Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices. I. Theory

Langevin-type two-dimensional (2-D) bipolar drift-diffusion (DD) and hydrodynamic (HD) noise models are presented for Si and SiGe devices, which are based on the new concept of modified Langevin forces, which ensure that the DD and HD models exactly reproduce the fluctuations of the full-band Monte Carlo (MC) model under homogeneous bulk conditions. All transport and noise parameters are generated by MC bulk simulations and stored in lookup tables, which must be built only once. As a consequence, the accuracy of the DD and HD models is improved without an increase in CPU time compared to models with analytical expressions for the parameters. Considering the full-band structure, a remarkably strong dependence of noise on crystal orientation is found.