Florian Rudolf

Modeling of Hot-Carrier Degradation in nLDMOS Devices: Different Approaches to the Solution of the Boltzmann Transport Equation

We propose two different approaches to describe carrier transport in n-laterally diffused MOS (nLDMOS) transistor and use the calculated carrier energy distribution as an input for our physical hot-carrier degradation (HCD) model. The first version relies on the solution of the Boltzmann transport equation using the spherical harmonics expansion method, while the second uses the simpler drift-diffusion (DD) scheme. We compare these two versions of our model and show that both approaches can capture HCD. We, therefore, conclude that in the case of nLDMOS devices, the DD-based variant of the model provides good accuracy and at the same time is computationally less expensive. This makes the DD-based version attractive for predictive HCD simulations of LDMOS transistors.

Automatic performance optimization in ViennaCL for GPUs

Highly parallel computing architectures such as graphics processing units (GPUs) pose several new challenges for scientific computing, which have been absent on single core CPUs. However, a transition from existing serial code to parallel code for GPUs often requires a considerable amount of effort. The Vienna Computing Library (ViennaCL) presented in the beginning of this work is based on OpenCL to support a wide range of hardware and aims at providing a high-level C++ interface that is mostly compatible with the existing CPU linear algebra library uBLAS shipped with the Boost libraries. As a general purpose linear algebra library, ViennaCL runs on a variety of GPU boards from different vendors pursuing different hardware architectures. As a consequence, the optimal number of threads working on a problem in parallel depends on the available hardware and the algorithm executed thereon. We present an optimization framework, which extracts suitable thread numbers and allows ViennaCL to automatically optimize itself to the underlying hardware. The performance enhancement of individually tuned kernels over default parameter choices range up to 25 percent for the kernels considered on high-end hardware, and up to a factor of seven on low-end hardware.

Physical modeling of hot-carrier degradation in nLDMOS transistors

Our physics-based HCD model has been validated using scaled CMOS transistors in our previous work. In this work we apply this model for the first time to a high-voltage nLDMOS device. For the calculation of the degrading behaviour the Boltzmann transport equation solver ViennaSHE is used which also requires high quality adaptive meshing. We discuss the influence of the different model components in the different device regions. Finally we compare the model to experimental degradation results and show that each one gives a significant contribution to the result and that all of them are needed in order to satisfactorily fit the experimental data.

The meshing framework ViennaMesh for finite element applications

The applicability of the meshing framework ViennaMesh for finite element simulations is investigated. Meshing tools are highly diverse, meaning that each software package offers specific properties, such as the conforming Delaunay property. The feasibility of these properties tends to be domain specific, thus restricting the general application of a meshing tool. For research purposes, it is desirable to have a rich toolset consisting of the various meshing packages in order to be able to quickly apply the various packages to the problem at hand. Different meshing tools have to be utilized to support a broader range of mesh properties. Further contributing to this problem is the lack of a common programming interface, impeding convenient switching of meshing backends. ViennaMesh tackles this challenge by providing a uniform meshing interface and reusable mesh-related tools, like CGAL, Gmsh, Netgen, and Tetgen. We depict the feasibility of our approach by discussing two applications relevant to finite element simulations, being a local mesh optimization and an adaptive mesh refinement application.

ViennaCL---Linear Algebra Library for Multi- and Many-Core Architectures

CUDA, OpenCL, and OpenMP are popular programming models for the multicore architectures of CPUs and many-core architectures of GPUs or Xeon Phis. At the same time, computational scientists face the question of which programming model to use to obtain their scientific results. We present the linear algebra library ViennaCL, which is built on top of all three programming models, thus enabling computational scientists to interface to a single library, yet obtain high performance for all three hardware types. Since the respective compute back end can be selected at runtime, one can seamlessly switch between different hardware types without the need for error-prone and time-consuming recompilation steps. We present new benchmark results for sparse linear algebra operations in ViennaCL, complementing results for the dense linear algebra operations in ViennaCL reported in earlier work. Comparisons with vendor libraries show that ViennaCL provides better overall performance for sparse matrix-vector and sparse mat...

