AN INTEGRATION ALGORITHM FOR THE FOURIER-BESSEL INTEGRAL SOLUTION OF A 5-LAYER STRUCTURE WITH A CIRCULAR EMBEDDED SOURCE

An integration algorithm for effective and accurate integration of the Fourier-Bessel integral temperature solution of a five-layer structure with a circular embedded source is reported. The circular source solution has the form of a single integration rather than the double integration of a solution for the structure with a rectangular source. Using the circular source solution, the computation time for temperature calculation is reduced by a factor of 10 compared with the rectangular source solution. To reduce the computation time further, this integration algorithm transforms the single integration into a fast-converging simple summation. The effectiveness of this algorithm is most evident when the point of calculation is far from the source. Based on the solution and algorithm, a software program PAMICE has been written. An important application for the solution and integration algorithm is the use of a circular source instead of a square one as unit source to produce the unit thermal profile for real-time thermal design of integrated circuits having large number of sources. The solution is also valuable for the thermal study and analysis of devices having circular sources such as power transistors and light emitting diodes. The algorithm can be applied to other similar solutions arising from structures with circular sources.