Light's interaction with water is a beautiful phenomenon that can be likened to X-ray diffraction analysis in crystalline solids. This technique allows us to understand the atomic structure of materials. The process involves directing radiation into a finely ground powder of the material and observing how it diffracts. The diffraction pattern tells us about the material's structure. One application of this technique is to measure thermal expansion of materials, which is crucial in the design of semiconductor packages. By understanding these principles, we can better design materials for the future.

The simplest of all modern X-ray analyses is powder analysis using an X-ray diffractometer. The technique can be used to characterize powders as well as polycrystalline materials. The material of interest is ground to produce a fine, randomly oriented powder, with each particle in the powder consisting of small single crystals or an aggregate of crystals 10 mm or less. The powder is placed into a recess of a plastic sample holder and leveled flat in the sample holder with a straight edge.

The key components of a modern diffractometer include a monochromatic radiation source, sample stage (or goniometer), radiation detection system, enclosure, and safety features. One of the most common configurations is the q-q upright. This type of diffractometer has a movable detector and X-ray source, rotating about the circumference of a circle centered on the surface of a flat powder specimen. The intensity of a diffracted beam is measured directly by an electronic solid-state detection system.

Software for peak location and intensity determination allows for significant time savings during the identification of an unknown specimen. Even with this luxury, experienced operators still examine each peak of every spectrum; inspecting peak positions and shapes, the presence or absence of peaks, and relative background levels. Using software packages without understanding the algorithms that are employed can lead to serious misinterpretation.

Thermal expansion is a phenomenon that influences the adhesion and mechanical properties of solid semiconductor packages. For example if layers of electronic materials are made of two dissimilar materials, an increase in temperature during device processing or operation results in each material expanding by different amounts. This is a result of differences in the coefficients of thermal expansion (or CTE, a). A classic example is an attachment of integrated circuit chips of silicon to alumina substrates using Cu or Sn-Pb solder bumps; note that each of these materials has a different CTE. In the case of good adherence between the layer and the substrate, the expansion of the layer is constrained by the expansion of the substrate and vice versa. Even small dimensional changes result in stress. When these stresses exceed a critical value, the material fails by either delamination or fracture. By measuring the change in lattice constant and knowing the elastic constant, one can calculate the thermal stress and determine the safe processing and operation conditions.

In-situ heating during X-ray diffraction analysis is a means by which to measure the thermal expansion of crystalline solids. As the temperature of the specimen increases, the lattice constant increases in each unit cell. The net effect is an increase in the overall length. The thermal expansion coefficient can be determined by measuring the increase in the lattice constant (the decrease of the 2q angle for a given diffraction peak) with increasing temperature. This technique can provide linear thermal expansion coefficients along different crystallographic axes for single or polycrystalline materials and can also provide information regarding volume changes.

In the simplest case, the cubic case, CTE is also equal to the fractional change in lattice constant per unit change in temperature.

CTE ( a) = (Da/a_i) (DD(DT^-1)

Starting with Bragg’s Law, a relationship for the relative change in lattice spacing with respect to the change in q is developed:

For the case of cubic materials,