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REVIEW 2 major objections 5 minor 6 references

Photoexcitation of PbS Nanosheets Leads to Highly Mobile Charge Carriers and Stable Excitons

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Photoexcited PbS nanosheets conduct charge carriers with DC mobilities of 550–1000 cm2/Vs and mostly form bound excitons.

desk verdict New THz data on PbS nanosheets, but the headline mobility numbers are overstated because the zero-frequency Drude-Smith limit includes a (1+c) factor the authors dropped. read the letter →

arxiv 1908.04711 v1 pith:EX4Q3KJI submitted 2019-08-13 physics.chem-ph cond-mat.mes-hallcond-mat.mtrl-sciphysics.optics

Jannika Lauth , Michele Failla , Eugen Klein , Christian Klinke , Sachin Kinge , Laurens D. A. Siebbeles This is my paper · ORCID
classification physics.chem-phcond-mat.mes-hallcond-mat.mtrl-sciphysics.optics
keywords PbSnanosheetstwo-dimensionalsemiconductorschargecarriermobilityexcitonbindingenergyopticalpump-terahertzprobespectroscopyexcitonsterahertzphotoconductivityfree-carrierdynamics
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 reports that colloidal two-dimensional PbS nanosheets, four to sixteen nanometers thick, conduct photogenerated charge carriers with a summed mobility between $550$ and $1000\ \mathrm{cm^2/Vs}$—comparable to bulk PbS and far above earlier field-effect measurements on nanosheet transistors. It also finds that photoexcitation creates mostly bound electron-hole pairs (excitons) rather than free charges, with exciton yields between $0.77$ and $0.90$ and free-carrier yields of roughly $0.1$--$0.2$. The thickness trend is explained by longer carrier scattering times in thicker sheets, where surface defects and ligands matter less. If these numbers hold, solution-processed PbS nanosheets become credible materials for ultrathin optoelectronics.

What carries the argument

The argument is carried by the frequency-dependent complex terahertz photoconductivity of photoexcited nanosheet films. The transient signal is decomposed as a sum of a free-carrier mobility with a backscattering correction, characterized by a common scattering time $\tau$ and a backscattering parameter $c$, and an excitonic response built from transitions between 2D exciton states, with oscillator strengths taken from the 2D exciton model in Ref. [30] and binding energies from Ref. [24]. Thickness-dependent electron and hole effective masses enter through a k·p calculation, and the resulting free-carrier mobility follows from $\mu = e\tau/m^*$. The exciton fractions inferred from the fits are cross-checked against the 2D equilibrium mass-action relation, which is what makes the decomposition persuasive rather than merely descriptive.

What would settle it

Extend the terahertz probe to the predicted first internal exciton transition, which the model places near $5E_b/9$: roughly $38$ meV for the 4 nm sheets and $12$ meV for the 16 nm sheets. If no absorption or dispersion feature appears at those energies, the exciton decomposition and the extracted free-carrier yields are wrong.

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Extended reading notes

Core claim

On its own terms, the paper establishes that in PbS nanosheets with inorganic thicknesses of 4, 6, and 16 nm, photoexcitation predominantly forms excitons, and the free carriers that are produced move with DC mobilities of $550\pm100$, $700\pm100$, and $1000\pm150\ \mathrm{cm^2/Vs}$, respectively. The frequency-dependent terahertz response is fit as a sum of a free-carrier contribution with scattering times of $25\pm4$, $29\pm4$, and $33\pm4$ fs and a 2D-exciton contribution with binding energies $68$, $49$, and $21$ meV. The fit gives free-carrier quantum yields of $0.14\pm0.04$, $0.23\pm0.04$, and $0.1\pm0.04$, and exciton yields of $0.86\pm0.04$, $0.77\pm0.04$, and $0.9\pm0.04$. The authors interpret the rising mobility with thickness as a consequence of weaker scattering by surface defects and ligands in thicker sheets, and they report that an equilibrium mass-action model for 2D systems reproduces the inferred exciton fractions.

