Temperature solution of five-layer structure with a circular embedded source and its applications

The temperature solution of a five-layer structure with a circular embedded source is reported. The solution is in the form of a single integration rather than the double integration of the solution for a structure with a rectangular source. An algorithm is developed for effective and accurate calculation of the integral solution. Based upon the solution and algorithm, a software program, PAMICE, has been written. Using the circular source solution, the CPU time for temperature calculation is reduced by a factor of 10 as compared to the rectangular source solution. An important application for the solution is the use of a circular source instead of square source as the unit source to produce the unit thermal profile for the real-time thermal design of integrated circuits. The solution is also valuable for the thermal study and analysis of devices having circular sources, such as power transistors, light emitting diodes, and laser diodes. Two application examples are presented