Process variability-aware statistical hybrid modeling of dynamic power dissipation in 65 nm CMOS designs

A generalized technique is proposed for modeling the effects of process variations on dynamic power by directly relating the variations in process parameters to variations in dynamic power of a digital circuit. The dynamic power of a 2-input NAND gate is characterized by mixed-mode simulations, to be used as a library element for 65mn gate length technology. The proposed methodology is demonstrated with a multiplier circuit built using the NAND gate library, by characterizing its dynamic power through Monte Carlo analysis. The statistical technique of Response. Surface Methodology (RSM) using Design of Experiments (DOE) and Least Squares Method (LSM), are employed to generate a "hybrid model" for gate power to account for simultaneous variations in multiple process parameters. We demonstrate that our hybrid model based statistical design approach results in considerable savings in the power budget of low power CMOS designs with an error of less than 1%, with significant reductions in uncertainty by atleast 6X on a normalized basis, against worst case design.

Device oriented statistical modeling method for process variability in 45nm analog CMOS technology

With the rapid scaling down of the semiconductor process technology, the process variation aware circuit design has become essential today. Several statistical models have been proposed to deal with the process variation. We propose an accurate BSIM model for handling variability in 45nm CMOS technology. The MOSFET is designed to meet the specification of low standby power technology of International Technology Roadmap for Semiconductors (ITRS).The process parameters variation of annealing temperature, oxide thickness, halo dose and title angle of halo implant are considered for the model development. One parameter variation at a time is considered for developing the model. The model validation is done by performance matching with device simulation results and reported error is less than 10%.© (2012) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Modeling of heat and mass transfer for solid state fermentation process in tray bioreactor

A mathematical model is developed to simulate oxygen consumption, heat generation and cell growth in solid state fermentation (SSF). The fungal growth on the solid substrate particles results in the increase of the cell film thickness around the particles. The model incorporates this increase in the biofilm size which leads to decrease in the porosity of the substrate bed and diffusivity of oxygen in the bed. The model also takes into account the effect of steric hindrance limitations in SSF. The growth of cells around single particle and resulting expansion of biofilm around the particle is analyzed for simplified zero and first order oxygen consumption kinetics. Under conditions of zero order kinetics, the model predicts upper limit on cell density. The model simulations for packed bed of solid particles in tray bioreactor show distinct limitations on growth due to simultaneous heat and mass transport phenomena accompanying solid state fermentation process. The extent of limitation due to heat and/or mass transport phenomena is analyzed during different stages of fermentation. It is expected that the model will lead to better understanding of the transport processes in SSF, and therefore, will assist in optimal design of bioreactors for SSF.

Voltage and Temperature Aware Statistical Leakage Analysis Framework Using Artificial Neural Networks

Artificial neural networks (ANNs) have shown great promise in modeling circuit parameters for computer aided design applications. Leakage currents, which depend on process parameters, supply voltage and temperature can be modeled accurately with ANNs. However, the complex nature of the ANN model, with the standard sigmoidal activation functions, does not allow analytical expressions for its mean and variance. We propose the use of a new activation function that allows us to derive an analytical expression for the mean and a semi-analytical expression for the variance of the ANN-based leakage model. To the best of our knowledge this is the first result in this direction. Our neural network model also includes the voltage and temperature as input parameters, thereby enabling voltage and temperature aware statistical leakage analysis (SLA). All existing SLA frameworks are closely tied to the exponential polynomial leakage model and hence fail to work with sophisticated ANN models. In this paper, we also set up an SLA framework that can efficiently work with these ANN models. Results show that the cumulative distribution function of leakage current of ISCAS'85 circuits can be predicted accurately with the error in mean and standard deviation, compared to Monte Carlo-based simulations, being less than 1% and 2% respectively across a range of voltage and temperature values.

Modeling of the cooling process on the runout table of a hot strip mill - A parallel approach

This paper deals with the development of a new model for the cooling process on the runout table of hot strip mills, The suitability of different numerical methods for the solution of the proposed model equation from the point of view of accuracy and computation time are studied, Parallel solutions for the model equation are proposed.

Three-dimensional computational modeling of momentum, heat, and mass transfer in a laser surface alloying process

A three- dimensional, transient model is developed for studying heat transfer, fluid flow, and mass transfer for the case of a single- pass laser surface alloying process. The coupled momentum, energy, and species conservation equations are solved using a finite volume procedure. Phase change processes are modeled using a fixed-grid enthalpy-porosity technique, which is capable of predicting the continuously evolving solid- liquid interface. The three- dimensional model is able to predict the species concentration distribution inside the molten pool during alloying, as well as in the entire cross section of the solidified alloy. The model is simulated for different values of various significant processing parameters such as laser power, scanning speed, and powder feedrate in order to assess their influences on geometry and dynamics of the pool, cooling rates, as well as species concentration distribution inside the substrate. Effects of incorporating property variations in the numerical model are also discussed.

