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REVIEW 3 major objections 6 minor 10 references

Tracking particles at fluences 5-10 $\cdot$1E16 $n_{eq}$/cm$^2$

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Very thin LGADs can keep tracking signals above 1 fC at fluences of 5–10×10^16 n_eq/cm2.

desk verdict A clear, well-aimed proposal for LGADs at 5–10e16 that would be stronger if its central 'will assure 1 fC' conclusion were backed by a quantitative model or data. read the letter →

arxiv 1908.11605 v1 pith:H3RF2HGC submitted 2019-08-30 physics.ins-det hep-ex

N. Cartiglia , H. Sadrozinski , A. Seiden This is my paper · ORCID
classification physics.ins-dethep-ex PACS 29.40.Gx29.40.Wk61.82.Fk
keywords LowGainAvalancheDiodeLGADsilicontrackingdetectorsradiationdamagechargemultiplicationimpactionizationthinsensorsfuturehadroncollider
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 very thin Low Gain Avalanche Diodes (LGADs), 25–50 µm thick, can still produce the ≥1 fC signal needed by readout chips after irradiation to $5\text{--}10\times10^{16}\,n_{\rm eq}/{\rm cm}^2$, roughly 30 times the fluence at which silicon's response has been directly tested. The idea is to split the amplification between two stages: at lower fluence the implanted gain layer multiplies the signal by 5–10, and as irradiation erases that layer and dopes the bulk, the bias voltage shifts multiplication into the bulk itself. If the argument holds, future hadron-collider trackers would not need thick silicon sensors, avoiding the leakage current, trapping, and high depletion voltage that make thick sensors impractical at such fluences. The authors present the proposal as an extrapolation whose load-bearing assumption is that impact ionization is not quenched in the $5\text{--}10\times10^{16}$ range.

What carries the argument

The load-bearing object is the electric-field profile of an LGAD, in which a thin buried gain layer creates a short, flat, bias-controlled region where the field approaches the critical ionization strength of roughly 250–300 kV/cm. The argument follows how equation (2), $N_A(\varphi)=g_{\rm eff}\varphi+N_A(0)e^{-c\varphi}$, evolves that profile: acceptor removal erases the gain layer while acceptor creation dopes the bulk, moving the high-field region deeper. Charge gain is computed as $N(x)=\int N(0)e^{\alpha(E)x}\,dx$, with $\alpha(E)^{-1}$ the drift distance needed to ionize; the mechanism works only while this distance is shorter than the carrier mean free path $\lambda$. A separate enabling piece is the proposed shallow-trench termination, which removes the interpad dead area and would allow 50×50 µm² pixels with near-100% fill factor.

What would settle it

Take a 25–50 µm LGAD, irradiate it to $10^{16}$–$10^{17}\,n_{\rm eq}/{\rm cm}^2$, and measure collected charge versus bias: if the signal stays below 1 fC at the highest sustainable voltage, or if gain does not increase as bulk multiplication turns on, the central claim fails.

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Extended reading notes

Core claim

The paper claims that a 25–50 µm thin LGAD can deliver more than 1 fC of signal at fluences of $5\text{--}10\times10^{16}\,n_{\rm eq}/{\rm cm}^2$ by switching its amplification site as radiation damage accumulates. It models the damage with $N_A(\varphi)=g_{\rm eff}\varphi+N_A(0)e^{-c\varphi}$: irradiation removes dopants from the gain layer while creating acceptor-like defects in the bulk, moving the high-field region from the gain layer into the bulk. Up to $0.1\text{--}0.3\times10^{16}$ the gain layer alone gives a stable factor of 5–10; above that, a bias near 500 V triggers impact ionization in the bulk and provides the same gain. A 20–25 µm sensor is singled out because it can remain fully depleted at $10^{17}\,n_{\rm eq}/{\rm cm}^2$, and its small initial signal of about 0.3 fC requires only moderate gain to reach the 1 fC threshold. The authors are explicit that current evidence for unquenched impact ionization reaches only $3\times10^{15}$.

Load-bearing premise

The argument stands or falls on the assumption that impact ionization is not quenched at $5\text{--}10\times10^{16}\,n_{\rm eq}/{\rm cm}^2$; the paper's evidence for unquenched multiplication reaches only $3\times10^{15}$, roughly a factor of 30 lower.

Editorial extensions

If this is right

  • Tracking layers at future hadron colliders could be built from 25–50 µm silicon instead of 100–200 µm, cutting material while keeping signals above the ~1 fC threshold set by front-end chips.
  • Thin sensors would remain fully depleted after extreme irradiation, avoiding the steep depletion-voltage rise and field distortion that disable thick sensors at high fluence.
  • The detector could keep working after its gain layer is erased, because bias-induced bulk multiplication takes over; the bias voltage becomes the control knob for sensor lifetime.
  • A shallow-trench LGAD with 50×50 µm² pixels would combine high radiation tolerance with close to 100% fill factor, solving the traditional dead-area problem of gain-terminating structures.

