The dimension of transistors shrinks with each new technology developed in the semiconductor industry. The extreme scaling of transistors introduces important statistical variations in their process parameters. A large digital integrated circuit consists of a very large number (in millions or billions) of transistors, and therefore the number of statistical parameters may become very large if mismatch variations are modeled. The parametric variations often cause to the circuit performance degradation. Such degradation can lead to a circuit failure that directly affects the yield of the producing company and its fame for reliable products. As a consequence, the failure probability of a circuit must be estimated accurately enough. In this paper, we consider the Importance Sampling Monte Carlo method as a reference probability estimator for estimating tail probabilities. We propose a Hybrid ISMC approach for dealing with circuits having a large number of input parameters and provide a fast estimation of the probability. In the Hybrid approach, we replace the expensive to use circuit model by its cheap surrogate for most of the simulations. The expensive circuit model is used only for getting the training sets (to fit the surrogates) and near to the failure threshold for reducing the bias introduced by the replacement.

中文翻译：

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混合重要性抽样蒙特卡罗方法用于电路设计中的成品率估计

随着半导体工业中开发的每一项新技术，晶体管的尺寸都在缩小。晶体管的极端缩放在其工艺参数中引入了重要的统计变化。大型数字集成电路由数量众多（数百万或数十亿个）的晶体管组成，因此，如果对不匹配变化建模，统计参数的数量可能会变得非常大。参数变化通常会导致电路性能下降。这种降级会导致电路故障，直接影响生产公司的产量及其对可靠产品的声誉。结果，必须足够准确地估计电路的故障概率。在本文中，我们将重要性抽样蒙特卡罗方法视为估计尾部概率的参考概率估计器。我们提出了一种混合ISMC方法，用于处理具有大量输入参数的电路，并提供了概率的快速估计。在混合方法中，对于大多数仿真，我们用便宜的代理代替了昂贵的电路模型。昂贵的电路模型仅用于获得训练集（以适应替代指标）并接近故障阈值，以减少替换带来的偏差。对于大多数仿真，我们用便宜的替代品代替了昂贵的电路模型。昂贵的电路模型仅用于获得训练集（以适应替代指标）并接近故障阈值，以减少替换带来的偏差。对于大多数仿真，我们用便宜的替代品代替了昂贵的电路模型。昂贵的电路模型仅用于获得训练集（以适应替代指标）并接近故障阈值，以减少替换带来的偏差。