Silicon

Single crystal silicon is aniostropic. The crystalline directions of interest include the <100>, the <110>, and the <111> crystal directions. Material properties in these crystalline directions can be calculated from basic crystal properties, and results of this analysis are shown in Appendix A. To simplify the initial design process I assume that the silicon crystal can be considered isotropic. Following the example of Spiering et al I choose a Young's Modulus of 150GPa, and a Poisson's ratio of 0.17 for all calculations. It is the opinion of these authors that these isotropic values best reflect the aniostropic behavior of silicon in the <100> plane.

Thermal expansion coefficient of silicon.

The following table is extracted from data from Milek.

Fracture Strength of Silicon

Since silicon used is single crystal it is assumed for all intents and purposes that the material does not yield until fracture occurs. I assume that the design failure stress should be the fracture strength of silicon. The fracture strength of silicon is given by Petersen as being 7000 MPa. This extremely high failure stress is contradicted by experience with anisotropically etched diaphragms where failures stresses are estimated to be in the order of 300 MPa. Sooriakumar tracked this discrepancy to the sharp corners introduced by aniostropic etching. Analysis of his data shows stress concentration factors of up to 33 at the sharp corners in aniostropically etched specimens. Rounding of the corners by isotropic etching reduced stress concentration and increased failure load for the specimens.

It is assumed in this design process that the fracture stress of silicon is 7000 MPa, with stress concentration factors of 33 possible at sharp corners produced by aniostropic etching.

Fracture Toughness

Silicon is a brittle material. Failure usually occurs along <111> cleavage planes. Analysis of failure in silicon can be helped by the use of fracture mechanics models. Using these models requires knowing the fracture toughness for the materials involved.

K_1c fracture toughness values are given for different crystal directions

• Spiering, V.L., Bouwstra, S., Spiering, R., On chip decoupling zone for package-stress reduction. Sensors and Actuators, A.39, 1993, 149-156.
• Petersen, K.E., Silicon as a mechanical material, Proc. IEEE., Vol. 70, No. 5, 1982
• Sooriakumar, Chan, Savage and Fugate, A comparative study of wet vs. dry isotropic etch to strengthen silicon micro-machined pressure sensor, Electrochemical Soc. Proc., Vol. 95-27.
• Ericson, F, et al., Hardness and fracture toughness of semiconducting materials studied by indentation and erosion techniques, Materials Science and Engineering, A 105/106 (1988) pp 131-141