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Optimizing high-temperature electron mobility in single-crystal Bi$_2$O$_2$Se based on its unconventional dependence on concentration

T0 review · 4 major / 9 minor · reviewed 2026-07-09 · glm-5.2

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Pith's one-line read Defect type, not defect count, controls mobility in Bi₂O₂Se

desk verdict Proposes Se_Bi antisite defects as the cause of the unconventional mobility-concentration trend in Bi2O2Se, but the defect assignment is not independently established and the causal chain rests on indirect evidence. read the letter →

arxiv 2607.07384 v1 pith:SORAH6WX submitted 2026-07-08 cond-mat.mtrl-sci

Antonín Sojka , Petr Knotek , Jan Zich , Martin Míšek , Roman Tesař , Kyo-Hoon Ahn , Petr Levinský , Jiří Navrátil
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Pavlína Ruleová Jiří Hejtmánek Karel Knížek Václav Holý Čestmír Drašar
This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords mobilityconditionscarrierconcentrationchargedefectshighse-rich
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 argues that the counterintuitive step-like increase in electron mobility with carrier concentration in Bi₂O₂Se arises because different growth conditions produce qualitatively different native point defects, which in turn alter the electronic band structure itself. Under selenium-rich conditions, Se atoms substitute onto Bi sites (Se_Bi defects); these introduce mid-gap states that push the material from a semiconductor into a semimetal with both electrons and holes, increase the carrier effective mass, and disrupt the Bi₂O₂ layer that serves as the primary conduction channel. Under selenium-poor conditions, selenium vacancies (V_Se) form instead; these donate electrons without disturbing the Bi₂O₂ channel, leave the effective mass low, and produce structurally cleaner crystals. The mobility 'increase with concentration' is thus not a scattering phenomenon but a switch between two distinct electronic regimes: low-concentration Se-rich samples are actually semimetallic with heavy, mixed carriers and poor mobility, while higher-concentration Se-poor samples are single-carrier metals with light electrons and high mobility. The authors further show that Se-rich growth produces macroscopic crystal defects—dislocations, extraneous phase lamellae, and surface protrusions—that compound the mobility loss. They conclude that room-temperature mobility is governed primarily by the structural perfection of the Bi₂O₂ conduction layer, since electron-phonon scattering at 300 K depends on whether defects have broken the phonon gap that normally isolates high-frequency Bi₂O₂ phonons from low-frequency Se-layer phonons.

What carries the argument

The argument rests on a comparison between two single crystals: Sample A (Se-rich, dominated by Se_Bi, low mobility, no SdH oscillations, multiple cyclotron resonance peaks) and Sample B (Se-poor, dominated by V_Se, high mobility, clean single-frequency SdH oscillations, single cyclotron resonance). DFT calculations in a 3×3×1 supercell using both mBJ and GGA potentials provide the band structures and effective masses for each defect type. HRXRD fitting and EDS provide compositional data, while AFM in PeakForce QNM and KPFM modes reveals the nanoscale structural and electrical differences between the two samples.

What would settle it

If a sample grown under Se-rich conditions were annealed to convert Se_Bi defects to V_Se without changing carrier concentration, and mobility did not increase, the defect-type mechanism would be undermined. Conversely, if Se-poor crystals with intentionally introduced Bi-site substitution showed the predicted mobility collapse, that would strengthen the claim.

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Extended reading notes

Core claim

The central object is the Se_Bi antisite defect and its effect on the Bi₂O₂ conduction channel. The authors show through DFT band-structure calculations that Se_Bi is the only native defect that creates mid-gap states, shifts the conduction band minimum from Γ to M, increases in-plane effective masses, and induces semimetallic behavior with both electrons and holes. This contrasts with V_Se, which shifts the Fermi level into the conduction band but preserves the basic band structure. The paper combines this computational result with transport measurements (Hall effect, Shubnikov-de Haas oscillations, THz cyclotron resonance), HRXRD structural analysis, and AFM nanomechanical mapping to build