Performance portability study of linear algebra kernels in OpenCL

The performance portability of OpenCL kernel implementations for common memory bandwidth limited linear algebra operations across different hardware generations of the same vendor as well as across vendors is studied. Certain combinations of kernel implementations and work sizes are found to exhibit good performance across compute kernels, hardware generations, and, to a lesser degree, vendors. As a consequence, it is demonstrated that the optimization of a single kernel is often sufficient to obtain good performance for a large class of more complicated operations.

A model for hot-carrier degradation in nLDMOS transistors based on the exact solution of the Boltzmann transport equation versus the drift-diffusion scheme

We present two schemes for carrier transport treatment to be used with our hot-carrier degradation (HCD) model. The first version relies on an exact solution of the Boltzmann transport equation (BTE) by means of the spherical harmonics expansion (SHE) method, whereas the second one uses a simplified drift-diffusion (DD) scheme to avoid the computationally expensive SHE approach. We use both versions of the model to simulate the change of the characteristics of an nLDMOS transistor subjected to hot-carrier stress and compare these theoretical degradation traces with the experimental ones. The similarity in the results of the SHE- and DD-based models together with the flexibility of the latter approach makes it attractive for fast and predictive HCD simulations for LDMOS devices.

Predictive and efficient modeling of hot-carrier degradation in nLDMOS devices

We present a physical model for hot-carrier degradation (HCD) which is based on the information provided by the carrier energy distribution function. In the first version of our model the distribution function is obtained as the exact solution of the Boltzmann transport equation, while in the second one we employ the simplified drift-diffusion scheme. Both versions of the model are validated against experimental HCD data in nLDMOS transistors, namely against the change of such device characteristics as the linear and saturation drain currents. We also compare the intermediate results of these two versions, i.e. the distribution function, defect generation rates, and interface state density profiles. Finally, we make a conclusion on the vitality of the drift-diffusion based version of the model.

Transformation invariant local element size specification

Quality and size of mesh elements are important for optimizing the accuracy and convergence of mesh-based simulation processes. Often, a priori information, like internal material properties, of regions of interest is available, which can be used to locally specify the mesh element size for finding a good balance between the mesh resolution on the one hand and the runtime and memory performance on the other. In many applications, like the optimization of geometric parameters, multiple meshes of similar objects are required. Typical mesh element size specification methods, like scalar fields, are inflexible because of their dependence on the geometry of the object. To avoid the creation of a mesh element size specifications for each object manually, a specification method based on the objects topology rather than on its geometry, is needed. We tackle this problem by extending our meshing software ViennaMesh with a dynamic framework for locally specifying the size of mesh elements. Our approach aims for convenient utilization by using a XML-based configuration with support for arithmetic expressions. To achieve a high level of flexibility and reusability, this configuration can be specified based on the objects topology, for example interfaces between different material regions. Additionally, geometric parameters, like the radius of the circumsphere of the object, are provided and can be used to, e.g., scale the local mesh element size according to the total size of the object. As a result, our configuration method is invariant under large set transformations, especially deformations, of the object enabling a high level of geometry independence. We depict the practicability of our approach by providing examples for meshes generated with this element sizing framework and discussing a geometry optimization application.

Dominant mechanisms of hot-carrier degradation in short- and long-channel transistors

Using our physics-based model for hot-carrier degradation (HCD) we analyze the role of such important processes as the Si-H bond-breakage induced by a solitary hot carrier, bond dissociation triggered by the miltivibrational excitation of the bond, and electron-electron scattering. To check the roles of these mechanisms we use planar CMOS devices with gate lengths varying between 65 and 300 nm as well as a high-voltage nLDMOS transistor. We show that the current HCD paradigm needs to be revised because the aforementioned processes can be crucial even under stress conditions at which they are supposed to be weak.