Accounting thermal noise in mathematical models of quasi-homogeneous regions in silicon devices

This work proposes stochastic generalizations of semiconductor fluid-dynamic and the Shockley equation systems for thermal-noise modeling in quasi-homogeneous regions of silicon devices. These stochastic systems include thermal-noise terms derived from the Langevin-equation theory. The Shockley-like stochastic model performs thermal-noise sources in drift-diffusion expressions in the form of the steady-state solution of the Langevin equation, rather than in the white-noise form. Differences from the previous drift-diffusion thermal-noise modeling and the relevant physical aspects are discussed. A quasi-stationary approximation for the Shockley-like stochastic system is considered and theoretically tested for resistor and p-n junction. The corresponding results agree with the expressions for spectral densities by H. Nyquist (1928) and M. Gupta (1982), and present a generalization in the latter case. The proposed models can be used in analytical techniques for device/circuit research/design or incorporated into CAE/CAD software and open for methods of stochastic-differential-equation theory to be applied to thermal-noise analysis within fluid-dynamic and drift-diffusion approaches