A Deterministic Approach to RF Noise in Silicon Devices Based on the Langevin–Boltzmann Equation

In this paper, a new deterministic approach to electron noise based on a spherical harmonics expansion (SHE) of the Langevin-Boltzmann equation in the frequency domain is presented for silicon devices. Compared to the standard Monte Carlo (MC) approach, the SHE method has many advantages. It can handle the full frequency range from zero to terahertz, low current levels, and slow processes, and it gives more insight into the physics of noise. This is demonstrated for RF noise in a nanoscale silicon N⁺NN⁺ structure and an n-p-n bipolar junction transistor, for which not only the terminal-current fluctuations are investigated but also the spatial origin of the noise, which is not possible by MC simulation. With respect to numerics, the new approach is similar to classical device simulation (e.g., drift-diffusion model), and the same well-known methods can be used (e.g., adjoint method, ac analysis, harmonic-balance technique, linear solvers, maximum entropy dissipation stabilization, box integration, etc.)