Process Variation Aware Estimation of Static Leakage Power in Nano-CMOS

We present a statistical methodology for leakage power estimation, due to subthreshold and gate tunneling leakage, in the presence of process variations, for 65 nm CMOS. The circuit leakage power variations is analyzed by Monte Carlo (MC) simulations, by characterizing NAND gate library. A statistical “hybrid model” is proposed, to extend this methodology to a generic library. We demonstrate that hybrid model based statistical design results in up to 95% improvement in the prediction of worst to best corner leakage spread, with an error of less than 0.5%, with respect to worst case design.

Modeling of the Effects of Process Variations on Circuit Delay at 65nm

A novel methodology for modeling the effects of process variations on circuit delay performance is proposed by relating the variations in process parameters to variations in delay metric of a complex digital circuit. The delay of a 2-input NAND gate with 65nm gate length transistors is extensively characterized by mixed-mode simulations which is then used as a library element. The variation in saturation current Ionat the device level, and the variation in rising/falling edge stage delay for the NAND gate at the circuit level, are taken as performance metrics. A 4-bit x 4-bit Wallace tree multiplier circuit is used as a representative combinational circuit to demonstrate the proposed methodology. The variation in the multiplier delay is characterized, to obtain delay distributions, by an extensive Monte Carlo analysis. An analytical model based on CV/I metric is proposed, to extend this methodology for a generic technology library with a variety of library elements.

A Long Memory Process Based Parametric Modeling and Recognition of PD Signal

We address the problem of recognition and retrieval of relatively weak industrial signal such as Partial Discharges (PD) buried in excessive noise. The major bottleneck being the recognition and suppression of stochastic pulsive interference (PI) which has similar time-frequency characteristics as PD pulse. Therefore conventional frequency based DSP techniques are not useful in retrieving PD pulses. We employ statistical signal modeling based on combination of long-memory process and probabilistic principal component analysis (PPCA). An parametric analysis of the signal is exercised for extracting the features of desired pules. We incorporate a wavelet based bootstrap method for obtaining the noise training vectors from observed data. The procedure adopted in this work is completely different from the research work reported in the literature, which is generally based on deserved signal frequency and noise frequency.

Wave propagation in elastic solids undergoing damage and growth process

Modeling and analysis of wave propagation in elastic solids undergoing damage and growth process are reported in this paper. Two types of diagnostic problems, (1) the propagation of waves in the presence of a slow growth process and (2) the propagation of waves in the presence of a fast growth process, are considered. The proposed model employs a slow and a fast time scale and a homogenization technique in the wavelength scale. A detailed analysis of wave dispersion is carried out. A spectral analysis reveals certain low-frequency bands, where the interaction between the wave and the growth process produces acoustic metamaterial-like behavior. Various practical issues in designing an efficient method of acousto-ultrasonic wave based diagnostics of the growth process are discussed. Diagnostics of isotropic damage in a ductile or quasi-brittle solid by using a micro-second pulsating signal is considered for computer simulations, which is to illustrate the practical application of the proposed modeling and analysis. The simulated results explain how an estimate of signal spreading can be effectively employed to detect the presence of a steady-state damage or the saturation of a process.

Modeling of dynamic material behavior in hot deformation: Forging of Ti-6242

A new method of modeling material behavior which accounts for the dynamic metallurgical processes occurring during hot deformation is presented. The approach in this method is to consider the workpiece as a dissipator of power in the total processing system and to evaluate the dissipated power co-contentJ = ∫o σ ε ⋅dσ from the constitutive equation relating the strain rate (ε) to the flow stress (σ). The optimum processing conditions of temperature and strain rate are those corresponding to the maximum or peak inJ. It is shown thatJ is related to the strain-rate sensitivity (m) of the material and reaches a maximum value(J max) whenm = 1. The efficiency of the power dissipation(J/J max) through metallurgical processes is shown to be an index of the dynamic behavior of the material and is useful in obtaining a unique combination of temperature and strain rate for processing and also in delineating the regions of internal fracture. In this method of modeling, noa priori knowledge or evaluation of the atomistic mechanisms is required, and the method is effective even when more than one dissipation process occurs, which is particularly advantageous in the hot processing of commercial alloys having complex microstructures. This method has been applied to modeling of the behavior of Ti-6242 during hot forging. The behavior of α+ β andβ preform microstructures has been exam-ined, and the results show that the optimum condition for hot forging of these preforms is obtained at 927 °C (1200 K) and a strain rate of 1CT•3 s•1. Variations in the efficiency of dissipation with temperature and strain rate are correlated with the dynamic microstructural changes occurring in the material.