Load-bearing premise

The load-bearing premise is that the terahertz response can be split cleanly into free-carrier and exciton parts using assumed exciton binding energies and the 2D oscillator-strength model; if the interpolated $21$ meV binding energy for the 16 nm sheets, or the applicability of the 2D formula to thicker sheets, is wrong, then the inferred exciton yields and the highest mobility value shift.

Editorial extensions

If this is right

  • PbS nanosheets of 4--16 nm thickness have contact-free DC mobilities of $550$--$1000\ \mathrm{cm^2/Vs}$, exceeding the $31$--$248\ \mathrm{cm^2/Vs}$ reported from field-effect transistors, so contacts rather than the material may have limited earlier transistor mobilities.
  • Photoexcitation mostly produces excitons, with quantum yields of $0.77$--$0.90$; free-carrier yields are only about $0.1$--$0.2$, which matters for photovoltaic and photodetector designs that rely on extracting free charges.
  • Carrier scattering times increase from about $25$ fs in 4 nm sheets to $33$ fs in 16 nm sheets, and backscattering weakens, supporting the conclusion that surface defects and ligands dominate scattering in thin sheets.
  • At 200 ps after excitation the quantum yields of both species fall by 35--62%, with thinner sheets losing more carriers and excitons, indicating stronger trapping or recombination at surfaces.
  • The inferred exciton binding energies ($68$, $49$, and $21$ meV) and linewidths ($131$--$153$ meV) are consistent with strongly bound, stable excitons at room temperature, which is the basis for the paper's optoelectronic claim.

Reading between the lines

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

  • Beyond the paper: if the free-carrier yield is as low as $0.1$--$0.2$ under short-pulse excitation, then devices that pre-ionize excitons or screen their binding by gating, doping, or dielectric engineering could exploit the same $550$--$1000\ \mathrm{cm^2/Vs}$ transport channel more fully than raw photoconductivity suggests.
  • Beyond the paper: the thickness-scattering trend predicts that even thicker PbS sheets, or sheets with improved ligand passivation, should approach or exceed the bulk PbS mobility, which can be tested with the same terahertz technique.
  • Beyond the paper: the same free-carrier versus exciton decomposition could be applied to other 2D colloidal semiconductors, where the balance between the two channels determines the efficiency of light-emitting and photovoltaic devices.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The manuscript reports optical pump-terahertz probe (OPTPS) measurements on colloidal PbS nanosheets with nominal thicknesses of 4, 6, and 16 nm. The complex THz response is analyzed as a sum of a Drude-Smith free-carrier contribution and a Kaindl-type exciton contribution. From the fits the authors extract free-carrier scattering times, backscattering parameters, exciton Bohr radii, and quantum yields, and they report DC mobilities of 550–1000 cm²/Vs increasing with thickness and exciton quantum yields of 0.77–0.9. The exciton yields are compared with a Saha model. The paper concludes that PbS nanosheets are promising for optoelectronics.

Significance. If the quantitative claims were correct, the demonstration of thickness-tunable carrier mobility approaching bulk PbS values in solution-processed nanosheets would be an important advance, bearing on optoelectronic applications. The study uses a well-established contactless technique and includes useful control analyses: the free-carrier-only fit fails for the imaginary component of the 6 nm sample (Fig. S4), and the 200 ps spectra are shown to be a scaled version of the 8 ps spectra. The decomposition into two species is physically motivated. However, the headline DC mobility values are internally inconsistent with the fitted Drude-Smith model, and the exciton-binding-energy input is used both to construct the fit and to validate the outcome. Both issues affect the central quantitative conclusions.

