This repository contains some Fortran codes that I wrote as part of the work for my Ph.D. dissertation. The codes essentially run classical percolation problems (site, bond, and mixed site/bond) for the square and triangular lattices. These codes were used as part of a model for zinc oxide (ZnO) transistor devices. The codes are a bit overkill for the transistor model but output quite a bit of information that I used to ensure that the percolation behaviors and statistics were correct according to basic mathematical theories.
The MATLAB codes take some of the output to create visualizations of the clusters on the square/triangular lattices. The SampleOutput directory contains images of the output of these codes at various stages during the process of adding sites or bonds to the lattice.
Since our application of these codes is to semiconductor devices, there are some Fortran and MATLAB codes that calculate the conductance once a lattice-spanning cluster is available. The lattice may be relatively unfilled, especially near or just above the percolation threshold; thus, it may be necessary to invert a sparse matrix to calculate the conductance (hence the use of special routines in the Fortran codes).
If this work is useful, please cite our paper on the percolation model for ZnO transistors and my Ph.D. dissertation:
I. P. Steinke and P. P. Ruden, “Percolation Model for the Threshold Voltage of Field-Effect Transistors with Nanocrystalline Channels,” Journal of Applied Physics, 111, 014510 (2012); doi: 10.1063/1.3676217.
I. P. Steinke, "Device Modeling of Field-Effect Transistors with Nanocrystalline Channels," Ph.D. dissertation. Department of Electrical and Computer Engineering, University of Minnesota - Twin Cities, Minneapolis, MN, USA, 2011. Available: hdl.handle.net/11299/112768.