Model and analysis of single event transient sensitivity based on uncertainty quantification

Single event transients (SETs) stand out as one of the major causes of soft errors in nanoscale CMOS integrated circuits. To reduce the need for exhaustive circuit simulations in the design of radiation-hard integrated circuits, the cost-effective approaches for characterization and modeling of SET generation effects in standard logic cells are required. In this work, a SPICE-based methodology for characterization of SET generation effects, employing two different SET current models, is presented. Based on the acquired simulation results, the empirical models for the two main SET generation metrics (SET critical charge and SET pulse width) are derived. The SET generation models and the respective model parameters are intended to be used as inputs for the higher-level analysis of SET effects in digital circuits designed with the characterized standard logic cells. By storing the model parameters for each gate in the look-up table, instead of storing the raw data obtained from SPICE simulations, the amount of characterization data can be significantly reduced, allowing to speed up the subsequent SET analysis of a complex circuit.

The main goal of this Focus Point volume is to explore new advances on theoretical and computational techniques for uncertainty quantification (UQ) of modeling and simulation in relevant problems appearing in physics sciences. The papers submitted to this volume were received by invitation. As a result we have collected a number of high-quality contributions dealing with a rich and update picture of UQ analysis that includes its interplay with laws in physics problems, mainly, formulated via differential equations. The following text highlights some of the primary aspects of the topics covered as well as the contributions of the published papers. The consideration of randomness in the analysis of mathematical models for analyzing relevant problems related to health is currently a main research topic. The paper "The role of noise in the tumor dynamics under chemotherapy treatment" proposes a two-dimensional stochastic nonlinear differential system, taking into account the impact of chemotherapy on both the tumor and the healthy cells. The randomness is driven by two uncorrelated Gaussian noises with different levels of intensity. Authors analyze this interesting problem combining a number of techniques that include bifurcation diagrams, phase portraits, time series and probability density plots. The contribution is aimed at offering a trustworthy explanation of tumor growth under medical treatment. The Focus Point volume continues with the study of a second model also belonging to Medicine, specifically, to Epidemiology. In "Random resampling numerical simulations applied to a SEIR compartmental model," authors revisit the SEIR model addressed to study the dynamics of COVID-19 in Spain during its first pandemic-wave in 2020. Authors concentrate on estimating model parameters taking into account data uncertainties by means of bootstrap sampling. The validation of the stochastic analysis is performed by different goodness-of-fit measures. They show that the point estimates obtained by the bootstrap samples improve the ones of the original data. The use of fractional and stochastic calculus has emerged, mainly, during the last decades with important applications in Physics. In "Hölder continuity of mild solutions of space-time fractional stochastic heat equation driven by colored noise," authors combine the Caputo fractional derivative with the fractional Laplace operator to analyze the heat equation with noise driven by a colored noise. The paper establishes Hölder continuity of mild random field solutions of the aforementioned PDE by, first, taking advantage of key properties associated to the space-time fractional Green function. In "Asymptotic controllability of nonlinear Fokker-Planck equations," the author studies a problem related with stabilization of the control for a Fokker-Plank PDE. This equation often appears in kinetic theory of statistical mechanics and, contains, as a particular case, the classical Einstein-Smoluchowski equation, which describes the time evolution of the probability density of Brownian particles in a field of forms with a given potential. In the paper, one identifies a class of final states (reachable states) for which the problem has solution. The results can have interesting applications in control theory and physics. The stochastic of multiphysics systems is often a challenging problem because different physical scales and physical effects must be properly combined to accurately conduct the corresponding analysis. When the study is done in the practical setting, it usually involves the rigorous treatment of large sets of data. In the paper "Random stick-slip oscillations in a multiphysics system" (Fig. 12 ), one combines stick-slip oscillations, electromechanical coupling and uncertainties to characterize and quantify the stochastic response of a multiphysics system in terms of two physical quantities, duration and position, which are dependent random variables that must be jointly studied.