major comments (2)
  1. [Section 3, Eq. (3) and paragraph beginning "From values of m* and τ..."] The quoted DC mobility is computed as μ_DC = eτ/m*, but the model actually fitted to the data is the Drude-Smith model of Eq. (3), whose zero-frequency real part is (eτ/m*)(1+c). With c = -0.82 ± 0.05 for the 4 nm sample and -0.62 ± 0.05 for the 6 nm sample (Table 1), the true DC mobilities are approximately 100 and 270 cm²/Vs, respectively, not 550 and 700 cm²/Vs as stated in the abstract and conclusion. Only the 16 nm sample (c ≈ 0) retains ~1000 cm²/Vs. The reported thickness trend is therefore exaggerated, and the comparison with FET mobilities and bulk PbS is distorted. The authors should report the DC mobility including the (1+c) factor, or explicitly re-label the quoted quantity as the Drude mobility parameter and adjust the discussion.
  2. [Section 2, Eqs. (4)-(5), Fig. 3(c), and SI Section 1] The exciton binding energies for the 4 and 6 nm samples are taken as fixed inputs from Yang and Wise (Ref. [24]), and the 16 nm value is assumed to be 21 meV. These same E_b values are then used in Eq. (4) to construct the exciton response and in the Saha model of Fig. 3(c) to 'confirm' the fitted exciton quantum yields. The paper therefore cannot claim that the data 'agree with' or 'confirm' the assumed binding energies or the absolute quantum yields; the agreement only shows internal consistency conditional on those inputs. In addition, the authors themselves note that the fitted Bohr radius for the 16 nm sample (a_B = 6 nm) is 'unreasonable' and that Eq. (5) may not apply for thicker sheets; this undermines the 16 nm exciton yield and, because the decomposition is coupled, could also bias the free-carrier scattering time for that sample. Please treat E_b as a fit parameter or, at minimum, present the quantum yields as explicitly conditional on the adopted E_b values.
minor comments (5)
  1. [Table 1] The reduced effective masses are listed as 0.08 ± 0.1, 0.07 ± 0.1, and 0.06 ± 0.1 m_e; if the uncertainty is truly 0.1, the resulting mobility has roughly 100% uncertainty and the error bars quoted in the text (±100, ±100, ±150 cm²/Vs) are not propagated. Please check whether these are typographical errors.
  2. [Figure 2(d) caption] The caption states 'N_K ∼ 5×10^4_ cm-2', which appears garbled; the text in Section 2 states N_K ∼ 5 × 10^13 cm^-2. Please correct.
  3. [SI Figure S3 caption] The caption reads 'Normalized THs response' and should read 'Normalized THz response'.
  4. [Section 2, last paragraph] The phrase 'rendering them leading-edge thin film 2D materials' is vague; consider replacing it with a more concrete statement about the measured values.
  5. [Eq. (1) in main text and Eq. (8) in Experimental Section] The displayed equation for S(ν,t) contains a typographical artifact in the numerator/denominator expression. Please clean up the notation.

Circularity Check

2 steps flagged · score 5.0 of 10

Exciton-yield 'Saha confirmation' reuses the same E_b and m* inputs that fixed the THz fit; 'agreement with binding energies' is therefore partly self-consistency, while the quoted DC mobility separately omits the fitted Drude-Smith (1+c) factor.

  1. fitted input called prediction [Section 2 (fixed E_b inputs, p. 9) and Conclusion (p. 13)]
    "By using values of 𝐸" for PbS-NSs with thickness of 4 and 6 nm from Yang and Wise,[24] and by assuming the value for 16 nm NSs to be ~21 meV ... we calculate the energies of higher exciton states according to 𝐸6 =... [25] ... Our data agree with substantial exciton binding energies from previously reported theoretical calculations."

    The conclusion that the data 'agree with' the Yang–Wise exciton-binding energies is not an independent empirical test. Those E_b values are fixed inputs to Equation (4) before the fits are made; c, τ, a_B, Γ, and Φ are the adjustable parameters. Saying the data can be described with the chosen E_b confirms only that the model with that imposed E_b is compatible with the data, not that the data validate E_b. The 'agreement' is therefore largely a restatement of the input assumption.

