Ensemble Monte Carlo for III-V and Si n-channel FinFETs considering non-equilibrium degenerate statistics and quantum-confined scattering

Abstract

Particle-based ensemble semi-classical Monte Carlo (MC) methods employ quantum corrections (QCs) to address quantum confinement and degenerate carrier populations to model tomorrow's ultra-scaled MOSFETs. Here we present new approaches to quantum confinement and carrier degeneracy effects in a three-dimensional (3D) MC device simulator, and illustrate their significance through simulation of n-channel Si and III-V FinFETs. Original contributions include our treatment of far-from-equilibrium degenerate statistics and QC-based modeling of surface-roughness scattering, as well as considering quantum-confined phonon and impurity scattering in 3D. Typical MC simulations approximate degenerate carrier populations as Fermi distributions to model the Pauli-blocking (PB) of scattering to occupied final states. To allow for increasingly far-from-equilibrium non-Fermi carrier distributions in ultra-scaled devices, we instead generate the final-state occupation probabilities used for PB by sampling the local carrier populations as a function of energy and energy valley. This process is aided by the use of fractional carriers or sub-carriers, which minimizes classical carrier-carrier scattering. Quantum confinement effects are addressed through quantum-correction potentials (QCPs) generated from Schr\"{o}dinger-Poisson solvers, as commonly done. However, we use our valley- and orientation-dependent QCPs not just to redistribute carriers in real space, or even among energy valleys, but also to calculate confinement-dependent phonon, impurity, and surface-roughness scattering rates. FinFET simulations are used to illustrate how, collectively, these quantum effects can substantially reduce and even eliminate otherwise expected benefits of In$_{\text{0.53}}$Ga$_{\text{0.47}}$As FinFETs over otherwise identical Si FinFETs, despite higher thermal velocities in In$_{\text{0.53}}$Ga$_{\text{0.47}}$As.