Development of an infrared polarized microscope for evaluation of high gradient stress with a small distribution area on a silicon chip

In this paper, a special microscope to evaluate stress in a silicon chip was developed based on the principle of photoelasticity. To facilitate stress measurements and to improve their precision, two methods were adopted. First, a six-step phase shifting technique was realized with the aid of two motorized rotation stages. During the implementation of this phase shifting technique, six digital images were captured at different rotation angles of the two stages and employed to automatically calculate the birefringence. Second, an algorithm was developed to correct deviations in the position of the specimen in the six images caused by mechanical vibration; thus, the most significant source of error was addressed. The precision of the system in terms of measuring the stress-birefringence phase difference was verified with a standard quarter wave plate; the results demonstrate that the system is precise to within at least 2°. With the developed system, we evaluated the stress distribution and its variations with thermal cycling around through-silicon vias on a silicon chip at room temperature; we found that stress initially increased with the number of thermal cycles before decreasing with further thermal cycles.