Bridging the gap between microscopic and macroscopic theories of noise in bipolar junction transistors

The major noise sources in a bipolar transistor are the base resistance thermal noise, or Johnson noise, the base current shot noise and the collector current shot noise. The shot noise is described by a spectral density of 2qI, I being the DC base, I_B, or collector, I_C, current. We present a detailed microscopic treatment of the transistor collector current shot noise, which is typically given as a macroscopic result of electrons passing through the EB junction barrier. The analysis can be applied to heterojunction bipolar transistors as well as to non-uniform doping cases. The critical assumptions behind the magic 2qI_C expression are identified. One of them is that the noise due to majority carrier velocity fluctuations is not included, which dominates at high injection. Velocity saturation and velocity overshoot can also cause deviation from 2qI_C. We show detailed modeling of the noise source within an incremental section, its propagation towards the transistor terminal, and the integration over all of the incremental sections for evaluation of the total terminal noise. The concept of scalar and vector Green´s functions as well as their equivalence to Schockley´s impedance field concept are illustrated with an emphasis on intuitive understanding. These concepts are essential to performing effective numerical noise simulation, which has recently become available in commercial TCAD tools.