The effect of negative bias temperature instability (NBTI) on a single event transient (SET) has been studied in a 130 nm bulk silicon CMOS process based on 3D TCAD device simulations. The investigation shows that NBTI can result in the pulse width and amplitude of SET narrowing when the heavy ion hits the PMOS in the high-input inverter; but NBTI can result in the pulse width and amplitude of SET broadening when the heavy ion hits the NMOS in the low-input inverter. Based on this study, for the first time we propose that the impact of NBTI on a SET produced by the heavy ion hitting the NMOS has already been a significant reliability issue and should be of wide concern, and the radiation hardened design must consider the impact of NBTI on a SET.

Identification of linear models in view of robust control design requires the identification of a control‐relevant nominal model, and a quantification of model uncertainty. In this paper a procedure is presented to quantify the model uncertainty of any prespecified nominal model, from a sequence of measurement data of input and output signals from a plant. By employing a nonparametric empirical transfer function estimate (ETFE), we are able to split the model uncertainty into three parts: the inherent uncertainty in the data due to data imperfections, the unmodelled dynamics in the nominal model, and the uncertainty due to interpolation. A frequency‐dependent hard error bound is constructed, and results are given for tightening the bound through appropriate input design.

Variations of single event transient induced by line edge roughness (LER) and temperature in FinFET

As technology down scales, single event transient (SET) is more vulnerable than before in combinational circuits. This paper proposes a novel layout technique to mitigate the SET effect in combinational circuits. Based on 65nm CMOS process, technology computer aided design (TCAD) SET simulations are conducted on conventional layout, source-isolation layout, dummy transistor layout and the proposed layout. Heavy ions with different liner energy transfer (LET) values, inject angles and striking locations are simulated. The results indicate that, the proposed layout have considerable effect on decreasing the SET pulse width than other layouts. Compare with dummy transistor the proposed enhance dummy transistor have no additional area cost.

The single event transients (SETs) are a common source of malfunction in nano-scale CMOS integrated circuits. For this reason, evaluation of the SET effects and application of appropriate measures for their mitigation are fundamental tasks in the design of advanced radiation hardened integrated circuits. In general, SET analysis is based on the multi-scale modeling and simulation approach comprising four main phases: modeling and simulation of radiation-matter interactions, device-level modeling and simulation, circuit-level modeling and simulation and logic-level modeling and simulation. In order to reduce the time and cost of the evaluation and design processes, a lot of effort is invested into the development of appropriate models which could provide accurate SET simulations at the circuit level. The circuit-level simulations provide a good trade-off between the complexity and speed of simulations, and at the same time ensure very good accuracy. This paper reviews the approaches for modeling and simulation of SET effects at the circuit level, emphasizing the major advantages and disadvantages of each approach.

Accurate needle placement is essential for prostate biopsy. Recently, transperineal prostate biopsies are receiving renewed interest due to concern over infection from conventional transrectal biopsies. However, accurate needle placement is more challenging in the transperineal approach than in the transrectal approach due to the long insertion distance leading to a large targeting error and repeated insertion attempts. Improved procedure planning tools that can predict the deviation of the needle can potentially reduce the targeting error and number of insertion attempts. Prediction of deflection magnitude requires a model of biopsy needle deflection, which in turn requires information about tissue material properties. However, material properties of tissue in patients cannot be easily obtained. Accounting for this uncertainty in patient tissue properties requires a model capable of quantifying uncertainty in needle deflection as a function of a distribution of tissue properties. A Monte Carlo uncertainty quantification requires 1000s of samples, but it is not possible to obtain this many samples in a short enough time for intraoperative procedure planning using published needle deflection predictionmodels. This work seeks to develop a model of needle deflection fast enough for use in intraoperative procedure planning, validate this model against experimental results, and integrate it into a Monte Carlo uncertainty quantificationmodel. This work used a mechanics-based model of biopsy needle deflection to train a Fourier feature neural network (FFNN) model in order to make predictions with a low computational cost. Both models were validated against experimental data. The neural network model was used in a Monte Carlo uncertainty quantification model to quantify uncertainty in needle deflection arising from uncertain tissue mechanicalproperties. This work (1) implemented a mechanics-based model and a FFNN model. Both models were validated against previously published experiments carried out with tissue phantoms. Both models showed close agreement with the experimental data. (2) We showed that our FFNN model was more accurate than a baseline ordinary least squares model, introducing only about 0.3-mm tip deflection error compared to the mechanics-based model. We also showed that our FFNN model makes unbiased predictions with respect to the amount of deflection. (3) We demonstrated a Monte Carlo uncertainty quantification model of needle deflection with a low computational cost of about 20 CPU s. We used our uncertainty quantification model to show how the depth, stiffness, and magnitude of uncertainty in a layer of tissue affect needle deflection. In addition, we showed a simple clinical example of the use of our model. This work demonstrates a Monte Carlo uncertainty quantification model of needle deflection with a low computational cost. This method shows promise for future applications in procedure planning for prostate biopsies as well as other transperineal procedures conducted with flexible needles such as cryoablation andbrachytherapy.