  2. fitted input called prediction [Section 2, p. 11 (Saha-model confirmation; Figure 3c)]
    "by means of the Saha model, 𝛷=Q is calculated as a function of the number of absorbed photons per unit area in a single PbS-NS, 𝑁K:‚ (see Supporting Information), and by using 𝐸" and 𝑚∗ values reported in Table 1. Calculations are shown in Figure 3(c) by solid lines. Triangles are EX fractions obtained from fits shown in Figure 2(d) at 8 ps. ... found values agree well with what predicted by the Saha model, confirming the validity of our approach."

    The Saha-model 'prediction' is presented as independent confirmation of the fitted exciton yield, but its inputs are the same E_b and m* values already fixed when Φ_EX was extracted from the THz data via Equations (3)–(5). Any error in E_b or m* shifts the fitted Φ_EX and the Saha curve in the same direction, so agreement between them verifies only internal consistency of reusing the same parameters. It does not test E_b, m*, or the exciton quantum yields against independent physics.

full rationale

The circularity is partial and localized. The THz analysis itself is a legitimate multi-parameter fit of the measured frequency-dependent spectra using the external Drude-Smith and Kaindl exciton models; that core fitting procedure is not circular. The circular element is the confirmation language: E_b values are fixed inputs from Yang and Wise (with an assumed ~21 meV for 16 nm sheets), yet the paper concludes the data 'agree with' those binding energies, and the Saha-model comparison uses exactly the same E_b and m* values to 'confirm' the fitted Φ_EX. This is a self-consistency check, not an independent prediction, and it directly supports the central exciton-yield claim. The authors' own admission that the 16 nm fit requires an 'unreasonable' Bohr radius of 6 nm and that Equation (5) may no longer apply for thicker sheets reinforces how assumption-bound the exciton extraction is. Separately, the abstract's DC mobility values are computed as μ = eτ/m*, omitting the (1+c) factor of the Drude-Smith model that was actually fitted; for c = -0.82 this reduces the 4 nm DC mobility to roughly 100 cm2/Vs. That is a serious model-consistency error and weakens the headline mobility claim, but it is not a circularity and is not counted in the score. Self-citations in the paper (e.g., Refs. 11 and 29) are methodological or background and are not load-bearing. Overall, the paper has independent measured data and a non-circular fitting procedure, but the central exciton-yield confirmation reduces in part to reusing the same fixed inputs, giving a score of 5.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities; the analysis is based on standard charge-carrier and exciton models. The free parameters, especially tau, c, Phi_ex, and the assumed E_b for 16 nm, carry most of the burden for the reported quantitative results.

free parameters (7)
  • Backscattering parameter c = -0.82, -0.62, 0.0 (4, 6, 16 nm)
    Fitted to the frequency-dependent THz response; Table 1.
  • Charge carrier scattering time tau = 25 +/- 4, 29 +/- 4, 33 +/- 4 fs
    Fitted to THz spectra and used to derive DC mobility via mu = e*tau/m*.
  • Exciton Bohr radius a_B = 3.7 +/- 0.5, 4.5 +/- 1.0, 6.0 +/- 1.0 nm
    Fitted through the oscillator strength model, Eq. (5); the 16 nm value is called 'unreasonable' by the authors.
  • Excitonic transition broadening Gamma = 153 +/- 30, 140 +/- 75, 131 +/- 80 meV
    Fitted; large uncertainties because the exciton resonance is above the THz probe range.
  • Quantum yields Phi_free and Phi_ex = Phi_free = 0.14/0.23/0.1; Phi_ex = 0.86/0.77/0.9
    Fitted with the constraint Phi_free + Phi_ex = 1; the central claim of dominant exciton formation.
  • Exciton binding energy for 16 nm PbS-NSs = 21 meV
    Assumed as an average between the 8 nm value (40 meV) and the bulk value (2.7 meV); Supporting Information Eq. (S1).
  • Effective mass m* = 0.08, 0.07, 0.06 m_e (errors +/- 0.1)
    Obtained by parabolic fit to k.p bands over a chosen k-range; the authors note values differ from Ref. [24] due to the range chosen. Directly enters mu_DC = e*tau/m*.
assumptions (6)
  • domain assumption The Drude-Smith model, Eq. (3), with a single backscattering parameter c describes the THz mobility of free carriers in PbS nanosheets.
    Section 2, Eq. (3); standard for colloidal films but c is a phenomenological parameter.
  • domain assumption The 2D exciton response model of Kaindl et al., Eqs. (4)-(5), and the hydrogenic exciton energy series E_n = E_b/n^2 apply to PbS nanosheets.
    Section 2, Eqs. (4)-(5); the authors note it may not be valid for thicker nanosheets.
  • domain assumption At t = 8 ps after 800 nm excitation, hot carriers have relaxed and free carriers and excitons are in thermal equilibrium at the band gap.
    Section 2, first delay time chosen to exclude hot-carrier contributions; no direct evidence provided.
  • domain assumption Exciton binding energies for 4 and 6 nm nanosheets from Yang and Wise are correct, and the bulk value from Eq. (S1) with epsilon_high = 17 is valid.
    Section 2 and Supporting Information; used as fixed inputs to Eq. (4) and the Saha model.
  • domain assumption The Saha model for 2D systems describes the equilibrium between free carriers and excitons.
    Section 2; used to check Phi_ex, but with the same E_b and m* values as the fit.
  • domain assumption The thin-film approximation, Eq. (1), relating the differential transmission to the sum of quantum-yield-weighted mobilities is valid for these films.
    Section 2 and Experimental Section; standard for optical pump-terahertz probe spectroscopy.