State Dependent Attempt Rate Modeling of Single Cell IEEE 802.11 WLANs with Homogeneous Nodes and Poisson Arrivals

Analytical models of IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known mean-field approximations proposed by Bianchi for saturated nodes. In this paper, we provide a new approach for modeling the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model M queues (one queue per node) served by the CSMA/CA protocol as standardized in the IEEE 802.11 DCF. The approximation is that, when n of the M queues are non-empty, the attempt probability of the n non-empty nodes is given by the long-term attempt probability of n saturated nodes as provided by Bianchi's model. This yields a coupled queue system. When packets arrive to the M queues according to independent Poisson processes, we provide an exact model for the coupled queue system with SDAR service. The main contribution of this paper is to provide an analysis of the coupled queue process by studying a lower dimensional process and by introducing a certain conditional independence approximation. We show that the numerical results obtained from our finite buffer analysis are in excellent agreement with the corresponding results obtained from ns-2 simulations. We replace the CSMA/CA protocol as implemented in the ns-2 simulator with the SDAR service model to show that the SDAR approximation provides an accurate model for the CSMA/CA protocol. We also report the simulation speed-ups thus obtained by our model-based simulation.

Stochastic Modeling of an Aircraft Traversing a Runway Using Time Series Analysis

Time series, from a narrow point of view, is a sequence of observations on a stochastic process made at discrete and equally spaced time intervals. Its future behavior can be predicted by identifying, fitting, and confirming a mathematical model. In this paper, time series analysis is applied to problems concerning runwayinduced vibrations of an aircraft. A simple mathematical model based on this technique is fitted to obtain the impulse response coefficients of an aircraft system considered as a whole for a particular type of operation. Using this model, the output which is the aircraft response can be obtained with lesser computation time for any runway profile as the input.

Modeling of Convection and Macrosegregation through Appropriate Consideration of Multiphase/Multiscale Phenomena during Alloy Solidification

Solidification processes are complex in nature, involving multiple phases and several length scales. The properties of solidified products are dictated by the microstructure, the mactostructure, and various defects present in the casting. These, in turn, are governed by the multiphase transport phenomena Occurring at different length scales. In order to control and improve the quality of cast products, it is important to have a thorough understanding of various physical and physicochemical phenomena Occurring at various length scales. preferably through predictive models and controlled experiments. In this context, the modeling of transport phenomena during alloy solidification has evolved over the last few decades due to the complex multiscale nature of the problem. Despite this, a model accounting for all the important length scales directly is computationally prohibitive. Thus, in the past, single-phase continuum models have often been employed with respect to a single length scale to model solidification processing. However, continuous development in understanding the physics of solidification at various length scales oil one hand and the phenomenal growth of computational power oil the other have allowed researchers to use increasingly complex multiphase/multiscale models in recent. times. These models have allowed greater understanding of the coupled micro/macro nature of the process and have made it possible to predict solute segregation and microstructure evolution at different length scales. In this paper, a brief overview of the current status of modeling of convection and macrosegregation in alloy solidification processing is presented.

Ferrous iron oxidation by foam immobilized Acidithiobacillus ferrooxidans: Experiments and modeling

Ferrous iron bio-oxidation by Acidithiobacillus ferrooxidans immobilized on polyurethane foam was investigated. Cells were immobilized on foams by placing them in a growth environment and fully bacterially activated polyurethane foams (BAPUFs) were prepared by serial subculturing in batches with partially bacterially activated foam (pBAPUFs). The dependence of foam density on cell immobilization process, the effect of pH and BAPUF loading on ferrous oxidation were studied to choose operating parameters for continuous operations. With an objective to have high cell densities both in foam and the liquid phase, pretreated foams of density 50 kg/m3 as cell support and ferrous oxidation at pH 1.5 to moderate the ferric precipitation were preferred. A novel basket-type bioreactor for continuous ferrous iron oxidation, which features a multiple effect of stirred tank in combination with recirculation, was designed and operated. The results were compared with that of a free cell and a sheet-type foam immobilized reactors. A fivefold increase in ferric iron productivity at 33.02 g/h/L of free volume in foam was achieved using basket-type bioreactor when compared to a free cell continuous system. A mathematical model for ferrous iron oxidation by Acidithiobacillus ferrooxidans cells immobilized on polyurethane foam was developed with cell growth in foam accounted by an effectiveness factor. The basic parameters of simulation were estimated using the experimental data on free cell growth as well as from cell attachment to foam under nongrowing conditions. The model predicted the phase of both oxidation of ferrous in shake flasks by pBAPUFs as well as by fully activated BAPUFs for different cell loadings in foam. Model for stirred tank basket bioreactor predicted within 5% both transient and steady state of the experiments closely for the simulated dilution rates. Bio-oxidation at high Fe2+ concentrations were simulated with experiments when substrate and product inhibition coefficients were factored into cell growth kinetics.