Low-Frequency Electronic Noise in Superlattice and Random-Packed Thin Films of Colloidal Quantum Dots

Adane Geremew; Alex Abelson; Alexander A. Balandin; Caroline Qian; Fariborz Kargar; Matt Law; Sergey Rumyantsev

REVIEW 3 major objections 5 minor 12 references

Low-Frequency Electronic Noise in Superlattice and Random-Packed Thin Films of Colloidal Quantum Dots

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read In PbSe colloidal quantum dot films, a single thermally activated process with an activation energy of about 0.3 eV dominates low-frequency noise regardless of film order or ligand chemistry, and ordered superlattices are consistently the…

desk verdict Solid comparative noise study of ordered vs disordered QD films; qualitative findings hold, but the universal 0.3 eV activation energy isn't yet supported beyond two samples. read the letter →

arxiv 1908.03791 v1 pith:3C4OSDM6 submitted 2019-08-10 cond-mat.mes-hall cond-mat.mtrl-sci

Adane Geremew , Caroline Qian , Alex Abelson , Sergey Rumyantsev , Fariborz Kargar , Matt Law , Alexander A. Balandin This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.mtrl-sci

keywords low-frequencynoisecolloidalquantumdotsgeneration-recombination1/fPbSedotsuperlatticephotodetectorsactivationenergy

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper shows that thin films of 6.5 nm lead selenide colloidal quantum dots, whether arranged into ordered superlattices, weakly ordered spin-cast films, or random-packed dip-coated films, all display the same two-part low-frequency noise spectrum: a 1/f flicker background plus a Lorentzian bump that behaves like generation-recombination noise from a single trap. Tracking the temperature at which that bump peaks at fixed frequencies yields an activation energy of about 0.3 eV, nearly identical across film ordering and ligand chemistry, even though the DC transport activation energies are much smaller (0.137–0.171 eV). Ordered superlattice films are consistently quieter than weakly ordered and random films, by up to two orders of magnitude at room temperature. Since low-frequency noise sets the detectivity floor of photodetectors, the result gives a concrete target for noise engineering in quantum dot optoelectronics.

What carries the argument

The load-bearing object is the Lorentzian (generation-recombination) component of the normalized noise spectral density, with corner frequency $f_c = 1/(2\pi\tau)$. Since $f_c$ is not directly visible at all temperatures, the paper uses a standard peak method: at a fixed measurement frequency $f$, the temperature $T_m$ where $S_I/I^2$ reaches a maximum is assumed to mark $2\pi f \tau(T_m)=1$; repeating this across frequencies produces an Arrhenius plot whose slope is the activation energy. This transforms raw noise spectra into a single number—the 0.3 eV activation energy—that the paper uses to argue that one thermally activated process underlies noise in all studied films.

What would settle it

Record noise spectra down to about 0.01 Hz at several temperatures for the same films and resolve the Lorentzian corner frequency $f_c$ directly; if $f_c$ does not fall on the Arrhenius line with slope 0.3 eV determined from the peak-shift method, or if more than one corner appears, the single-process interpretation fails. Equivalently, changing film thickness, contact geometry, or bias should not move the peak temperatures if the 0.3 eV process is a bulk property.

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Extended reading notes

Core claim

The paper reports that the normalized dark-current noise spectral density, $S_I/I^2$, of PbSe colloidal quantum dot films always contains a Lorentzian component $S_0/[1+(2\pi f\tau)^2]$ sitting on top of a $1/f$ background. Because the Lorentzian corner frequency $f_c = 1/(2\pi\tau)$ moves with temperature, the authors locate it by recording $S_I/I^2$ versus temperature at fixed measurement frequencies and taking the peak temperature $T_m$ to satisfy $2\pi f \tau(T_m)=1$. An Arrhenius plot of $\ln f_c$ versus $1/T_m$ gives an activation energy of about 0.3 eV for both an ordered superlattice film (SL #1) and a random-packed dip-coated film (DC SCN #1). This value is much larger than the nearest-neighbor hopping activation energies of 0.171 eV and 0.137 eV extracted from resistivity, leading the authors to conclude that the conductivity and the noise are governed by different mechanisms, and to suggest that the noise process may involve charge exchange between donor- and acceptor-like states with an energy separation near the bulk PbSe band gap of 0.29 eV. The same activation energy appearing across films with different spatial order and surface ligands is the paper's central universality claim.

Load-bearing premise

The extracted 0.3 eV activation energy assumes that the temperature at which the noise spectrum peaks at a given frequency is set by a single thermally activated process obeying $2\pi f \tau(T_m)=1$, and that the overlapping $1/f$ background and any additional trap levels do not shift that peak.

