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Model for Thermal Noise in Semiconductor Bipolar Transistors at LowCurrent Operation as Multidimensional Diffusion Stochastic Process
Yevgeny V.MAMONTOV Magnus WILLANDER
Publication
IEICE TRANSACTIONS on Electronics
Vol.E80C
pp.10251042 Publication Date: 1997/07/25 Online ISSN:
DOI: Print ISSN: 09168516 Type of Manuscript: Category: Electronic Circuits Keyword: silicon bipolar transistor, compact model, carriervelocityfluctuation noise, Ito's stochastic differential equation, diffusion stochastic process, semiconductordevice simulation, spectral density, highfrequency noise, circuit simulation,
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Summary:
This work presents a further development of the approach to modelling thermal (i.e. carriervelocityfluctuation) 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 wellknown 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.


