35302520151050-5-101 10 100 1000 10000 100000Fig. 8Comparison between the measurement and the simulation withselected nodes (S) for averaging24-26 September 2008, Rome, Italyfast compared to the measurement. However, in term ofthermal resistor, the maximum temperature and themeasurement give similar results. On the other side, use thetemperature average by considering all fingers also has notgiven successful results. The condition for a good agreementbetween the thermal impedance determination by averagingand the measurement is to remove from the averagetemperature the side effects due to the external finger and theend of fingers. This can be explained somehow by thecurrent focalization (collapse of current gain) [13] resultingfrom electric-thermal interaction phenomena which is nottaken into account in a pure thermal simulation and whichcan significantly increase the temperature in the centralfingers. However, a more thorough study should be carriedout to lead to a conclusion.504030Fig. 9 Selection of mesh nodes (S) for average temperatureAs can be seen by only considering the maximumtemperature, the thermal impedance reveals faster timeconstants than measurement ones. Such an observation hasalready been noticed in a previous campaign ofcharacterization led on SiGe HBTs [10]. The determinationof Z th with the averaging which includes temperatures of allfingers has also not given satisfying results. In that case, thesteady state representing the thermal resistor is no morereached. Only the selection of the retained nodes traducescorrectly the thermal behavior of the transistor.Within the framework of a model development whereelectrothermal interaction occurs in temperature-dependentdevices, the thermal model is commonly represented by anelectrical equivalent circuit which consists in a parallelcombination of thermal resistances and thermal capacitancesand voltage controlled current sources [11]. In our case, theequivalent circuit is generated as a SPICE netlist filecompatible with most of commercial electrical circuitsoftware.VI. COMPARISONS BETWEEN MEASUREMENT AND REDUCEDMODEL WITH AVERAGING AND DISCUSSIONFor the characterization campaign, GaAs HBTs and theirlayouts have been provided by United MonolithicsSemiconductors (UMS). The experimental impedanceextraction has been performed from 1 Hz to 100 kHzfrequency range for the transistor brazed on both carriers:Copper and Kovar. The simulations with reduced modelsand temperature averaging have been compared with themeasurements as shown on Fig. 10. The comparison exhibitsa really good agreement.As seen in previous sections, the results raise someinteresting and relevant points. The first interesting pointrelies on the fact that the dynamic behaviour of the thermalimpedance can be only obtained if we consider an averagetemperature. In fact, if we only take into account of themaximum temperature node, the temperature increases toZth (°C/W)20100-101 10 100 1000 10000 100000 1000000Fig. 10 Thermal impedance measurements and simulations for the GaAsHBT brazed on both carriersMore about the results in themselves, we can see from thethermal impedance curves and regarding the differencesbetween the results obtained for the transistor brazed onCopper carrier and on the Kovar carrier, that two main areascan be distinguished. Beyond 100 Hz, curves are sensitivelythe same, meaning that the first thermal time constants aremainly due to the transistor response. Below 100 Hz, theinfluence of the differences between carriers appears. Lowfrequencies correspond to both transistor and carrier thermalresponses. This observation shows and underlines theimportance of the carrier. Moreover, additional simulationshave shown that the thermal chuck should also be taken intoaccount if the carrier is not massive enough to consider auniform temperature at its bottom. Consequently, the thermalimpedance assigned to the transistor (only) should berigorously extracted considering the thermal environmentbecause the deduced thermal resistor can vary by a factor ofalmost two in our case (for the Kovar carrier). Obviously,carrier, package, thermal bridge or even ballast emitterresistor play an important role in the determination of theoperating junction temperature in high power transistors.VII. CONCLUSIONWe have performed a complete thermal study on HBTdevices. From a 3D FE simulation, an equivalent thermalcircuit obtained with model order reduction technique hasbeen proposed and validated with the measurement results.Those results exhibit on one hand, the need to average theoperating temperature to capture the dynamic thermal©<strong>EDA</strong> <strong>Publishing</strong>/THERMINIC 2008 193ISBN: 978-2-35500-008-9
