Temperature Dependence of Thermal Expansion of Materials for Electronics Packages

  • R. Chanchani
  • Peter M. Hall


One severe limitation on the reliability of modern electronic circuits is the stress caused by thermal expansion. Consequently, temperature cycling and temperature shock are standard methods of evaluating new products and processes. To understand these stresses and evaluate the tests, it is important to know the expansivity (sometimes called CTE, or coefficient of thermal expansion) of each material involved. In particular, finite element thermal stress analysis studies need the best data available. Values for the expansivities of many of the materials are available,1 but such tables usually provide only one value for the expansivity. The temperature dependence of the expansivity is often ignored. In addition, the reported values are often averaged over a substantial temperature range, such as 25°C to 300°C. Most of the data in the literature are derived from lattice parameter measurements made by X-ray diffraction, or “z”-direction measurements made by dilatometers. Lattice parameter measurements are valid for single-phase materials. Dilatometer measurements depend on the vertical (“z”-direction) displacement of a low-expansivity piston resting on a sample of material. Dilatometer measurements may include an error if the sample “bows” when heated. In-plane measurements can be made by standing the piece on end, but then verticality must be assured and maintained, which is not easy.


Elastic Limit Aluminum Nitride Beryllium Oxide Lattice Parameter Measurement Expansivity Curve 
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© Van Nostrand Reinhold 1993

Authors and Affiliations

  • R. Chanchani
  • Peter M. Hall

There are no affiliations available

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