1/f noise in electrical conductors arising from the heterogeneous detrapping process of individual charge carriers

Typically it is assumed that trapping and detrapping in semiconductor materials are Poisson processes. When both processes are indeed Poisson then the signal will have Lorentzian power spectral density. Most well-known models (like McWhorter or van der Ziel models) assume that the superposition of Lorentzian power spectral densities is necessary to obtain 1/f noise. While that assumption is correct, it is not the only way to obtain 1/f noise in a model of semiconductor material [1].

In we have studied a trapping-detrapping process assuming that detrapping rates are heterogeneous. Namely, detrapping rates were assumed to be randomly sampled from the uniform distribution. This allows to obtain 1/f noise even when a single charge carrier generates the signal.

This repository contains the code used to perform the simulations reported in [1]. Simulations can be run by running sim.sh script. Figures can be reproduced by running fig.sh script.

On the difference between the two sim_*.py files

Two different simulation scripts are used. This section briefly discussed the main differences between them.

sim_poiss_upoiss_single.py script performs simulations assuming that the signal is created by a single charge carrier. It uses specifically tailored algorithm to calculate power spectral densities. This simulation script is designed in the same way as the duration based simulation scripts from flicker-snorp repository (which is based on an earlier article [2]).

sim_poiss_upoiss_multi.py allows user to specify the number of charge carriers to use in simulations. The user could choose to simulate a single charge carrier, and obtain results similar to the ones that would be obtained using sim_poiss_upoiss_single.py. Though the results won't be identical even for the same seed, because scripts are designed differently, and they require slightly different input arguments. Drawback of using sim_poiss_upoiss_multi.py is that it first generates signal, taking fixed number of samples using predefined sampling period, and then stores it in memory (it is a big memory hog!). Only afterwards it uses a generic scipy.signal.periodogram function to calculate power spectral density.

References

1. A. Kononovicius, B. Kaulakys. arXiv:2306.07009 [math.PR].
2. A. Kononovicius, B. Kaulakys. 1/f noise from the sequence of nonoverlapping rectangular pulses. Physical Review E 107: 034117 (2023). doi: 10.1103/PhysRevE.107.034117. arXiv:2210.11792 [cond-mat.stat-mech].