Isotropic Behavior of an Anisotropic Material: Single Crystal Silicon
Douglas R. McCarter1, Roger A. Paquin2
McCarter Machine, Inc, dba McCarter Technology, Inc., Deer Park, TX
Zero defect single crystal silicon (Single-Crystal Si), with its diamond cubic crystal structure, is completely isotropic in most properties important for advanced aerospace systems. This paper will identify behavior of the three most dominant planes of the Single-Crystal Si cube (110), (100) and (111). For example, thermal and optical properties are completely isotropic for any given plane. The elastic and mechanical properties however are direction dependent. But we show through finite element analysis that in spite of this, near-isotropic behavior can be achieved with component designs that utilize the optimum elastic modulus in directions with the highest loads. Using glass frit bonding to assemble these planes is the only bonding agent that doesn’t degrade the performance of Single-Crystal Si.
The most significant anisotropic property of Single-Crystal Si is the Young’s modulus of elasticity. Literature values vary substantially around a value of 145 GPa. The truth is that while the maximum modulus is 185 GPa, the most useful <110> crystallographic direction has a high 169 GPa, still higher than that of many materials such as aluminum and invar. And since Poisson’s ratio in this direction is an extremely low 0.064, distortion in the plane normal to the load is insignificant. While the minimum modulus is 130 GPa, a calculated average value is close to the optimum at approximately 160 GPa. The minimum modulus is therefore almost irrelevant. The (111) plane, referred to as the natural cleave plane survives impact that would overload the (110) and/or (100) plane due to its superior density. While mechanical properties vary from plane to plane each plane is uniform and response is predictable. Understanding the Single-Crystal Si diamond cube provides a design and manufacture path for building lightweight Single-Crystal Si systems with near-isotropic response to loads.
It is clear then that near-isotropic elastic behavior is achievable in Single-Crystal Si components and will provide sub-second thermal equilibrium and sub-micron creep.
(Our paper can be downloaded here or email Doug McCarter at email@example.com.)