Editorial extensions

If this is right

Photodetector engineers can treat the ~0.3 eV process as the dominant low-frequency noise source in PbSe QD films and target it with passivation or doping.
The consistently lower noise of superlattice films (down to two orders of magnitude below random-packed films) adds a concrete performance incentive for developing longer-range colloidal QD order.
Since conductivity and noise have different activation energies, lowering dark current by changing transport barriers will not by itself lower the noise floor.
The $S_I \sim I^2$ scaling and absence of Joule-heating artifacts mean that the measured noise differences reflect material properties rather than measurement-induced damage.
Because $1/f$ noise components cannot be suppressed by longer integration times, the reported noise gap between ordered and disordered films directly maps to a detectivity gap in an actual detector.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the 0.3 eV process is universal, then magnetotransport or capacitance transient measurements that reveal the same energy level would identify the specific defect; the paper itself leaves the microscopic identity open.
Varying the QD diameter to change the confined band gap would discriminate between a process tied to donor-acceptor energy separation near the bulk gap and one tied to ligand or surface states: the 0.3 eV value should shift in the former case and stay fixed in the latter.
Repeating the noise-versus-temperature method on films with different thicknesses and contact separations could test whether the peak temperatures are bulk properties or contact effects; if peaks shift with geometry, the extracted activation energy is not intrinsic.
A direct lower-frequency measurement (0.01 Hz and below) could resolve the Lorentzian in spectra rather than through peaks, providing a model-free check of the single-time assumption.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This is a credible experimental paper and worth a serious look, but the headline number—a universal 0.3 eV activation energy for the Lorentzian noise component across all film types—is less solid than the rest of the paper.

What's new: no one has systematically compared low-frequency noise in epitaxial QD superlattices with weakly ordered and random-packed films under different ligand chemistries. The observation that SL films are quieter by up to two orders of magnitude, and that spectra show a Lorentzian bump on a 1/f background, is directly supported by the figures. The authors checked the current scaling (SI ~ I^2), which suggests the measurements aren't distorted by Joule heating or contact effects. The sample prep is described in detail, and the paper is appropriately careful about not over-interpreting the causes of the noise differences.

The soft spot is the Arrhenius analysis. The activation energy is extracted from the temperature at which SI/I2 at fixed frequency peaks, assuming 2πfτ(Tm)=1. That's a standard method, but only safe if the 1/f background and other T-dependent prefactors (n(T), F(1-F)) don't shift the peak. The paper itself notes the Lorentzian is masked by 1/f at high T, yet no subtraction or decomposition is shown. And the Arrhenius plot is presented for two of six samples (SL #1 and DC SCN #1), without error bars. So the claim of a common 0.3 eV process across different sample types is not established as stated. It's a testable hypothesis, not a demonstrated result. The qualitative conclusions are unaffected, and the suggested interpretations (bulk PbSe bandgap, ligand-related) are appropriately speculative.

The paper is honest about its limits: it explicitly says the relative contributions of order, ligand chemistry, cracks, and connectivity can't be separated. It's a clean experimental report, not an overreach. The weak point is fixable—fit the spectra to A/f + B/(1+(ωτ)^2) for all samples, or at least qualify the abstract and conclusion to say the 0.3 eV value came from two representative samples.

Who should read it: anyone working on colloidal QD photodetectors or on noise in disordered/ordered nanostructures. The data are useful and likely to be cited. It deserves peer review; I'd send it out but ask referees to focus on the generality of the activation energy. I'd accept after a minor revision that narrows or supports that claim.

Referee Report

3 major / 5 minor

Summary. The paper reports low-frequency (1 Hz–10 kHz) electrical noise measurements on thin films of 6.5 nm PbSe colloidal quantum dots with three levels of spatial order: epitaxial superlattices (SL), weakly-ordered spin-coated films (SC), and random-packed dip-coated films (DC), with different ligand chemistries. The authors find that the normalized current noise spectral density SI/I2 follows an approximately I2 dependence, that the noise level is lower in the ordered SL films than in the weakly-ordered and random-packed films (by a factor of 2 to more than two orders of magnitude depending on conditions), and that the noise spectra contain a Lorentzian component superimposed on a 1/f background. From the temperature dependence of SI/I2 at fixed frequencies, they extract peak positions and construct an Arrhenius plot, obtaining an activation energy of ~0.3 eV for the noise process in both an SL film and a DC film. The paper interprets this as evidence for a common generation-recombination-type process across different film ordering and ligand chemistries, and suggests that the lower noise of ordered superlattices is relevant for photodetector applications.

