# Thoughts on Rheology, by Dr. Andy Mackie

Folks,

Indium Corp.’s product manager, Semiconductor Assembly Materials Dr. Andy Mackie is an expert on solder paste rheology (a word that we’ll explain in a minute). The following is a summary of a chat I had with him recently.

Dr. Ron: What is rheology?
Dr. Andy Mackie: Rheology is the study of the deformation and flow of matter. My fellow Lincolnshire (England) native Sir Isaac Newton postulated that if a fluid were flowing uniformly over a surface that it would exert a stress, t, (force per unit area) on that surface proportional to the gradient of the fluid’s velocity with respect to distance from that surface. The proportionality constant is called the viscosity, usually designated by m. The equation describing this relationship is:

It’s a lot more complicated if you figure in both non-laminar flow, and boundary layer effects as you get closer to the surface, but is a good guide to what is happening in the bulk of the fluid. For laminar flow, if the viscosity remains the same regardless of the shear rate, then this is a true “Newtonian fluid.” Glycerine is a good example.

Unfortunately, scientists soon found out that, for many fluids of engineering interest, viscosity is often not a constant, but varies with the fluid’s velocity gradient (often called the shear rate.) When the viscosity decreases with increasing shear rate the material is called a shear-thinning or “plastic” material. This needs to be differentiated from a “thixotropic” material, in which the viscosity decreases with time, although often the two are seen in tandem. There is also a phenomenon called “rheopexy,” where viscosity increases with time, then relaxes to its original viscosity — something you can experience if you grab a handful of wet sand at the beach, then watch it crumble back to its original relaxed state.

DR: Thixotropic or shear-thinning materials seem counter intuitive. Can you explain them in layman’s terms?
AM: Your kids see it every time they shake a bottle of ketchup. If you imagine that there is a very open structure built of little Lego bricks that holds the ketchup rigid in the bottle, then shaking temporarily smashes up the structure, making the ketchup much lower in viscosity and easier to pour. However, unlike Legos, the gel structure will eventually rebuild itself (a process called relaxation), the speed of which is primarily dictated by particle diffusion kinetics.

DR: What are some common thixotropic materials?
AM: Solder paste is a great example. Its shear-thinning nature is ideal for the printing process. The paste’s viscosity is low as it is experiences a high shear rate when forced through the stencil aperture, ensuring good hole fill and a high transfer efficiency. Then as the solder paste deposit rests on the leadframe, or wafer UBM or PWB pad, the viscosity is high, since the shear rate is near zero, enabling the deposit to maintain its shape and avoid “slump.” Any viscosity changes with time must then ideally either be small or have short relaxation time.

DR: Any final thoughts?
AM: The thixotropic and shear-thinning nature of solder pastes (and other similar electronics materials, for that matter) are very important, but are only part of the whole equation of solder paste stability and performance, as Indium scientists and process engineers are very well aware. I could get into another discussion about whether customers need “tack” or a means of keeping components in place, but I think I’ll leave that for another time. Cheers!

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