Numerical modeling of electron noise in nanoscale Si devices

摘要

A deterministic solver for the Langevin Boltzmann equation is presented, which is based on a spherical harmonics expansion, box integration, and a maximum entropy dissipation principle. The numerical properties of this method are very similar to the classical approaches (drift-diffusion or hydrodynamic models), and the same numerical methods can be used (ac analysis, adjoint method, harmonic balance, etc). Since the equations can be solved directly in the frequency domain, the full frequency range down to zero frequency is accessible. In addition, rare events can be simulated without excessive CPU times. This is demonstrated for a silicon NPN BJT. Not only the terminal current noise is calculated, but also the spatial origin of noise and the corresponding Green's functions.