Significance. If the reported trends hold, the paper provides useful experimental noise characterization for a technologically relevant class of solution-processed infrared photodetector materials. The systematic comparison of ordered superlattices, weakly-ordered films, and random-packed films with different ligand treatments is valuable, and the observation of a Lorentzian noise component superimposed on 1/f noise is a concrete, falsifiable result. The claim of a universal ~0.3 eV activation energy, if properly supported, would point to a common microscopic noise mechanism and would be a significant finding. However, the support for this central claim is currently thin: it rests on only two of the six fabricated samples, with no error bars or background-subtraction analysis, and the peak-extraction method assumes an ideal single-Lorentzian response. The qualitative noise-level ordering is better supported by the data presented.

major comments (3)

[Figure 6 and Discussion (p. 8)] The central claim that 'an activation energy of ~0.3 eV was extracted from the temperature dependence of the noise spectra' for both superlattice and random-packed films is not supported by the data shown. The Arrhenius plot in Figure 6 contains only two samples, SL #1 and DC SCN #1, selected from the six samples listed in Table I. No error bars, confidence intervals, or goodness-of-fit statistics are provided for the linear fits. The other four samples—including DC SCN #2, which has a noise level at 100 K nearly three orders of magnitude higher than DC SCN #1, and the EDA-treated films—are absent from the analysis. Please either provide the Arrhenius analysis for all samples with appropriate uncertainties or explicitly limit the conclusion to the two studied samples.
[Section before Figure 5 / Figures 5 and 6] The method of extracting the characteristic frequency fc from the temperature Tm at which SI/I2(T) has a maximum assumes that the G-R Lorentzian term alone determines the peak, i.e., that the peak occurs at 2πfτ = 1 and that the 1/f background and temperature-dependent prefactors do not shift the maximum. The manuscript itself states that 'at high temperatures, the Lorentzian components are barely noticeable because they are masked by the 1/f noise' (p. 7), indicating that the background is not negligible in the analyzed range. No subtraction of the 1/f component or decomposition of the measured spectra into A/f + B/(1+(2πfτ)2) is shown before locating the maxima. A temperature-dependent 1/f amplitude, the n(T) dependence in Eq. (1), or the trap-occupancy factor F(1−F) can shift Tm relative to the true 2πfτ = 1 condition, biasing the extracted activation energy. Please demonstrate, e.g., by fitting the spectra in Figure 3 or by numerical simulation, that the extracted fc values are insensitive to these effects.
[Abstract and Table I] The abstract states that 'for all samples, the normalized noise spectral density of the dark current revealed a Lorentzian component,' but the spectra that show the Lorentzian component are presented only for SL #1 and DC SCN #1 (Figures 3 and 5). Figure 4(c) shows only SI/I2 at f = 10 Hz for all samples, not full spectra. The paper should state explicitly how many of the six samples exhibited resolvable Lorentzian components and provide representative spectra for each film type, or modify the claim to indicate that the Lorentzian component was observed in the samples for which full spectra were measured.

minor comments (5)

[Equation (1)] Equation (1) appears to contain a typographical error: the numerator is rendered as 'ττ(1−τ)' instead of the intended 'τF(1−F)'. Please correct the typesetting and define F clearly.
[Page 5] The phrase 'with a n electron mobility' should be 'with an electron mobility'.
[Figure 2 caption] The caption states that sample names in the legend correspond to Table I, but it does not specify which sample is which (e.g., SL #1 vs SL #2). Please clarify the legend labels or state that only representative samples are shown.
[Noise measurement section, p. 6] The dynamic signal analyzer is identified only as 'Stanford Research'; please specify the model (e.g., SR760 or SR785) and the measurement bandwidth.
[Supplemental Figures S4 and S5] The Supplemental Material includes Figures S4 and S5 showing normalized noise spectra at various temperatures, but these figures are not referenced in the main text. Please reference them where the spectra of the ordered and random samples are discussed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: purely experimental measurement with standard Arrhenius analysis; self-citations are methodological only.