Reading between the lines

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

  • The paper's own evidence stops at $3\times10^{15}\,n_{\rm eq}/{\rm cm}^2$, so the $5\text{--}10\times10^{16}$ prediction is a testable extrapolation; measuring gain versus bias on thin LGADs irradiated past $10^{16}$ would settle the bulk-multiplication handoff directly.
  • If the damage-saturation picture in Section 1 is correct, leakage current and effective doping should plateau rather than keep rising with fluence, which would make the proposed operating point easier to reach than a linear extrapolation predicts.
  • Because the mechanism relies only on field strength and carrier scattering, the gain-layer-to-bulk transfer could be tested in simpler thin silicon diodes before committing to full LGAD fabrication.
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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

3 major / 6 minor

Summary. Cartiglia, Sadrozinski, and Seiden propose using 25–50-µm-thick Low Gain Avalanche Diodes (LGADs) as tracking sensors at fluences of 5–10×10^16 n_eq/cm^2. They argue that at low fluence the gain layer provides a gain of about 5–10, while at high fluence the irradiation-increased bulk doping, combined with a bias voltage around 500 V, will induce charge multiplication in the bulk, preserving signals above 1 fC. The paper reviews known non-linear radiation-damage effects, thin-sensor advantages, stable electric-field configurations for internal gain, irradiation effects on doping and ionization, and a trench-isolated high-density LGAD design for near-100% fill factor. It contains no new measurements and no quantitative device simulation; the central claim is presented as a physics-based extrapolation and a design goal.

Significance. The paper gives a clear and honest summary of why thin LGADs are interesting for extreme fluences, and it explicitly identifies the main unknown: whether impact ionization survives at fluences above about 3×10^15 n_eq/cm^2. Its proposal to rely on both gain-layer and bulk multiplication is physically plausible and falsifiable, and the trench-isolation idea addresses a real fill-factor problem. The contribution is useful as a roadmap for future R&D, but as it stands it does not demonstrate its central quantitative claim: there is no gain-versus-fluence curve, no field simulation, and no measurement beyond 3×10^15 n_eq/cm^2. The value of the paper is therefore prospective rather than evidential.

major comments (3)
  1. [Sections 4, 5, and 6] The central quantitative claim—that more than 1 fC will be delivered up to 5–10×10^16 n_eq/cm^2—is not established by the material in the paper. Section 4 states that “current studies have proven that up to fluences 3·10^15 n_eq/cm^2 impact ionization is not quenched,” and then calls the dependence of gain on irradiation “one key question to be addressed in future R&D.” Section 5 concludes only that the possibility of gain in the 5–10×10^16 interval “looks possible,” yet the Conclusion asserts that the interplay of gain-layer and bulk multiplication “will assure” more than 1 fC. No calculation of gain versus fluence, no simulation of the electric-field and avalanche evolution, and no measured data at fluences above 10^16 n_eq/cm^2 are presented. The factor-of-17-to-33 extrapolation from 3×10^15 n_eq/cm^2 is load-bearing and needs either a quantitative model with realistic defect densities and impact-ionization coefficients, or an explicit softening of the conclusion to a conjecture.
  2. [Section 1, Fig. 2] The saturation argument uses a Poisson model with a_o = 1 Ų, a value chosen without justification even though the paper itself notes that damaged clusters extend over tens of ångströms. The choice determines the quantitative conclusion: for a_o = 1 Ų, the probability that a particle hits an untouched square after 5×10^16 cm^-2 is exp(-5) ≈ 0.7%, whereas clusters with ten times larger area would make the same probability exp(-50). More importantly, the model computes the geometric overlap of damaged regions, not the density of electrically active scattering centers that could shorten the carrier mean free path λ below α(E)^{-1}; the latter is what determines whether impact ionization is quenched. The model therefore cannot carry the weight of the claim that multiplication persists to 5–10×10^16 n_eq/cm^2.
  3. [Section 5] The proposed operating scenario depends on a thin sensor that can be over-depleted at about 500 V after irradiation, with a high-density trench-isolated electrode structure and near-100% fill factor. None of these requirements is demonstrated in the paper. The trench design is supported only by a workshop reference [9]; no measured breakdown voltage, no pixel-isolation data, and no post-irradiation results are shown. Because the entire scenario fails if the sensor cannot hold the bias needed for bulk multiplication, this is a second load-bearing gap rather than a cosmetic detail.
minor comments (6)
  1. [Section 3, Eq. (1)] Equation (1) as written, N(x) = ∫ N(o) e^{α(E)x} dx, is dimensionally inconsistent and not the correct integral form for avalanche gain; the intended expression is N(x) = N0 exp(∫_0^x α(E(x')) dx') or equivalently dN/dx = αN. Please correct the notation.
  2. [Section 1, Fig. 2] For a_o = 1 Ų and fluence 1×10^16 cm^-2, the model gives exp(-1) ≈ 0.37, not the 30% stated in the text; please either quote the correct value or explain the fit or approximation used for the curve.
  3. [Section 4, Eq. (2)] The sentence defining Eq. (2) contains typos and a garbled clause (“andc”, “the initial (after a fluence φ) acceptor density”), which makes the definition of c and the acceptor densities hard to parse.
  4. [Abstract] The abstract states “above 1·10^16 n_eq/cm^2” while the title and Section 5 specify 5–10×10^16 n_eq/cm^2; these ranges should be harmonized.
  5. [Section 4] The statement that impact ionization is “not quenched” up to 3×10^15 n_eq/cm^2 is given without a specific citation; please add the reference to the measurement or measurements that support this claim.
  6. [Figures 5 and 7] The captions refer to tones of red indicating doping levels, but the grayscale rendering in the posted version makes these levels hard to distinguish; explicit labels or a colormap legend would improve clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the proposal is a forward extrapolation from independently measured irradiation data, not a prediction that reduces to its inputs.

