This work deals with thermal-noise modeling for silicon vertical bipolar junction transistors (BJTs) and relevant integrated circuits (ICs) operating at low currents. The two-junction BJT compact model is consistently derived from the thermal-noise generalization of the Shockley semiconductor equations developed in work which treats thermal noise as the noise associated with carrier velocity fluctuations. This model describes BJT with the Itô non-linear stochastic-differential-equation (SDE) system and is suitable for large-signal large-fluctuation analysis. It is shown that thermal noise in silicon p-n-junction diode contributes to "microplasma" noise. The above model opens way for a consistent-modeling-based design/optimization of bipolar device noise performance with the help of theory of Itô's SDEs.

The theoretical modelling bandgap narrowing and percentage of ionized impurity atoms for uncompensated uniformly doped silicon containing conventional impurities (B, P, As, Sb) under thermodynamic-equilibrium conditions is presented. As distinct from existing approaches, this modelling is valid for impurity concentrations up to electrically-active-impurity-concentration limits and for the temperature range from 40 K up to 400 K. A relevant and efficient calculation software is proposed. The results of the calculations are compared with the results extracted by many authors from measurement data. A good agreement between these results is noted and possible reasons of some discrepancies are pointed out. The present modelling and software can be used for investigation of BJT charge-neutral regions as well as diffused or implanted resistors.

This work presents a further development of the approach to modelling thermal (i.e. carrier-velocity-fluctuation) noise in semiconductor devices proposed in papers by the present authors. The basic idea of the approach is to apply classical theory of Ito's stochastic differential equations (SDEs) and stochastic diffusion processes to describe noise in devices and circuits. This innovative combination enables to form consistent mathematical basis of the noise research and involve a great variety of results and methods of the well-known mathematical theory in device/circuit design. The above combination also makes our approach completely different, on the one hand, from standard engineering formulae which are not associated with any consistent mathematical modelling and, on the other hand, from the treatments in theoretical physics which are not aimed at device/circuit models and design. (Both these directions are discussed in more detail in Sect. 1). The present work considers the bipolar transistor compact model derived in Ref. [2] according to theory of Ito's SDEs and stochastic diffusion processes (including celebrated Kolmogorov's equations). It is shown that the compact model is transformed into the Ito SDE system. An iterative method to determine noisy currents as entries of the stationary stochastic process corresponding to the above Ito system is proposed.