Karl Rupp

The Economic Limit to Moore's Law

There have been numerous papers and discussions about the lives and deaths of Moores Law, all of them dealing with several technological questions. In this paper, we consider economic limitations to the exponential growth of the number of components per chip. As the presented growth model shows, economics constitute indeed a potential slow-down mechanism.

Predictive Hot-Carrier Modeling of n-Channel MOSFETs

We present a physics-based hot-carrier degradation (HCD) model and validate it against measurement data on SiON n-channel MOSFETs of various channel lengths, from ultrascaled to long-channel transistors. The HCD model is capable of representing HCD in all these transistors stressed under different conditions using a unique set of model parameters. The degradation is modeled as a dissociation of Si-H bonds induced by two competing processes. It can be triggered by solitary highly energetical charge carriers or by excitation of multiple vibrational modes of the bond. In addition, we show that the influence of electron-electron scattering (EES), the dipole-field interaction, and the dispersion of the Si-H bond energy are crucial for understanding and modeling HCD. All model ingredients are considered on the basis of a deterministic Boltzmann transport equation solver, which serves as the transport kernel of a physics-based HCD model. Using this model, we analyze the role of each ingredient and show that EES may only be neglected in long-channel transistors, but is essential in ultrascaled devices.

PROGRAMMING CUDA AND OPENCL: A CASE STUDY USING MODERN C++ LIBRARIES ∗

We present a comparison of several modern C++ libraries providing high-level interfaces for programming multi- and many-core architectures on top of CUDA or OpenCL. The comparison focuses on the solution of ordinary differential equations (ODEs) and is based on odeint, a framework for the solution of systems of ODEs. Odeint is designed in a very flexible way and may be easily adapted for effective use of libraries such as MTL4, VexCL, or ViennaCL, using CUDA or OpenCL technologies. We found that CUDA and OpenCL work equally well for problems of large sizes, while OpenCL has higher overhead for smaller problems. Furthermore, we show that modern high-level libraries allow us to effectively use the computational resources of many-core GPUs or multicore CPUs without much knowledge of the underlying technologies.

On the feasibility of spherical harmonics expansions of the Boltzmann transport equation for three-dimensional device geometries

Accurate simulation of carrier transport requires the solution of Boltzmanns transport equation (BTE), which can be obtained by higher-order spherical harmonics expansion (SHE) techniques. Unfortunately, the high computational effort of the SHE method has so far prevented its application to 3D geometries. We refine the SHE method by suggesting and evaluating numerical techniques which allow for efficient solution of higher-order expansions even in the unchartered 3D regime.

GPU-Accelerated non-negative matrix factorization for text mining

An implementation of the non-negative matrix factorization algorithm for the purpose of text mining on graphics processing units is presented. Performance gains of more than one order of magnitude are obtained.

Modeling of hot carrier degradation using a spherical harmonics expansion of the bipolar Boltzmann transport equation

Recent studies have clearly demonstrated that the degradation of MOS transistors due to hot carriers is highly sensitive to the energy distribution of the carriers. These distributions can only be obtained in sufficient detail by the simultaneous solution of the Boltzmann transport equation (BTE) for both carrier types. For predictive simulations, the energy distributions have to be thoroughly resolved by including the fullband structure, impact ionization (II), electron electron scattering (EE), as well as the interaction of minority carriers with the majority carriers. We demonstrate that this challenging problem can be efficiently tackled using a deterministic approach based on the spherical harmonics expansion (SHE) of the BTE.

Matrix compression for spherical harmonics expansions of the Boltzmann transport equation for semiconductors

We investigate numerical solution schemes for the semiconductor Boltzmann transport equation using an expansion of the distribution function in spherical harmonics. A complexity analysis shows that traditional implementations using higher-order expansions suffer from huge memory requirements, especially for two- and three-dimensional devices. To overcome these complexity limitations, a compressed matrix storage scheme using Kronecker products is proposed, which reduces the asymptotic memory requirements for the storage of the system matrix significantly. The total memory requirements are then dominated by the memory required for the unknowns. Numerical results demonstrate the applicability of our method and confirm our theoretical results.

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.

Pipelined Iterative Solvers with Kernel Fusion for Graphics Processing Units

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.