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Model for Thermal Noise in Semiconductor Bipolar Transistors at Low-Current Operation as Multidimensional Diffusion Stochastic Process
Yevgeny V.MAMONTOV Magnus WILLANDER
IEICE TRANSACTIONS on Electronics
Publication Date: 1997/07/25
Print ISSN: 0916-8516
Type of Manuscript: Category: Electronic Circuits
silicon bipolar transistor, compact model, carriervelocity-fluctuation noise, Ito's stochastic differential equation, diffusion stochastic process, semiconductor-device simulation, spectral density, high-frequency noise, circuit simulation,
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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.  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.