The objective of this work is to provide and use both experimental fluid dynamics (EFD) data and computational fluid dynamics (CFD) results to validate a regular-wave uncertainty quantification (UQ) model of ship response in irregular waves, based on a set of stochastic regular waves with variable frequency. As a secondary objective, preliminary statistical studies are required to assess EFD and CFD irregular wave errors and uncertainties versus theoretical values and evaluate EFD and CFD resistance and motions uncertainties and, in the latter case, errors versus EFD values. UQ methods include analysis of the autocovariance matrix and block-bootstrap of time series values (primary variable). Additionally, the height (secondary variable) associated with the mean-crossing period is assessed by the bootstrap method. Errors and confidence intervals of statistical estimators are used to define validation criteria. The application is a two-degrees-of-freedom (heave and pitch) towed Delft catamaran with a length between perpendiculars equal to 3 m (scale factor equal to 33), sailing at Froude number equal to 0.425 in head waves at scaled sea state 5. Validation variables are x-force, heave and pitch motions, vertical acceleration of bridge, and vertical velocity of flight deck. Autocovariance and block-bootstrap methods for primary variables provide consistent and complementary results; the autocovariance is used to assess the uncertainty associated with expected values and standard deviations and is able to identify undesired self-repetition in the irregular wave signal; block-bootstrap methods are used to assess additional statistical estimators such as mode and quantiles. Secondary variables are used for an additional assessment of the quality of experimental and simulation data as they are generally more difficult to model and predict than primary variables. Finally, the regular wave UQ model provides a good approximation of the desired irregular wave statistics, with average errors smaller than 5% and validation uncertainties close to 10%.

Metamodeling may substantially reduce the computational expense of individual-level state transition simulation models (IL-STM) for calibration, uncertainty quantification, and health policy evaluation. However, because of the lack of guidance and readily available computer code, metamodels are still not widely used in health economics and public health. In this study, we provide guidance on how to choose a metamodel for uncertainty quantification. We built a simulation study to evaluate the prediction accuracy and computational expense of metamodels for uncertainty quantification using life-years gained (LYG) by treatment as the IL-STM outcome. We analyzed how metamodel accuracy changes with the characteristics of the simulation model using a linear model (LM), Gaussian process regression (GP), generalized additive models (GAMs), and artificial neural networks (ANNs). Finally, we tested these metamodels in a case study consisting of a probabilistic analysis of a lung cancer IL-STM. In a scenario with low uncertainty in model parameters (i.e., small confidence interval), sufficient numbers of simulated life histories, and simulation model runs, commonly used metamodels (LM, ANNs, GAMs, and GP) have similar, good accuracy, with errors smaller than 1% for predicting LYG. With a higher level of uncertainty in model parameters, the prediction accuracy of GP and ANN is superior to LM. In the case study, we found that in the worst case, the best metamodel had an error of about 2.1%. To obtain good prediction accuracy, in an efficient way, we recommend starting with LM, and if the resulting accuracy is insufficient, we recommend trying ANNs and eventually also GP regression.

