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24 SMT Magazine • June 2014 ADvAnCeD THeRMAL MAnAgeMenT SOLuTIOnS continues a substitute material of which the thermal conductivity in the perpendicular direction is equivalent to the hollow cylinder shaped cop- per vias with a wall thickness of 25 µm (Figure 11b). In this way a virtual thermal conductivity lsub of the via can be calculated on the base of the thermal conductivity lCu of copper, the cross sections of the copper walls ACu and of air (DK6) or epoxy (DK2) in real vias [7] : (5) where d is the drilling diameter and the ther- mal conductivity of air or epoxy is neglected in comparison to lCu. Results The thermal simulation revealed that un- der normal operation conditions all three investigated packaging concepts allow to keep the LED-chip surface temperature at moderate levels between 27.5°C (LED-in-Cavity concept) and 45.5°C (FR4-DK concept) and that very high temperature gradients (more than 200°C/ mm) exist in the silicone glob top immediately above the chip surface. In all cases the tempera- ture maximum is found at glob top surface (ca. 85°C at the IMS, ca. 95°C at the FR4-DK, ca. 70°C at the LED-in-Cavity samples). Figure 12 depicts the temperature distribution of a LED- in-Cavity sample. For reasons of comparability, in all cases the shape of the color converter was assumed as spherical glob tops. It should be noted that in a real case of the LED-in-Cavi- ty the color converter does not tower above the PCB top surface. Therefore, the height of the color converter and therewith the maximum temperature is even lower than considered in our simulation. The quite remarkable tempera- ture differences inside LED chip and color con- verter of the three concepts can be understood by considering the temperature course along the perpendicular symmetry axis. In spite of a heat flux density of more than 80 W per square centimeter the LED-in-cavity set-up keeps the LED chip at a temperature level below 28°C due to the 70 µm thick copper base layer and the shortest possible heat conduction path. The most significant temperature drops can be found in the thermal interface layer (TIM) between the heat sink and the copper base layer and in the adhesive layer under the LED chip (Figure 13). The IMS module shows a LED-chip temper- ature between 32°C and 34°C. The most signif- icant temperature drop is caused by the dielec- tric between the copper layer and the alumi- num plate. The excellent thermal conductivity of the aluminum plate and the 35 µm thick copper layer can be recognized by the almost negligible temperature change inside the layer. The highest temperature differences be- tween heat sink and LED chip are found in the FR-4-DK samples. Due to the fact that the ther- feaTure figure 11: Thermal model of the fr-4-dk test sample: a) entire model; b) detailed view thermal via array.