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

The main focus of this manuscript is to provide a general physically plausible explanation for the 1/f phenomenon. Also to derive Hooge's parameter value often used to characterize the strength of 1/f noise in different conducting materials. Thus suggesting first principles explanation for the 1/f phenomenon in conducting materials. In that sense, we do not consider any specific materials or experimental data.

Nevertheless, a connection to some experimental works can be drawn, as a response to the comment made by the reviewer. A quick search of the existing experimental literature suggests that there are no works that would consider direct measurements of detrapping rates in any (semiconductor or other) materials. But, as long as Arrhenius's law applies, we can relate detrapping rates to the trap activation energies (depth of the trap in the band gap). If the detrapping rates are assumed to be uniform within some range of values, then the activation energy distribution should also be exponential within some range of energies. Some of the works we found suggest that activation energy distribution could be exponential (with other common alternatives being normal and uniform distributions). Although, in different materials there could be other mechanisms leading to uniform detrapping rate distribution.

Notably, there are experimental evidence for Hooge's parameter being inversely proportional to the mean free-flight time in wide range of materials. From theoretical perspective this requires assuming homogeneous spatial distribution of traps, as we have assumed in the proposed model.

Our responses to suggested changes: 1. Appropriate changes will be made. 2. Number of references will be reduced. 3. We can make additional references to existing experimental literature, but our own consideration is from a theoretical perspective. 4. The aforementioned arXiv draft is an early iteration of this submission to SciPost. It is not a separate paper, nor is it submitted to any other journal besides SciPost.

We do agree with the reviewer that our model does not describe physics of a pure electrical conductor, but typical materials and devices are not pure. These impurities could be of semiconductor nature themselves, or effectively work as traps in the semiconductors. Furthermore majority of experimental literature regarding 1/f noise in materials primarily focus on either semiconductor materials or devices incorporating semiconductors. We will add clarifications as necessary when updating the manuscript.

As for Hooge's relation, we chose this form, because our model primarily describes the movement of charge carriers, and primarily corresponds to the fluctuations in current. Although, dependent on how the measurement is conducted one could also observe fluctuations in effective resistance and voltage of the conducting material. We will add an extended comment on this when updating the manuscript.

Regarding the similarities with our recent PRE paper, it is important to highlight that the primary emphasis of the PRE paper lies in the mathematical aspects of modeling 1/f noise. It specifically demonstrates that 1/f noise is observable when gap (or pulse) duration follows a distribution with a power-law tail. While previously others have also demonstrated similar results, they overlooked a crucial additional condition – the duration of pulses (or gaps) must be relatively long. Essentially, the PRE paper shows that achieving pure 1/f noise is impossible using a point process model. Even if this condition is satisfied, the resulting 1/f noise still exhibits a low-frequency cutoff, which, for the most reasonable parameter sets, becomes effectively unobservable. This fact was also overlooked in the existing literature.

Although there is an overlap in the mathematical content presented in our manuscript and the PRE paper, we have minimized overlaps to as much as is necessary to maintain the self-contained nature of the manuscript. Proper references are provided whenever we reuse previous results or insights. The primary focus of our manuscript is to introduce a straightforward physical model that explains why the gap duration could follow a power-law distribution. This model enables us to derive a compact expression for the Hooge parameter (Section 4) and offers an alternative solution to the low-frequency cutoff paradox (Section 3).