Load-bearing premise

The identification of Se_Bi as the dominant defect in the Se-rich sample and V_Se as dominant in the Se-poor sample rests on HRXRD fitting that the authors themselves describe as non-unique, and is in tension with both the EDS stoichiometry (which shows much smaller non-stoichiometry than HRXRD implies) and the authors' own DFT formation energies (which rank O_Se, not Se_Bi or V_Se, as the lowest-energy defect). The entire causal chain from defect type to effective mass toMob

Editorial extensions

If this is right

  • Growing Bi₂O₂Se under Se-poor conditions at 800–830°C with controlled V_Se concentration should maximize room-temperature mobility, since V_Se donates electrons without disrupting the Bi₂O₂ conduction channel.
  • Any doping strategy that substitutes on the Bi site will harm mobility by breaking the phonon gap that isolates the Bi₂O₂ layer from low-frequency Se-layer phonons, making ionized impurity and electron-phonon scattering worse simultaneously.
  • Reported effective masses in the literature ranging from 0.032m₀ to 0.23m₀ may reflect different defect populations rather than measurement error or anisotropy, since Se_Bi increases m* while V_Se does not.
  • The 'hidden direct band gap' observed in some ARPES experiments may be a signature of Se_Bi-induced mid-gap states rather than an intrinsic feature of the band structure.
  • Hall mobility measurements in Se-rich samples are systematically unreliable because bipolar transport (electrons plus holes) can produce artificially low apparent Hall concentrations and mobilities.

Reading between the lines

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

  • If the defect-type-switching mechanism is correct, then the entire literature trend of mobility vs. concentration in Bi₂O₂Se could be re-plotted as mobility vs. growth stoichiometry, and the step should collapse onto a continuous curve within each defect regime.
  • The discrepancy between the authors' own DFT formation energies (where O_Se has the lowest energy, not Se_Bi or V_Se) and the defect assignments they make suggests that kinetic factors during crystal growth—cooling rate, temperature gradient, annealing—may dominate over thermodynamic equilibrium in determining which defects actually form.
  • If Se_Bi defects create a semimetal with both carrier types, then samples near the borderline concentration (~10¹⁷ cm⁻³) might exhibit magnetoresistance signatures (e.g., non-linear Hall effect) that could serve as a diagnostic for defect type without requiring HRXRD or cyclotron resonance.
  • The phonon-gap argument implies that isotope substitution on the Bi or O sites—without changing defect chemistry—could test whether phonon anharmonicity in the Bi₂O₂ layer is truly the room-temperature mobility bottleneck.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 9 minor

Summary. This manuscript investigates the counterintuitive step-like increase in Hall mobility with carrier concentration in single-crystal Bi2O2Se, proposing that the effect arises from different native defect structures under Se-rich versus Se-poor growth conditions. The authors compare two representative samples (A: Se-rich, low mobility; B: Se-poor, high mobility) using HRXRD, EDS, AFM, DFT band-structure calculations, cyclotron resonance, and magnetotransport. The central claim is that Se_Bi antisite defects (Se-rich) destroy the Bi2O2 conduction channel, increase the effective mass, and induce semimetallic behavior with multiple carrier types, while V_Se defects (Se-poor) preserve the channel with lower effective mass. The argument is supported by a convergence of multiple experimental and computational techniques, though the defect identification is acknowledged as non-unique.

Significance. The manuscript addresses a genuinely puzzling transport anomaly in a technologically relevant semiconductor and proposes a physical mechanism (defect-dependent effective mass and bipolar transport) that is more specific than prior explanations. The DFT calculations of band-structure modifications by individual point defects, the AFM nanomechanical mapping of crystal inhomogeneity, and the cyclotron resonance data are valuable contributions. The Hall ambiguity analysis (SM section 1) providing a quantitative framework for how bipolar transport can artifactually reduce apparent mobility is a useful falsifiable tool. The practical growth guidelines (Se-poor, 800-830 degrees C, controlled V_Se) are actionable for the community.

