Inverse circuit simulation based low-frequency noise extraction in SiGe HBTs

Transistor low-frequency noise is an important issue in both base hand and RF circuits of a wireless transceiver [I]. In a bipolar transistor, the major low-frequency noise source lies in the base current. Experimentally, it bas been established that this hase current noise source is located between the internal base and emitter nodes in an equivalent circuit [I]. This base current low-frequency noise, denoted as ibn. is often measured indirectly from the collector voltage noise by presenting to the transistor base a Source impedance much greater than the input impedance, as shown in Fig. 1. The measured collector voltage noise is converted to collector current noise using SI, = SVc/Ri,e88' which is then converted to the base current noise using SI , = . Y ~ ~ / f l , $ with Bo, being the low-frequency small signal oc current gain. Bo, is often determined from Gummel characteristics measured under a biasing condition close to that used in the noise measurement. We note that the hase current noise can also be measured "dtrectly" from the base using a high precision current amplifier with an input impedance much lower than transistor input impedance. Each method has its advantages and disadvantages in practice, as discussed in [I] . In general, the indirect method is easier to implement, and widely used. We focus on the indirect method in this work. Similar limitations and assumptions exist in the "direct" measurement method as well. The widely used conventional measurement method, however, is based on a simplified equivalent circuit derived under isothermal condition. While in modem SiGe HBTs, self-heating can be significant, in part due to high operating current density. To enable high current density operation, the collector doping is increased with device scaling, which then increases collector-base junction field and thus avalanche multiplication. One can therefore expect errors in the low-frequency noise measured using the conventional method in high speed SiGe HBTs. The purpose of this work is to develop a new method -