Multi-Dimensional Operational Domain Computation for Silicon Dangling Bond Logic

This repository provides supplementary data for the paper Multi-Dimensional Operational Domain Computation for Silicon Dangling Bond Logic by M. Walter, J. Drewniok, S. S. H. Ng, K. Walus, and R. Wille submitted to TCAD (under review).

Operational Domain Analysis

The Operational Domain was proposed as a methodology to evaluate the extent of physical parameter variations that an SiDB logic gate can tolerate by plotting the logical correctness of that gate's behavior across a predetermined range of physical parameters. Given an SiDB layout L and a Boolean function f : *, the operational domain of *L given f is defined in the parameter space as the set of coordinate points for which L implements f. To determine whether L implements f at any given coordinate point (x, y, z), this point can be sampled, i.e., by conducting 2 physical simulationsone for each possible input pattern of L.

Benchmark Layouts

We performed operational domain analyses for benchmark layouts taken from the literature. The layouts are provided in the benchmarks/ folder in *.sqd format. This format is supported in the SiDB CAD tool SiQAD. Utilizing this tool, the layouts can be visualized and their behavior can be validated by physical simulations. Both tasks can also be performed in the Munich Nanotech Toolkit (MNT) fiction.

SiQAD

The SiQAD gates are taken from the paper "SiQAD: A Design and Simulation Tool for Atomic Silicon Quantum Dot Circuits" by S. S. H. Ng, J. Retallick; H. N. Chiu, et al. published in IEEE Transactions on Nanotechnology (TNANO) 2019.

In this repository, they are located in the benchmarks/siqad/ folder.

Bestagon

The Bestagon gates are taken from the paper "Hexagons are the Bestagons: Design Automation for Silicon Dangling Bond Logic" by M. Walter, S. S. H. Ng, K. Walus, and R. Wille in the Design Automation Conference (DAC) 2022.

In this repository, they are located in the benchmarks/bestagon/ folder.

Plots

In this work, we present two novel algorithms for the obtainment of operational domains: Flood Fill and Contour Tracing. Additionally, we compare these algorithms to the state-of-the-art Grid Search algorithm while also mentioning Random Sampling in the paper.

Operational domain data generated with all applicable algorithms for all benchmark layouts is provided in the operational_domains/ folder in various file formats.

CSV

The raw operational domain data is provided in CSV format. Each file contains the operational domain data for a single benchmark layout. The columns represent the evaluated physical parameters and the logical correctness of the gate at the respective parameter values.

Such a (2D) CSV file might look as follows:

csv epsilon_r, lambda_tf, operational status 3.15 , 1.90 , 0 2.20 , 7.85 , 0 7.75 , 6.70 , 1 8.25 , 7.90 , 1 1.70 , 1.75 , 0 6.05 , 6.85 , 1 1.90 , 9.25 , 0 ...

PNG

The operational domain plots are visualized in PNG format.

For 2D spaces, each file contains a plot of the operational domain for a single benchmark layout using a single algorithm. The plot shows the logical correctness of the gate at the respective parameter values in purple. Non-operational samples are shown in gray.

For 3D spaces, all benchmark layouts' plots are depicted from three azimuth angles: 45, 135, and 225, with a constant elevation angle of 30. In 3D plots, non-operational samples are omitted while operational samples are colored according to their location in the parameter space.

HTML

The 3D operational domain plots are additionally visualized in interactive HTML format.

For each benchmark layout and algorithm, an HTML file is provided that contains an interactive 3D plot of the operational domain using the same color scheme as in the PNG case. The plot can be rotated and zoomed in any web browser.

[!NOTE] The HTML files must be downloaded to be viewed. Large files may break the plot rendering in some browsers.

Acknowledgements

The Munich Nanotech Toolkit has been supported by the Bavarian State Ministry for Science and Arts through the Distinguished Professorship Program.

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