major comments (4)
  1. Section III.A and SM section 3: The HRXRD fitting yields nearly identical compositions for both samples (Bi1.89O2Se1.11 for A vs Bi1.90O2Se1.10 for B), with Se_Bi at approximately 10% of Bi sites in both cases. The authors acknowledge the fit is non-unique ('an equally good fit would have been obtained if parameters 4 and 5 had been fitted instead of parameter 6'). Since the central causal chain depends on sample A being Se_Bi-dominated and sample B being V_Se-dominated, the fact that HRXRD cannot distinguish the two samples by defect type is a load-bearing gap. The authors should either (i) provide an additional independent diagnostic that distinguishes the defect types between A and B (e.g., positron annihilation for vacancies, or XANES/EXAFS for local bonding), or (ii) reframe the claim as a hypothesis grounded in the totality of indirect evidence rather than an established assignment
  2. Section III.A and SM section 2: The EDS stoichiometries (Se1.005 +/- 0.01 for A; Se0.995 +/- 0.02 for B) overlap within error bars at Se approximately 1.00, while HRXRD gives Bi1.9O2Se1.1 for both. The three-orders-of-magnitude discrepancy between EDS non-stoichiometry and carrier concentration is noted but not resolved. The compositional distinction between 'Se-rich' and 'Se-poor' is marginal by EDS and identical by HRXRD. The manuscript should explicitly state that the Se-rich/Se-poor labeling is derived primarily from transport behavior (carrier concentration relative to the borderline n_b) rather than from direct compositional measurement, and discuss the implications for the defect assignment
  3. Section III.B and Table S5: The authors' own DFT formation energies show O_Se has the lowest formation energy (GGA: -0.05 eV; mBJ: 0.99 eV), while Se_Bi (3.27-3.76 eV) and V_Se (2.65-4.77 eV) are substantially higher. If O_Se dominates in both samples, the stoichiometric shift driving the A/B distinction must come from defects present at much lower concentrations. The authors argue O_Se has negligible band-structure impact, but the tension between O_Se being thermodynamically favored and Se_Bi/V_Se being the proposed dominant defects is not adequately addressed. A quantitative discussion of defect concentrations at the relevant chemical potentials (or a justification for why kinetic factors during growth would favor Se_Bi over O_Se) would strengthen the argument
  4. SM section 4: The cyclotron resonance data for sample A is described as 'preliminary' with 'many signals' that could be 'interference fringes and cyclotron resonance on various charge carriers.' While the authors appropriately flag this uncertainty, the data are used in the main text (section III.B) as supporting evidence for multiple carrier types in sample A. The claim should either be softened to match the preliminary status or additional measurements with multiple laser lines should be presented to substantiate the multi-carrier interpretation
minor comments (9)
  1. Section I: The sentence beginning 'The connection between low both carrier concentration and mobility in Se-rich conditions' contains a grammatical error ('low both'). Should be revised for clarity
  2. Table I: The entries 'Diluted semimetal' and 'Diluted metal' for charge transport are labeled as 'assumed' in parentheses. The table caption should clarify that these are model assignments rather than measured quantities
  3. Figure 2 caption: The effective mass values labeled with negative signs (e.g., m*=-0.82, m*=-2.20) should be clarified as referring to hole-like curvature of the band, or the convention should be stated explicitly
  4. Table II: The 'BP' column (band position relative to E_F) uses codes 1, 2, 3 but the legend is terse. Adding explicit energy values or a clearer cross-reference to the colored lines in Figure 2 would help the reader
  5. Section III.E: The text references 'Figure 3' when discussing transport data, but Figure 3 shows AFM/KPFM images. The correct figure reference (Figure 5) should be verified and corrected
  6. Section III.E, Figure 5b: The mobility temperature dependence is described as mu_H approximately T^2.3, but the exponent value and fitting range are not specified in the figure caption. Adding a fit annotation would help the reader
  7. SM section 3: The fitted parameter x_S values contain formatting artifacts ('x_S = . +/- . ' for sample A). These should be corrected to show the numerical values clearly
  8. The DFT supercell (3x3x1, 90 atoms) is a reasonable compromise, but the defect concentration it represents (~1.1%) is orders of magnitude higher than the actual carrier concentration (~10^17 cm^-3). A brief comment on the applicability of the band-structure results at realistic defect concentrations, particularly for the semimetallic state claim, would be valuable
  9. References [9] (dated 2026) and several others appear to have incomplete or future-dated publication information. These should be verified for accuracy and updated with complete citation details and DOIs

