Direct Solution of the Boltzmann Transport Equation and Poisson–SchrÖdinger Equation for Nanoscale MOSFETs

We propose an efficient and fast algorithm to solve the coupled Poisson-Schrodinger and Boltzmann transport equations (BTE) in two dimensions. The BTE is solved in the relaxation time approximation within each subband obtained from the direct solution of the Schrodinger equation. The proposed approach, considering a subband-based transport formalism, allows to fully explore the entire range from drift-diffusion to ballistic regime in nanoscale field-effect transistors. Quantum effects are also fully taken into account by the direct solution of the Schrodinger equation. The model is implemented in the NanoTCAD2D device simulator and used to study the device performance of a 25-nm channel-length MOSFET. The influence of scattering on the electron distribution function and on device characteristics is analyzed in detail.