Gaussian process regression for virtual metrology of microchip quality and the resulting strategic sampling scheme

Manufacturing of integrated circuits involves many sequential processes, often ex- ecuted to nanoscale tolerances, and the yield depends on the often unmeasured quality of intermediate steps. In the high-throughput industry of fabricating microelectronics on semi-conducting wafers, scheduling measurements of product quality before the electrical test of the complete IC can be expensive. We therefore seek to predict metrics of product quality based on sensor readings describing the environment within the relevant tool during the processing of each wafer, or to apply the concept of virtual metrology (VM) to monitor these intermediate steps. We model the data using Gaussian process regression (GPR), adapted to simultaneously learn the nonlinear dynamics that govern the quality characteristic, as well as their operating space, expressed by a linear embedding of the sensor traces’ features. Such Bayesian models predict a distribution for the target metric, such as a critical dimension, so one may assess the model’s credibility through its predictive uncertainty. Assuming measurements of the quality characteristic of interest are budgeted, we seek to hasten convergence of the GPR model to a credible form through an active sampling scheme, whereby the predictive uncertainty informs which wafer’s quality to measure next. We evaluate this convergence when predicting and updating online, as if in a factory, using a large dataset for plasma-enhanced chemical vapor deposition (PECVD), with measured thicknesses for ~32,000 wafers. By approximately optimizing the information extracted from this seemingly repetitive data describing a tightly controlled process, GPR achieves ~10% greater accuracy on average than a baseline linear model based on partial least squares (PLS). In a derivative study, we seek to discern the degree of drift in the process over the several months the data spans. We express this drift by how unusual the relevant features, as embedded by the GPR model, appear as the in- puts compensate for degrading conditions. This method detects the onset of consistently unusual behavior that extends to a bimodal thickness fault, anticipating its flagging by as much as two days.Mechanical Engineerin

Heurísticas bioinspiradas para el problema de Floorplanning 3D térmico de dispositivos MPSoCs

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Informática, Departamento de Arquitectura de Computadores y Automática, leída el 20-06-2013Depto. de Arquitectura de Computadores y AutomáticaFac. de InformáticaTRUEunpu

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques

A survey on scheduling and mapping techniques in 3D Network-on-chip

Network-on-Chips (NoCs) have been widely employed in the design of multiprocessor system-on-chips (MPSoCs) as a scalable communication solution. NoCs enable communications between on-chip Intellectual Property (IP) cores and allow those cores to achieve higher performance by outsourcing their communication tasks. Mapping and Scheduling methodologies are key elements in assigning application tasks, allocating the tasks to the IPs, and organising communication among them to achieve some specified objectives. The goal of this paper is to present a detailed state-of-the-art of research in the field of mapping and scheduling of applications on 3D NoC, classifying the works based on several dimensions and giving some potential research directions

The Thermal-Constrained Real-Time Systems Design on Multi-Core Platforms -- An Analytical Approach

Over the past decades, the shrinking transistor size enabled more transistors to be integrated into an IC chip, to achieve higher and higher computing performances. However, the semiconductor industry is now reaching a saturation point of Moore’s Law largely due to soaring power consumption and heat dissipation, among other factors. High chip temperature not only significantly increases packing/cooling cost, degrades system performance and reliability, but also increases the energy consumption and even damages the chip permanently. Although designing 2D and even 3D multi-core processors helps to lower the power/thermal barrier for single-core architectures by exploring the thread/process level parallelism, the higher power density and longer heat removal path has made the thermal problem substantially more challenging, surpassing the heat dissipation capability of traditional cooling mechanisms such as cooling fan, heat sink, heat spread, etc., in the design of new generations of computing systems. As a result, dynamic thermal management (DTM), i.e. to control the thermal behavior by dynamically varying computing performance and workload allocation on an IC chip, has been well-recognized as an effective strategy to deal with the thermal challenges. Over the past decades, the shrinking transistor size, benefited from the advancement of IC technology, enabled more transistors to be integrated into an IC chip, to achieve higher and higher computing performances. However, the semiconductor industry is now reaching a saturation point of Moore’s Law largely due to soaring power consumption and heat dissipation, among other factors. High chip temperature not only significantly increases packing/cooling cost, degrades system performance and reliability, but also increases the energy consumption and even damages the chip permanently. Although designing 2D and even 3D multi-core processors helps to lower the power/thermal barrier for single-core architectures by exploring the thread/process level parallelism, the higher power density and longer heat removal path has made the thermal problem substantially more challenging, surpassing the heat dissipation capability of traditional cooling mechanisms such as cooling fan, heat sink, heat spread, etc., in the design of new generations of computing systems. As a result, dynamic thermal management (DTM), i.e. to control the thermal behavior by dynamically varying computing performance and workload allocation on an IC chip, has been well-recognized as an effective strategy to deal with the thermal challenges. Different from many existing DTM heuristics that are based on simple intuitions, we seek to address the thermal problems through a rigorous analytical approach, to achieve the high predictability requirement in real-time system design. In this regard, we have made a number of important contributions. First, we develop a series of lemmas and theorems that are general enough to uncover the fundamental principles and characteristics with regard to the thermal model, peak temperature identification and peak temperature reduction, which are key to thermal-constrained real-time computer system design. Second, we develop a design-time frequency and voltage oscillating approach on multi-core platforms, which can greatly enhance the system throughput and its service capacity. Third, different from the traditional workload balancing approach, we develop a thermal-balancing approach that can substantially improve the energy efficiency and task partitioning feasibility, especially when the system utilization is high or with a tight temperature constraint. The significance of our research is that, not only can our proposed algorithms on throughput maximization and energy conservation outperform existing work significantly as demonstrated in our extensive experimental results, the theoretical results in our research are very general and can greatly benefit other thermal-related research