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

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.