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Pith. "Pith review of Photoexcitation of PbS Nanosheets Leads to Highly Mobile Charge Carriers and Stable Excitons." pith.science (2026). https://pith.science/paper/EX4Q3KJI

@misc{pith2026190804711,
  author       = {Pith},
  title        = {Pith review of: Photoexcitation of PbS Nanosheets Leads to Highly Mobile Charge Carriers and Stable Excitons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EX4Q3KJI}},
  note         = {Machine review of arXiv:1908.04711}
}
read the original abstract

Solution-processable two-dimensional (2D) semiconductors with chemically tunable thickness and associated tunable band gaps are highly promising materials for ultrathin optoelectronics. Here, the properties of free charge carriers and excitons in 2D PbS nanosheets of different thickness are investigated by means of optical pump-terahertz probe spectroscopy. By analyzing the frequency-dependent THz response, a large quantum yield of excitons is found. The scattering time of free charge carriers increases with nanosheet thickness, which is ascribed to reduced effects of surface defects and ligands in thicker nanosheets. The data discussed provide values for the DC mobility in the range 550 - 1000 cm2/Vs for PbS nanosheets with thicknesses ranging from 4 to 16 nm. Results underpin the suitability of colloidal 2D PbS nanosheets for optoelectronic applications.

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Works this paper leans on

6 extracted references · 6 canonical work pages

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    Fits of the THz response at 8 ps for PbS-NSs with different thickness (indicated at the top of panels)

    Fits of the THz response in the frequency domain Figure S1. Fits of the THz response at 8 ps for PbS-NSs with different thickness (indicated at the top of panels). In the right panels the total response (same color as the sample), EX response (yellow) and free charge carrier response (magenta) from fits are shown in a wider frequency range. Note that with...

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    2D-SYNETRA

    Conclusion In conclusion, we have determined the frequency-dependent complex THz-response of photogenerated free charge carriers and excitons in colloidal PbS-NSs with different thickness. From analysis of our data, we find DC mobilities as high as 550 to 1000 cm2/Vs for 4 to 16 nm thick PbS-NSs, rendering them leading-edge thin film 2D materials. The inc...

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    Comparison of normalized THz spectra at 8 and 200 ps after photoexcitation, showing that the later time response can be described by a scaling factor

    Normalized THs response at 8 and 200 ps Figure S3. Comparison of normalized THz spectra at 8 and 200 ps after photoexcitation, showing that the later time response can be described by a scaling factor. In the main manuscript, this is related to the reduction of the fraction of free charge carriers only. 5. Fits of the THz response by considering free char...

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