BJTs are highly sensitive to self-heating, and accurate modeling of BJTs at high bias levels requires electrothermal models. This paper presents a new technique to measure and extract the thermal admittance for BJTs based on AC data and analytic models.
INTRODUCIIONSemiconductor device behavior depends on temperature.When BJTs operate at high current and voltage, self-heating becomes important. Output resistance, critical for many analog circuits, is especially sensitive to self-heating. So it is important to be able to model self-heating for BJTs.Modeling of electrothermal (self-heating) effects is conceptually straightforward [l], see Fig. 1, although it can be tedious and complex to implement in practice. A thermal network is included with the device electrical model, the power driving the thermal network is calculated as the sum of individual powers of the non-storage branches of the model's electrical network [2], and the local temperature AT rise from the thermal network is coupled back to the branch constitutive equations of the electrical network.Most techniques to characterize the thermal admittance address DC behavior only. Some results based on transient measurements have been reported [3]. For MOSFETs, electrothermal characterization based on AC data has proved effective 141. Here we apply and extend this AC technique to the electrothermal characterization and modeling of BJTs.The data are from a WxL=0.8xlO.Opm, 5 emitter stripe SiGe HBT, with V,=l.SV and Vk=0.84, 0.85,0.86V.
sELF-HEATI"l'IN EFFECT ON SMALL-SIGNAL PARAMETERSAt high frequencies the device thermal response cannot keep up with variations in applied electrical bias, and the output conductance is just the intrinsic, purely electrical output conductance. At low frequencies the device temperature changes with the time variations of the applied bias, so the effective output conductance differs from the electrical only value. The magnitude and frequency dependence of this difference allow the thermal admittance yTH to be determined.Consider a BJT operating in the forward active region, out of saturation and at V,, below where avalanche multiplication is significant. Ignoring series resistance and the temperature dependence of capacitance, a simplified equivalent small-signal network for the model is as Fig. 2 shows.Ic(Vb, V,, T) and Ib(Vb, T) are the DC collector and base currents, T = Tambient + AT, and the DC thermal power is In small-signal operation the AC terminal currents are -I, , = Icv, + Ibvb. Fig. 1. Modeling of self-heating.ib = (g, + ja(cbe cbc))Vb -jacbcVc gbti (1) iC = (gm-jacbc)vb+ (go+jw(cbc+c,,))Vc+gct~ (2) where ?b and Vc are the AC voltages driving the base and collector, respectively, T is the induced small-signal local temperature variation, g, = aIb/avb is the intrinsic electrical input conductance, go = aI,/aVC is the intrinsic output conductance, g, = aIc/aVb -go is the intrinsic transconductance, and gbt = &b/&T and gct = dI,/dAT are the thermal transconductances. Applying the through variable conservation law at the l...