Tunneling Models Py (TM-py)

TM-py aims to simplify fitting experimental J(V) or I(V) data to theoretical tunneling models, comparing tunneling models with one another and evaluating different fit methods. The python module lmfit is used to define tunneling models and perform fits. With this:

• Multiple option for optimization functions are available (see here) and can easily be combined (e.g. first a grid search, then Levenberg-Marquardt)
• models can be combined to compound models (esp. interesting for ensemble molecular junctions with parameters varying over junction area)

In the long term there should be a GUI and data analysis techniques such as noise analysis and outlier detection should be featured Models and utility functions are implemented in TunnelingModels.py

FitGruverman.py and FitSimmons.py showcase fitting experimental data to the Gruverman or the Simmons model, using a grid search and then local optimization on the 50 best results. The following output files are generated:

• [filename]-[modelname]-fitresult_{i}.png: Best fit result of the i-th column in the provided data plotted together with the data
• [filename]-[modelname]-fitresult_{i}.csv: csv with data and best fit result at the evaluated voltages
• [filename]-[modelname]-best_trials_{i}.csv: Parameter sets of the best trials (so the user can check whether 'more physical' combinations may yield reasonable fits as well)
• [filename]-best_fit_params_{i}.csv: fit_report of the best fit after global->local optimization.

FitBDR.py is similar to those, but with a much simpler interface.

evaluator.py showcases the usage of the evaluation function to simulate tunneling current from given parameters and a given model.

papereval.py was a practical implementation to calculate on/off ratios of memristive devices where the switching was caused by a shift in tunneling barrier height on one side.

combined.py demonstrates the generation of a combined model, that could e.g. be used to model parallel conduction paths.

Utility functions

brute then local

Starts with a brute force attempt (grid search) in the parameter space to determine the 50 most promising candidates for optimization and then uses a local optimization on all of the candidates to determine the best fit.

calc_tvs

Calculates transition voltage spectra (for n=2 this corresponds to Fowler Nordheim analysis).

Models

Simmons

'Classical' Simmons model, that describes tunneling through a thin, trapezoidal, symmetric barrier (same barrier height on both sides)

DOI:10.1063/1.1702682

Gruverman

'Classical' Gruverman model, that describes tunneling through a thin, trapezoidal, asymmetric barrier (barrier height different, depending on the side), specifically developped for ferroelectric tunneling junctions. Derived from the BDR model and WKB approximation given small voltages (eV/2 < barrier heights) and "thick" barriers (d ((2m/hbar)^2*phi)^1/2 >> 1)

DOI:10.1021/nl901754t

Brinkman, Dynes and Rowell (BDR)

Tunneling through a trapezoidal asymetric barrier

DOI: 10.1063/1.1659141

Authors

• Julian Dlugosch - initial work