Model for Thermal Noise in Semiconductor Bipolar Transistors at Low-Current Operation as Multidimensional Diffusion Stochastic Process

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概要

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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. The present work considers the bipolar transistor compact model derived in 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. The simplest approximation according to this method presents the multidimensional Ornstein-Uhlenbeck stationary stochastic process. The spectral-density matrix in the multidimensional case is rigorously derived within this approximation. The corresponding numerical results for auto spectral densities of emitter, base, and collector currents in one of the high-speed/low-current silicon bipolar transistors for medium and high frequencies are presented. They are compared with the corresponding data according to standard engineering formulae. A generalization for circuit simulation is also proposed and discussed.

• 社団法人電子情報通信学会の論文
• 1997-07-25

著者

• Willander Magnus

  Laboratory Of Physical Electronics And Photonics Department Of Microelectronics And Nanoscience Chal

• MAMONTOV Yevgeny

  Laboratory of Physical Electronics and Photonics, Department of Microelectronics and Nanoscience, Ch

• Mamontov Yevgeny

  Laboratory Of Physical Electronics And Photonics Department Of Microelectronics And Nanoscience Chal

関連論文

• ASYMPTOTIC METHOD OF FINITE EQUATION FOR BOUNDED SOLUTIONS OF NONLINEAR SMOOTH ODES
• Model for Thermal Noise in Semiconductor Bipolar Transistors at Low-Current Operation as Multidimensional Diffusion Stochastic Process

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