Thermal Analysis: VCSELs on an SiOB

This paper introduces a method combining a general electrothermal network π-model in system level and the associated mathematical technique, Green's theorem, in terms of the adopted materials and system geometries to build up an equivalent electrothermal circuit model (EETCM) for efficient thermal analysis and behavior prediction in a thermal system. Heat conduction and convection equations in integral forms are derived using the theorem and successfully applied for the thermal analysis of a 3-D optical stack, vertical-cavity surface-emitting lasers (VCSELs) on a silicon optical bench. The complex stack structure in conventional simulators can be greatly simplified using the method by well-predicting probable heat flow paths, and the simplification can eventually achieve the goal of CPU time saving without having complicated mesh designing or scaling. By comparing the data from the measurement, the finite-element simulation, and the method calculation shows that an excellent temperature match within ±~0.5 °C and 90% CPU time saving can be realized.