Single-event transients (SETs) in 16-/14-nm bulk fin field effect transistor (finFET) logic chains have been measured using a custom-designed test IC. A variety of logic gate chains were designed, and SET pulse widths were obtained across a wide range of supply voltages. In light of the increased SET response at reduced supply voltages, the efficacy of filter-based mitigation is assessed by analyzing the voltage dependence of SET duration against the characteristic electrical inverter delay.

This paper is one in a sequence of presentations that consider the problem of uncertainty quantification (UQ) in model verification and validation. The particular sub-topic considered here is uncertainty quantification in modeling. The objectives of the paper are to enumerate some of the various sources of uncertainty in models, as-built systems and experimental data, to define uncertainty and errors and differences between them, to introduce different types of comparative difference metrics that can be used for uncertainty quantification, and to present examples illustrating their uses. Particular emphasis is placed on the ability to quantify modeling uncertainty that includes model form uncertainty, i.e. an epistemic uncertainty that results from an incomplete understanding of the physics of the phenomenon being modeled, and/or undetected modeling error.

Recent efforts to ensure the reliability of computational model-based predictions in healthcare, such as the ASME V&V40 Standard, emphasize the importance of uncertainty quantification (UQ) and sensitivity analysis (SA) when evaluating computational models. UQ involves empirically determining the uncertainty in model inputs—typically resulting from natural variability or measurement error—and then calculating the resultant uncertainty in model outputs. SA involves calculating how uncertainty in model outputs can be apportioned to input uncertainty. Rigorous comprehensive UQ/SA provides confidence that model-based decisions are robust to underlying uncertainties. However, comprehensive UQ/SA is not currently feasible for whole heart models, due to numerous factors including model complexity and difficulty in measuring variability in the many parameters. Here, we present a significant step to developing a framework to overcome these limitations. We: (i) developed a novel action potential (AP) model of moderate complexity (six currents, seven variables, 36 parameters); (ii) prescribed input variability for all parameters (not empirically derived); (iii) used a single “hyper-parameter” to study increasing levels of parameter uncertainty; (iv) performed UQ and SA for a range of model-derived quantities with physiological relevance; and (v) present quantitative and qualitative ways to analyze different behaviors that occur under parameter uncertainty, including “model failure”. This is the first time uncertainty in every parameter (including conductances, steady-state parameters, and time constant parameters) of every ionic current in a cardiac model has been studied. This approach allowed us to demonstrate that, for this model, the simulated AP is fully robust to low levels of parameter uncertainty — to our knowledge the first time this has been shown of any cardiac model. A range of dynamics was observed at larger parameter uncertainty (e.g., oscillatory dynamics); analysis revealed that five parameters were highly influential in these dynamics. Overall, we demonstrate feasibility of performing comprehensive UQ/SA for cardiac cell models and demonstrate how to assess robustness and overcome model failure when performing cardiac UQ analyses. The approach presented here represents an important and significant step toward the development of model-based clinical tools which are demonstrably robust to all underlying uncertainties and therefore more reliable in safety-critical decision-making.

The variations of single event transient (SET) pulse width of high-LET heavy ion irradiation in 16-nm-thick bulk silicon fin field-effect transistor (FinFET) inverter chains with different driven strengths are measured at different temperatures. Three-dimensional (3D) technology computer-aided design simulations are carried out to study the SET pulse width and saturation current varying with temperature. Experimental and simulation results indicate that the increase in temperature will enhance the parasitic bipolar effect of bulk FinFET technology, resulting in the increase of SET pulse width. On the other hand, the increase of inverter driven strength will change the layout topology, which has a complex influence on the SET temperature effects of FinFET inverter chains. The experimental and simulation results show that the device with the strongest driven strength has the least dependence on temperature.

Parameter identification and uncertainty quantification in stochastic state space models and its application to texture analysis