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee correctly identifies that our central defect assignment (Se_Bi-dominated vs. V_Se-dominated) rests on indirect evidence rather than a single definitive diagnostic. We agree that the manuscript should be revised to state this more explicitly and to soften claims where the supporting data are preliminary. We address each major comment below.

read point-by-point responses

  1. Referee: HRXRD yields nearly identical compositions for both samples, the fit is non-unique, and HRXRD cannot distinguish defect types between A and B. The referee requests either an additional independent diagnostic or a reframing of the claim as a hypothesis.

    Authors: The referee is correct that HRXRD alone cannot uniquely distinguish Se_Bi from V_Se between samples A and B. We acknowledge this as a genuine limitation of our structural characterization. We do not have positron annihilation or XANES/EXAFS data available at this time, and we agree that obtaining such measurements would substantially strengthen the defect assignment. Accordingly, we will revise the manuscript to reframe the defect assignment as a hypothesis grounded in the totality of indirect evidence—HRXRD, EDS, DFT formation energies, band-structure calculations, cyclotron resonance, AFM nanomechanical mapping, and magnetotransport—rather than presenting it as an established structural determination. We will add explicit language in Section III.A and the abstract making clear that the Se_Bi/V_Se assignment is inferred from the convergence of transport behavior, DFT-predicted band-structure modifications, and AFM-observed inhomogeneity, not directly confirmed by a single defect-specific probe. revision: yes

  2. Referee: EDS stoichiometries overlap within error bars at Se~1.00, and the three-orders-of-magnitude discrepancy between EDS non-stoichiometry and carrier concentration is not resolved. The Se-rich/Se-poor labeling is marginal by EDS and identical by HRXRD. The manuscript should state that the labeling is derived primarily from transport behavior.

    Authors: We agree with this assessment. The EDS data alone cannot robustly distinguish Se-rich from Se-poor conditions given the error bars, and the discrepancy between EDS non-stoichiometry (~10^19-10^20 cm^-3 equivalent) and measured carrier concentration (~10^17 cm^-3) is a real and unresolved issue that we have not adequately discussed. We will revise the manuscript to explicitly state that the Se-rich/Se-poor classification is derived primarily from transport signatures (carrier concentration relative to the borderline n_b, Hall mobility, RRR, and presence/absence of SdH oscillations) rather than from direct compositional measurement. We will also add a discussion of the stoichiometry-carrier concentration discrepancy, noting that it implies either compensation among multiple defect types (as we briefly mention in SM section 2 with examples like 3V_Se + 2Se_Bi + 2V_O) or that the electrically active defect concentration is much smaller than the total non-stoichiometry. This is an important clarification that we will incorporate. revision: yes

  3. Referee: DFT formation energies show O_Se has the lowest formation energy, while Se_Bi and V_Se are substantially higher. The tension between O_Se being thermodynamically favored and Se_Bi/V_Se being the proposed dominant defects is not adequately addressed.

    Authors: This is a fair point. Our DFT calculations do show O_Se with the lowest formation energy (GGA: -0.05 eV; mBJ: 0.99 eV), which is at odds with the published literature where V_Se is typically the lowest-energy defect. We note that the formation energies of native defects in Bi2O2Se are highly inconsistent across published DFT studies, as we mention in the text. The key argument in our manuscript is that O_Se, regardless of its concentration, has negligible impact on band structure and effective mass (see Figure 2 and Table II), and thus does not explain the transport differences between samples A and B. The physically relevant defects for transport are those that modify the electronic structure—Se_Bi and V_Se—even if they are not the most thermodynamically abundant. We agree, however, that we should provide a more quantitative discussion of why Se_Bi and V_Se might be present at concentrations sufficient to affect transport despite their higher formation energies. We will add a discussion of kinetic factors during crystal growth (the samples are grown far from equilibrium via gas-phase transport over one month, with different thermal histories) and the role of chemical potentials under Se-rich vs. Se-poor growth conditions. We will also explicitly acknowledge the tension between our formation energy calculations and the proposed defect assignments as a limitation. revision: partial

  4. Referee: Cyclotron resonance data for sample A is described as 'preliminary' in SM section 4 but is used as supporting evidence in the main text. The claim should be softened or additional measurements presented.

