The effects of ternary alloys on thermal resistances of HBTs, HEMTs, and laser diodes

Thermal resistances in InP-based HBTs have been determined by electrical measurement and finite-difference calculation. These devices contain substantial layers of ternary alloys, whose thermal conductivities are not well documented, although they are known to be much smaller than those of the corresponding binary compounds. Therefore a comparison of measurement and calculation gives a valuable check on the thermal conductivities, and is important for validating temperature estimates in a wide variety of HBTs, HEMTs and laser diodes. The measurements employed the V_be-shift technique, while the calculations employed a high-resolution 3-D nodal network model of the transistor structure, including emitter metal interconnects, and the chip carrier. This was solved iteratively, with the best estimates for thermal conductivities from the literature. Comparisons were made from 25 to 200°C baseplate temperature. At 25°C the measurement and calculation yield temperature rises (normalized to power per unit area) of 31.0 and 28.9°C.μm²/mW respectively, i.e. there is agreement to within 7%. At higher temperatures, the calculation is hampered by lack of knowledge of the temperature coefficients (n) for the thermal conductivities of the ternary alloys. So these were all assumed to have the same value, which was used as a fitting parameter. A good fit was obtained with n=1.0. These results suggest that the published thermal conductivity value for Ga₄₇In₅₃As is accurate to within ±10%, and to first order a GaInAs/AlInAs superlattice can be treated as just two layers of the constituent materials with thermal conductivities equal to the bulk values. Also n=1.0 for these compounds, either separately, or as the net effect for this device structure.