Self-Assembly of 2-D Resistive Electric Grids

A new algorithmic model (cTAM) of self-assembly of electronic resistive circuits akin to models for DNA self-assembly has been recently introduced and a complete characterization of their shape and properties has been given for one-dimensional electric ladders. Growth is controlled by thresholding o...

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Bibliographic Details
Published in:IEEE transactions on nanotechnology 2019, Vol.18, p.562-566
Main Authors: Yan, Yan, Garzon, Max, Deaton, Russell
Format: Article
Language:English
Subjects:
Biological system modeling
block toeplitz matrices
circuit Tile Assembly Model (cTAM)
Circuits
Electric potential
Energy distribution
Integrated circuit modeling
Ladders
Mathematical model
Matrix Möbius Transformations
Nanoelectronics
resistive electric circuits
Resistors
Self-assembly
Two dimensional displays
Two dimensional models
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Summary:A new algorithmic model (cTAM) of self-assembly of electronic resistive circuits akin to models for DNA self-assembly has been recently introduced and a complete characterization of their shape and properties has been given for one-dimensional electric ladders. Growth is controlled by thresholding of the energy required for attachments of new components to a growing assembly. In this sequel, we characterize an analogous family of two-dimensional resistive circuit grids self-assemblable in the cTAM model. These circuits have remained unresolved for some time in full generality. Fundamental questions concerning the size, shape, and energy distribution of the assembly sequences and their steady-state in large scales are addressed in full.
ISSN:1536-125X
1941-0085
DOI:10.1109/TNANO.2019.2917142