full rationale

The paper reports measured noise spectra and extracts an activation energy from temperature-dependent data using a standard method (plotting SI/I2 versus temperature at fixed frequencies, locating the maxima, and fitting an Arrhenius plot). The extracted ~0.3 eV is not an input to a model that is then used to predict the same quantity. The only self-citations (Refs 46-48 and 53-54) concern measurement procedures and a published analysis technique; they are not invoked as uniqueness theorems or loaded with the result. The claim that both SL and DC films give ~0.3 eV is a direct comparison of independently measured data, and the interpretation linking this energy to the bulk PbSe bandgap is explicitly speculative ('One of the possibilities is...'). The limitation that the Arrhenius plot covers only two of six samples and the possible peak-shift by the 1/f background are concerns about robustness and statistical support, not circularity. Therefore, no circular step is present.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's central observations are measurements. The only fitted parameters are activation energies (noise and hopping), which are standard empirical characterizations. The modeling assumptions (Lorentzian G-R noise, Arrhenius behavior, hopping transport) are established physics in the noise and quantum dot communities, not ad hoc to this paper. No new entities are introduced.

free parameters (3)

Noise activation energy Ea_noise = ~0.3 eV
Extracted from the slope of the ln(fc) versus 1/Tm Arrhenius plot in Figure 6. This is a fit to the measured noise data, not an independently derived quantity.
NNH activation energy for DC film = 0.171 eV
Extracted from an Arrhenius plot of resistivity for dip-coated films (page 6). Provides context but is not central to the noise claim.
NNH activation energy for SL film = 0.137 eV
Extracted from an Arrhenius plot of resistivity for superlattice films (page 6). Provides context but is not central to the noise claim.

assumptions (4)

domain assumption Generation-recombination noise produces a Lorentzian spectral density S(f) = S0/(1+(2πfτ)^2).
Used on page 7 to interpret the observed Lorentzian component in the noise spectra as G-R noise from a trap with a characteristic time τ.
domain assumption The maxima in SI/I² versus T at fixed frequency satisfy 2πfτ(Tm) = 1.
Invoked on page 8 to convert noise-vs-temperature maxima into values of the characteristic frequency fc, allowing the Arrhenius analysis.
domain assumption The characteristic time τ follows an Arrhenius temperature dependence: τ = τ0 exp(Ea/kBT).
Used to construct the Arrhenius plot in Figure 6 and extract the activation energy.
domain assumption Transport in the QD films is by hopping conduction (NNH at high temperature, VRH at low temperature).
Used on page 6 to interpret the resistivity temperature dependence and to extract hopping activation energies.

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Cite this review

Pith. "Pith review of Low-Frequency Electronic Noise in Superlattice and Random-Packed Thin Films of Colloidal Quantum Dots." pith.science (2026). https://pith.science/paper/3C4OSDM6

@misc{pith2026190803791,
  author       = {Pith},
  title        = {Pith review of: Low-Frequency Electronic Noise in Superlattice and Random-Packed Thin Films of Colloidal Quantum Dots},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3C4OSDM6}},
  note         = {Machine review of arXiv:1908.03791}
}

read the original abstract

We report measurements of low-frequency electronic noise in ordered superlattice, weakly-ordered and random-packed thin films of 6.5 nm PbSe quantum dots prepared using several different ligand chemistries. For all samples, the normalized noise spectral density of the dark current revealed a Lorentzian component, reminiscent of the generation-recombination noise, superimposed on the 1/f background (f is the frequency). An activation energy of 0.3 eV was extracted from the temperature dependence of the noise spectra. The noise level in the ordered films was lower than that in the weakly-ordered and random-packed films. A large variation in the magnitude of the noise spectral density was also observed in samples with different ligand treatments. The obtained results are important for application of colloidal quantum dot films in photodetectors.

Figures

Figures reproduced from arXiv: 1908.03791 by the authors.

**Figure 1.** Scanning electron microscope images of QD films with varying degrees of longrange order. (a – b) Dip-coated films, corresponding to samples “DC SCN #1”, “DC SCN #2” and “DC EDA #1” in Table I. (c – d) Spin-coated films with short-range order, corresponding to sample “SC EDA #1” in Table I. (e – f) Epi-superlattice films with long-range order, corresponding to samples “SL #1” and “SL #2” in Table I [PITH_FULL_IMAGE… view at source ↗

**Figure 2.** (a) Schematics of the QD devices showing perspective (top panel) and crosssectional (bottom panel) views. (b) Electrical resistivity of the SL, SC, and DC films as a function of temperature. The decrease in resistivity with increasing temperature is consistent with hopping transport [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗

Figures from the paper (1 more)

**Figure 3.** Figure 3: (a) Normalized current noise spectral density, SI/I2 , as a function of frequency at different temperatures. The data are presented for two samples: ordered SL #1 (dashed lines) and random DC SCN #1 (solid lines). (b) Normalized current noise spectral density, SI/I 2 ,…

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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