    Authors: The referee is correct that the cyclotron resonance data for sample A are preliminary and that the main text should reflect this status more carefully. We do not have additional measurements with multiple laser lines available at this time. We will revise Section III.B of the main text to explicitly state that the cyclotron resonance data for sample A are preliminary, that the multiple signals could arise from interference fringes as well as from multiple carrier types, and that the multi-carrier interpretation is suggestive rather than conclusive. The claim will be softened from presenting the CR data as supporting evidence to presenting it as consistent with—but not independently confirming—the multi-carrier hypothesis. We will also make clear that the multi-carrier interpretation for sample A rests primarily on the DFT band-structure calculations showing semimetallic behavior with Se_Bi, the Hall ambiguity analysis (SM section 1), and the absence of SdH oscillations, rather than on the CR data alone. revision: yes

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; DFT predictions are independent of transport measurements they are compared against

full rationale

The paper's central derivation chain is: (1) EDS and growth conditions independently classify sample A as Se-rich and B as Se-poor; (2) standard defect chemistry associates Se-rich conditions with Se_Bi antisites and Se-poor with V_Se; (3) DFT calculations independently compute band structures and effective masses for each defect type without fitting to transport data; (4) these DFT predictions (Se_Bi → semimetal, multiple carrier types, higher effective mass; V_Se → single carrier type, lower effective mass) are compared against independent measurements (cyclotron resonance showing multiple vs single carriers, SdH presence/absence, Hall mobility). This is a pattern-matching argument between independent calculations and independent experiments, not a circular derivation. The Hall ambiguity analysis (SM §1) is presented as an interpretation caveat, not as a fitted input repackaged as prediction. Self-citations ([12] Zich et al. for phonon context, [43] Sojka et al. for Mn-doping comparison) are not load-bearing for the central defect→effective-mass→mobility chain. The paper is transparent about uncertainties: HRXRD fitting is acknowledged as non-unique ('the measured data cannot distinguish between these scenarios'), DFT formation energies favor O_Se over Se_Bi, and cyclotron resonance data for sample A is called 'preliminary.' These are correctness risks, not circularity. The minor score of 2 reflects the presence of self-citations that, while not load-bearing, contribute to the contextual framing.

Assumptions & free parameters 3 free parameters · 4 assumptions · 1 invented entities

The paper's argument depends on three load-bearing assumptions: (1) the defect assignment (Se_Bi vs V_Se) is correct despite non-unique HRXRD fits and inconsistent EDS data; (2) the Bi₂O₂ layer phononic isolation model from self-cited ref [12] applies; (3) bipolar Hall ambiguity explains the low-mobility regime. No new entities are invented. The free parameters are standard experimental/DFT choices, not ad hoc constants introduced to make a derivation work.

