A self-consistent solution of the Poisson, Schrödinger and Boltzmann equations by a full Newton-Raphson approach for nanoscale semiconductor devices

We present a full Newton-Raphson approach for solving the Poisson, Schrödinger and Boltzmann equations in a deterministic framework with Fourier harmonics expansion for a 2D nanoscale device. The effects of the Schrödinger equation are included via first order perturbation theory and prove to have a significant impact. A comparison to the Gummel type iteration scheme yields superiority of the full Newton-Raphson method in convergence speed and solver time. The full Newton-Raphson method is also of particular relevance to small-signal analyses in this framework.