin Stokes in obtaining test data is gratefully acknowledged, as is the help of Nathan Masters in obtaining the SEM photographs. This work was supported by the National Science Foundation (NSF) under Grant No. ECS-9528238, an NSF CAREER Award under Grant No. DMI-9624574, an NSF
References (12)
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