free parameters (3)
  • HRXRD fitted parameters (Bi-Se plane distance, thermal B factor, Se-at-Bi occupancy, primary intensity, background) = z_(Bi-Se) = 0.355c; x_S ≈ 0.11 (Bi₁.₉O₂Se₁.₁) for both samples
    Fitted to diffraction peak intensities in a semikinematic model. Parameters were correlated and could not be fitted simultaneously; only 5 of 9 possible parameters were fitted. The authors note an equally good fit would result from fitting Bi/Se site occupancies instead.
  • DFT supercell size (3×3×1, 90 atoms) = 11.673 × 11.673 × 12.213 Å
    Chosen as a compromise between computational accuracy and calculation time. Defect concentration in the supercell (~1.1%) is orders of magnitude higher than the actual carrier concentration (~10¹⁷ cm⁻³), which the authors acknowledge.
  • Hall measurement field (±0.8 T) = ±0.8 T
    Used for Hall coefficient extraction. The paper's own SM section 1 shows that in bipolar systems, the extracted Hall concentration and mobility depend on the measurement field and carrier ratio, introducing systematic uncertainty.
assumptions (4)
  • domain assumption The dominant native defects in Bi₂O₂Se are V_Se (Se-poor) and Se_Bi (Se-rich), with O_Se present but band-structure-inert.
    Stated in Section III.A and III.B. This assignment is based on HRXRD fitting that the authors describe as non-unique (SM section 3) and on DFT formation energies that show O_Se as lowest, not Se_Bi. The axiom is necessary for the entire causal chain from defect type to mobility.
  • domain assumption The Bi₂O₂ layer is the primary conduction channel, and its phononic isolation from the Se layer (large phonon gap) is preserved in defect-free crystals.
    Invoked in Section III.D to explain room-temperature mobility. Based on ref [12] (self-cited, by overlapping authors). The argument that Se_Bi defects in the Bi₂O₂ layer break this phononic isolation is central to the high-temperature mobility explanation.
  • domain assumption Hall mobility in Se-rich samples is underestimated due to bipolar transport (electrons + holes from Se_Bi-induced semimetallic state).
    Invoked in Section IV and SM section 1 to explain the step-like mobility increase. While the SM provides a formal analysis, the actual carrier concentrations and mobilities in samples A and B are not independently determined to confirm bipolar transport is operative.
  • standard math mBJ potential is appropriate for Bi₂O₂Se band structure because the bands near the Fermi surface are predominantly s and p character.
    Stated in Section II.D. This is a standard choice in DFT for s-p compounds, but the paper also uses GGA for comparison, and the two potentials give quantitatively different band structures and formation energies.
invented entities (1)
  • None independent evidence
    purpose: N/A
    The paper does not introduce new particles, forces, dimensions, or postulated entities. Se_Bi, V_Se, O_Se are standard point defects whose existence is established in the Bi₂O₂Se literature. The 'Fermi lakes' concept is cited from ref [22] (Behnia, 2015), not invented here.

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Cite this review

Pith. "Pith review of Optimizing high-temperature electron mobility in single-crystal Bi$_2$O$_2$Se based on its unconventional dependence on concentration." pith.science (2026). https://pith.science/paper/SORAH6WX

@misc{pith2026260707384,
  author       = {Pith},
  title        = {Pith review of: Optimizing high-temperature electron mobility in single-crystal Bi$_2$O$_2$Se based on its unconventional dependence on concentration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SORAH6WX}},
  note         = {Machine review of arXiv:2607.07384}
}
abstract

Quasi-2D Bi$_2$O$_2$Se is part of an intensive materials research effort aimed at finding new semiconductors that outperform silicon-based electronics in terms of speed and power consumption. This material exhibits exceptionally high carrier mobility at low temperatures but mediocre mobility at 300 K. Its high mobility is generally associated with its high permittivity ($\varepsilon_r$~500), which is also associated with metallicity persisting down to very low carrier concentrations. This material exhibits a counterintuitive increase in carrier mobility as the concentration increases. The connection between low both carrier concentration and mobility in Se-rich conditions, and both high carrier concentration and mobility in Se-poor conditions suggests that the increase is related to native defects. We demonstrate that these defects can alter the effective mass of charge carriers. Specifically, substitutional Se(Bi) defects, which appear under Se-rich conditions, destroy the Bi$_2$O$_2$ channel and compromise charge transport properties. These defects increase the effective mass of charge carriers transforming the original semiconductor into a semimetal and introducing holes into charge transport. Additionally, we show that single crystals are generally inhomogeneous, particularly those grown under Se-rich conditions. Unlike Se-poor conditions, Se-rich conditions induce a higher concentration of dislocations and extraneous phases. These findings suggest that the perfection of the Bi$_2$O$_2$ channel is crucial for mobility, particularly at room temperature.

Figures

Figures reproduced from arXiv: 2607.07384 by the authors.

Figure 1
Figure 1. FIG 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. FIG 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG 5 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: FIG 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

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