We revisit the implementation of iterative solvers on discrete graphics processing units and demonstrate the benefit of implementations using extensive kernel fusion for pipelined formulations over conventional implementations of classical formulations. The proposed implementations with both CUDA and OpenCL are freely available in ViennaCL and are shown to be competitive with or even superior to other solver packages for graphics processing units. The highest-performance gains are obtained for small to medium-sized systems, while our implementations are on par with vendor-tuned implementations for very large systems. Our results are especially beneficial for transient problems, where many small to medium-sized systems instead of a single big system need to be solved.

Detailed investigations of charge trapping mechanisms have revealed a very specific picture of defects in the oxide of MOSFETs. Important features of these defects, such as the existence of metastable states, were indicated by time-dependent defect spectroscopy. These insights, together with the theoretical foundation provided by the non-radiative multi-phonon (NMP) theory, led to the development of the four-state NMP model. This model describes charging processes of oxide defects microscopically, and it is able to unify reliability phenomena such as bias temperature instability, random telegraph noise and stress-induced leakage currents. Furthermore, it correctly describes the continuous degradation measured on large-area devices and the discrete trapping events observed on nanoscale devices, using the same parameters. We finally also demonstrate how this comprehensive validity can be exploited to efficiently extract the physical model parameters in order to simulate the variability and reliability of nanoscale devices.

This paper presents an extensive statistical study on the impact of bias temperature instability (BTI) on digital circuits. A statistical framework for the evaluation of BTI at the electrical (SPICE) level, enhanced by an atomistic model for BTI, is introduced. This framework is then employed to perform the timing analysis of different combinational paths using cells from a given library, aiming to statistically model BTI at the higher abstraction level. A statistical static timing analysis (SSTA) method is then performed and the results are compared to detailed simulations using atomistic models based on experimental data. The comparison between the two methods shows that for large paths both methods converge to the same distribution for the delay while for short paths the delay distributions are different causing the SSTA method to generate misleading results. An analysis is then performed in order to understand and formalize the results.

We discuss discretization schemes for the Poisson equation, the isothermal drift-diffusion equations, and higher order moment equations derived from the Boltzmann transport equation for general coordinate systems. We briefly summarize the method of dimension reduction when the problem does not depend on one coordinate. Discretization schemes for dimension-reduced coordinate systems are introduced, which provide curvilinear coordinate systems. In addition to the reduction of the dimensionality, another benefit of these curved coordinate systems is that the domain approximation is more accurate, and therefore, the mesh point density can be kept smaller compared to the original problem. We obtain a discretization scheme for the isothermal drift-diffusion equation in closed from. For higher order transport equations, we use the approximation method of optimum artificial diffusivity and generalize it for non-Cartesian coordinate systems. For the special case of cylindrical coordinates, we can show that it is not necessary to introduce special discretization schemes apart from the standard Scharfetter-Gummel scheme.

For process and device simulation, very high mesh densities are often required to obtain accurate simulation results. Unfortunately, the required mesh densities depend often on a direction. Conventional mesh-refinement strategies generate isotropic meshes with a high amount of mesh points, reaching the memory and time limits in particular for three-dimensional simulations. For a better resolution of the carrier concentrations, for instance, a boundary-conforming mesh-generation method with tunable mesh spacings in almost orthogonal directions was developed. Similar to elliptic mesh generation, the mesh points are placed inside the simulation regions based on the solution of partial differential equations. The method used can produce highly anisotropic mesh densities in the regions of particular interest. In contrast to elliptic grid generation, which produces structured grids, the method used generates triangular or tetrahedral (unstructured) Delaunay meshes in two or three dimensions, respectively, which are very well suitable for the process and device simulators.

Since Stratton published his famous paper four decades ago, various transport models have been proposed which account for the average carrier energy or temperature in one way or another. The need for such transport models arose because the traditionally used drift-diffusion model cannot capture nonlocal effects which gained increasing importance in modern miniaturized semiconductor devices. In the derivation of these models from Boltzmann's transport equation, several assumptions have to be made in order to obtain a tractable equation set. Although these assumptions may differ significantly, the resulting final models show various similarities, which has frequently led to confusion. We give a detailed review on this subject, highlighting the differences and similarities between the models, and we shed some light on the critical issues associated with higher order transport models.