Thermal Analysis of Multilayer Printed Circuit Boards with Embedded Carbon Black-Polymer Resistors

The pressure towards increasing miniaturization and interconnection density forces the printed circuit board (PCB) manufacturers to integrate electronic components into multilayer PCBs. Goal of this work was a thorough thermal investigation of the thermal behavior of embedded carbon black-polymer resistors with special attention on dimensions and sheet resistance values relevant for the industrial application in multilayer PCBs. For this purpose demonstrator boards with embedded resistors were fabricated. Two independent temperature measuring methods were applied: calibrated embedded resistors used as miniaturized temperature sensors and thermography. The calibration process including an accelerated aging process in order to obtain stable temperature/resistance characteristics is crucial and described in detail. Due to the small dimensions of the resistors (width in the 100 mum range) it was decisive to consider the anisotropic nature of the glass fiber reinforced epoxy resin laminate. Although this kind of material is used for PCB manufacturing since decades no reliable data were available to describe its thermal behavior sufficiently accurate. For this reason we established the thermal conductivity of the applied substrate materials independently in the lateral direction by reverse modeling and in the perpendicular direction in a separate measurement. Using these data the thermal performance of embedded resistors and the influence of design parameters of the multilayer is investigated by thermal simulation. Comparisons of calculated and measured temperatures showed an outstanding agreement.