impedance behaviour and on the other hand, it has beenshown the great influence of the carrier and generally thedevice environment for the good operating temperatureprediction.The aim of the study led in this paper shows the difficultyto interpret in a coherent way the comparison between purethermal simulations and results of an electric methodbecause the electrothermal coupling can hardly be evaluatedwithin the transistor. For further works, a distributedelectrothermal model should be used and would be moresuitable for a better description of the phenomena within themulti-fingers transistors.AKNOWLEDGEMENTThe authors would like to thank UMS for providingHBTs.24-26 September 2008, Rome, ItalyREFERENCES[1] M. N. Sabry, “Compact thermal models for electronic systems”, inTHERMINIC, 2001, pp. 197-202.[2] D. T. Zweidinger, S. G. Lee, and R. M. Fox, “Compact modelling ofbjt self-heating in spice”, IEEE Trans. On CAD of Intergated Circuitsand Systems, vol. 12, pp. 1368-1375, 1993.[3] O. Mueller, “Internal thermal feedback in four-poles especially intransistors”, Proceedings of the IEEE, vol. 52, no. 8, pp. 924-930,Aug. 1964.[4] S. Marsh, “Direct extraction technique to derive the junctiontemperature of HBT's under high self-heating bias conditions”,Electron Devices, IEEE Transactions on, vol. 47, no. 2, pp. 288-291,Feb 2000.[5] N. Bovolon, P. Baureis, J.-E. Muller, P. Zwicknagl, R. Schultheis andZanoni, “A simple method for the thermal resistance measurement ofAlGaAs/GaAs heterojunction bipolar transistors“,Electron Devices,IEEE Transactions on, vol. 45, no. 8, pp. 1846-1848, Aug 1998.[6] J. Lonac, A. Sabtarelli, I. Melczarsky and F. Filicori, “A simpletechnique for measuring the thermal impedance and the thermalresistance of HBTs”, in Gallium Arsenide and Other SemiconductorApplication Symposium, 2005. EGAAS 2005. European, 3-4 Oct2005, pp. 197-200.[7] A.A.L. de Souza, J.-C.Nallatamby, M. Prigent, and R. Quéré,“Dynamic impact of self-heating on input impedance of bipolartransistors”, in Electronics Letters, vol. 42, no. 13, 22 June 2006, pp.777-778.[8] T. Peyretaillade, M. Perez, S. Mons, R. Sommet, P. Auxemery, J.Lalaurie, and R. Quere, “A pulsed-measurement based electrothermalmodel of hbt with thermal stability prediction capabilities,” inMicrowave Symposium Digest, 1997., IEEE MTT-S International,vol. 3, 1997, pp. 1515–1518 vol.3.[9] E. B. Rudnyi, J. Lienemann, A. Greiner, and J. G. Korvink,“mor4ansys: Generating compact models directly from ansysmodels,” Technical Proceedings of the 2004 NanotechnologyConference and Trade Show, Nanotech 2004, Boston, Massachusetts,USA, vol. 2, pp. 279–282, March 7-11, 2004.[10] A. Xiong, A. A. Lisboa de Souza, R. Sommet, R. Quéré and B.Barbalat, “Détermination d’impédance thermique de TBH SiGe parmesures électriques basses fréquences”, 15 ème Journées NationalesMicroondes, Toulouse 2007.[11] D. Lopez, R. Sommet, and R. Quere, “Spice thermal subcircuit ofmultifinger HBT derived from ritz vector technique of 3D thermalsimulation for electrothermal modelling”, in GAAS – Londres, 2001,pp. 207-210.[12] E. Wilson and M.W.Yuan, “Dynamic Analysis by directsuperposition of Ritz vectors”, in Earthquake Eng. StructuralDynamics, vol. 10, no. 6, pp. 813-821, 1982.[13] E. Koenig, S. Ulrich, J. Schneider, U. Erben and H. Schumacher,“Impact of thermal distribution and emitter length on theperformance of microwave heterojunction bipolar transistors”, inElectron Devices, IEEE Transactions on, vol. 38, no. 4, pp.775-779,Apr. 1995.©<strong>EDA</strong> <strong>Publishing</strong>/THERMINIC 2008 194ISBN: 978-2-35500-008-9
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