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of the emitter area A E , where AR is defined as the ratio L/W,with L and W being the length and width of the emitterstripe, respectively (see Fig. 1). In Fig. 2, good agreementbetween the “differential”, the “flyback” approach, and thesimulations is displayed. On the contrary, the methodsuggested for HBTs by Dawson et al. overestimates thevalue of R TH in our BJTs due to a non-negligible Early effectthat is not compensated for.III. RESULTS AND DISCUSSIONThe influence of the emitter area on R TH for differentaspect ratios is shown in Fig. 3. When increasing A E , thethermal resistance decreases almost linearly (whenconsidering a logarithmic x-axis) for a fixed aspect ratio. It isnoteworthy that the absolute value of the slope of each lineincreases with AR; in other words, the influence of anyvariation of the emitter area is more pronounced for higheraspect ratios. This can be also observed in Fig. 4, where R THis plotted as a function of the emitter area for differentdistances of the emitter stripe from the trenches. As can beseen, for a fixed A E and distance from the trenches, thehigher the aspect ratio L/W is, the lower the thermalThermal resistance [K/W]2400022000200001800016000140001200010000devB, AR=2.5devB, AR=5devB, AR=10devB, AR=20devB, AR=3080001 10 100 1000Emitter area [µm 2 ]Fig. 3. Experimental thermal resistance as a function of emitter area forvarious values of the aspect ratio of the emitter stripe. All data refer togeometry devB.Thermal resistance [K/W]250002250020000175001500012500AR=5devAdevBdevC100001 10 100 1000Emitter area [µm 2 ]AR=20Fig. 4. Experimental thermal resistance as a function of emitter area forgeometries devA (squares), devB (circles), and devC (triangles); twoaspect ratio values are considered for the emitter stripe, namely, 5 and 20.24-26 September 2008, Rome, Italyresistance becomes.The influence of the spacing between trench and emitterstripe can be quantified from Fig. 5a. As verified by bothexperiments and simulations, for a fixed A E , the thermalresistance is lower when the trench is further away, that is,when the silicon island is larger. For a specific distancebetween emitter and trench (and constant emitter area), thethermal resistance reduces by about 15-20% when increasingAR from 1.25 to 20. However, it should be noted that all themeasurements and simulations reported in Fig. 5a are carriedout by keeping constant distances from the trenches (i.e., forconstant values of S 1 and S 2 ). This implies that a variation inAR results also in a change of the silicon island, where theheat can easily spread. Therefore, numerical simulationshave been also performed to estimate the AR influence for afixed geometry of the silicon island (i.e., by adjusting S 1 andS 2 ). This analysis is illustrated in Fig. 5b, where three siliconislands are considered. For each case, the reduction of R TH isof about 5% when varying AR from 1.25 to 20.Another possibility to reduce R TH relies on integratingmaterials with sufficiently high thermal conductivity that, atthe same time, do not deteriorate the electrical performance.In SOG technology, this can be done using AlNThermal resistance [K/W]Thermal resistance [K/W]25000225002000017500(a)ExperimentalSimulationsdevAdevBdevDEmitter area=20 µm 2150001 10 50Aspect ratio23000220002100020000190001800017000(b)Trench area=12x25 µm 2Trench area=21x25 µm 2Trench area=29x32 µm 216000Emitter area=20 µm 2150001 10 50Aspect ratioFig. 5. Thermal resistance as a function of aspect ratio (a) for differentdistances of the emitter stripe from the trenches [experimental data(circles) are compared to numerical results (squares)], and (b) fordifferent silicon area (only numerical results). In all cases, the emitterarea is kept constant and equal to 20 μm 2 .©EDA Publishing/THERMINIC 2008 103ISBN: 978-2-35500-008-9