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STEAM: Spline-based tables for efficient and accurate device modelling

机译：STEAM：基于样条的表格，可进行高效，准确的设备建模

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A common complaint from users of device models is that the “better” the model, the longer it takes to simulate. Modelling based on interpolation between sampled data points is attractive in this context because it offers low model evaluation times. Although such “table-based” modelling has a long history, important conceptual and implementation issues have been obscure in the literature. These issues include: separating the algebraic (“DC”) and dynamic (“charge/flux”) components properly; extrapolation outside sampled regions; smoothness; accuracy vs. computation vs. memory tradeoffs; and suitability of the table-based model for various analyses (such as DC, AC, transient, RF, etc., analyses). In this paper, we clarify precisely what functions should be sampled for a table-based device model to work properly in any analysis. We re-visit interpolation, showing that well-implemented cubic splines provide excellent smoothness and arbitrarily great accuracy at low, almost-constant evaluation cost. However, memory requirements increase with accuracy. We present a novel extrapolation scheme using passivity concepts that aids convergence. Using Berkeley MAPP, we demonstrate speedups of 150× in core BSIM model evaluations (translating to overall simulation speedups of 6-18×) with relative errors of 0.001%. Our approach can convert any existing device model to a smooth/accurate table-based model with small, fixed evaluation cost. Unlike previous work, our code will be released as open source, serving as a platform for the community to evaluate and experiment with table-based models quickly and conveniently.
机译：设备模型用户普遍抱怨的是，模型越“好”，则模拟花费的时间就越长。在这种情况下，基于采样数据点之间的插值进行建模很有吸引力，因为它提供了较短的模型评估时间。尽管这种“基于表”的建模已有很长的历史，但是重要的概念和实现问题在文献中还是晦涩难懂的。这些问题包括：适当地分离代数（“ DC”）和动态（“电荷/通量”）分量;在采样区域外进行外推;光滑度准确性vs.计算vs.内存权衡;基于表的模型对各种分析（例如DC，AC，瞬态，RF等）的适用性。在本文中，我们精确地阐明了应该为基于表的设备模型采样哪些功能，以使其在任何分析中都能正常工作。我们重新研究了插值法，结果表明，实施良好的三次样条以极低的，几乎恒定的评估成本提供了出色的平滑度和任意高的精度。但是，内存要求随着精度的提高而增加。我们提出了一种使用无源概念的新颖外推方案，该方案有助于收敛。使用Berkeley MAPP，我们在核心BSIM模型评估中展示了150倍的加速（转换为6-18倍的整体仿真速度），相对误差为0.001％。我们的方法可以将任何现有设备模型转换为平滑/准确的基于表的模型，而固定的评估成本却很小。与以前的工作不同，我们的代码将作为开源发布，为社区提供了一个平台，以方便快捷地评估和试验基于表的模型。

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