MCEN5228-011/4228-011: Microsystems Integration

Homework #8, Due Date: Wednesday, April 5

The Word file of the homework is posted on the class web site. Email your PDF or Word file with answers to efore the class on the 5th. There is a penalty, e.g. 5 to 25 points, for late submission.

Name: ______, Email: ______

  1. (10 points) What is the equation to describe a stress distribution as a function of radius in a region very close to a sharp, 90o corner? The solder bumps have solder pads with different radii; however, they maintain an angle close to 90o. If a solder bump is pushed by a mechanical load as shown below. Please describe a procedure to develop a FEM model and conduct an experiment to determine the critical stress intensity factor. A high level description is good enough. Do we expect to obtain very different critical stress intensity factors when different solder joints are pushed to crack? Or, do we expect those critical values to be close to each other? Why?
  1. (15 points) To characterize the fatigue life of an underfill epoxy, we introduced a concept to apply the difference between the maximum and the minimum stress intensity factors for the estimation. Please take a table out of the results presented in the lecture slides and prove that this approach works well. What is the main assumption in this concept? Identify only one assumption and explain it with one paragraph. What’s the difference between this approach and the one using FEM simulation/inelastic strain energy?
  2. (15 points) Read the first two pages of a proposal on flexible thermal ground planes and understand how to present Figure 1, i.e. Fig. II.1 in a proposal. The proposal is posted next to this Word file. Come up with a Figure 1 for a potential proposal to ask for $20M to develop a 1-mm thin smartphone as discussed in the class. The concept is attached below for your reference, and its Power Point slide is also posted next to the Word file. You are not asked to change this figure; however, you are expected to identify major innovative components or technologies to complete Figure 1.


  1. (10 points) Read a review article posted at You can download any one of the review articles except the three articles on 3D packaging, thermal ground planes and stretchable electronics. Write a half page to summarize the article and identify three issues that are not covered in the class.