This work presents the first comprehensive full-band Monte Carlo model for the simulation of silicon/silicon-germanium devices with arbitrary germanium profiles. The model includes a new CPU and memory efficient method for the discretization of the Brillouin zone based on adaptive nonuniform tetrahedral grids and a very efficient method for transfers through heterointerfaces in the case of irregular -space grids. The feasibility of the FB-MC simulation is demonstrated by application to an industrial HBT with a graded germanium profile and different aspects of the microscopic carrier transport are discussed. Internal distributions of the transistor are calculated with a very low noise level and high efficiency allowing a detailed investigation of the device behavior.

In this work it is shown for the first time how to calculate in advance by momentum-based noise simulation for stationary Monte Carlo (MC) device simulations the CPU time, which is necessary to achieve a predefined error level. In addition, analytical expressions for the simulation-time factor of terminal current estimation are given. Without further improvements of the MC algorithm MC simulations of small terminal currents are found to be often prohibitively CPU intensive.

The full-band Monte Carlo technique is currently the most accurate device simulation method, but its usefulness is limited because it is very CPU intensive. This work describes efficient algorithms in detail, which raise the efficiency of the full-band Monte Carlo method to a level where it becomes applicable in the device design process beyond exemplary simulations. The k-space is discretized with a nonuniform tetrahedral grid, which minimizes the discretization error of the linear energy interpolation and memory requirements. A consistent discretization of the inverse mass tensor is utilized to formulate efficient transport parameter estimators. Particle scattering is modeled in such a way that a very fast rejection technique can be used for the generation of the final state eliminating the main cause of the inefficiency of full-band Monte Carlo simulations. The developed full-band Monte Carlo simulator is highly efficient. For example, in conjunction with the nonself-consistent simulation technique CPU times of a few CPU minutes per bias point are achieved for substrate current calculations. Self-consistent calculations of the drain current of a 60nm-NMOSFET take about a few CPU hours demonstrating the feasibility of full-band Monte Carlo simulations.