full rationale

The paper's derivation chain is a forward extrapolation. The target claim is that a 25-50 micron thin LGAD can deliver more than 1 fC at fluences of 5-10x10^16 n_eq/cm2 via gain-layer multiplication at low fluence and bulk multiplication at high fluence. None of the target quantities are used to set the model inputs. The acceptor-density evolution in Eq. (2) is taken from prior irradiation studies cited as [6,8], and the parameters geff and c are not fitted to the 5-10x10^16 n_eq/cm2 prediction. The empirical statement that impact ionization is not quenched up to 3x10^15 n_eq/cm2 is presented as a measured result, not as a consequence of the paper's own model. The Poisson saturation argument with a 1 Angstrom-squared target is illustrative and does not feed the signal prediction in a way that would make the conclusion equivalent to its assumptions. Although the authors cite their own prior work, that work provides independent measurement-based inputs rather than a self-referential uniqueness theorem or ansatz. The conclusion's 'will assure' is stronger than the body's 'looks possible,' but this is an extrapolation risk, not circularity. No equation, fitted parameter, or self-citation reduces the central claim to its inputs by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The proposal relies on known radiation-damage formulas and a few hand-picked parameter values rather than new physical entities. The load-bearing assumptions are extrapolations to fluences beyond current measurements, especially the continuation of impact ionization and the ability to hold 500 V bias.

free parameters (3)
  • ao (damage cluster area) = 1 square Angstrom
    Hand-picked in Section 1 as the area of a typical damage cluster for the Poisson saturation estimate; no data fit or uncertainty is given.
  • geff (effective acceptor creation coefficient) = 0.02 cm^-1 standard, 0.01 cm^-1 saturated
    Used in Eq. (2) and Figure 3 to estimate depletion voltage at 1e17 n_eq/cm2; taken from prior irradiation measurements, but the value is uncertain and the paper brackets it rather than fits it.
  • electron and hole carrier lifetimes after 1e16 n_eq/cm2 = 0.2 ns electrons, 0.15 ns holes
    Assumed in Section 2 to estimate roughly 80% charge collection efficiency in a 50 micrometer sensor; values are predictions from prior irradiation studies, not fitted here.
assumptions (5)
  • domain assumption Radiation damage parametrization NA(phi) = geff phi + NA(0) exp(-c phi) remains valid at high fluence.
    Eq. (2) is taken from references [6,8] and is used throughout; its behavior at fluences above 1e16, particularly whether geff saturates, is not established.
  • domain assumption The first 50 micrometers near the n-p junction maintain a linear electric field up to 1e16 n_eq/cm2.
    Cited to reference [1] in Section 2; this underlies the claim that thin sensors can be over-depleted and operated stably.
  • domain assumption Impact ionization is not quenched at fluences up to 5 to 10e16 n_eq/cm2.
    Section 4 cites evidence only up to 3e15 n_eq/cm2 and extrapolates over more than a decade of fluence; the paper itself flags this as an open R&D question.
  • ad hoc to paper Damage saturation can be modeled by independent Poisson hits on clusters of area 1 square Angstrom.
    Section 1 introduces a simplified 2-dimensional model with ao = 1 square Angstrom; the paper acknowledges that the actual cluster overlap calculation is beyond its scope.
  • domain assumption Thin sensors can be biased near 500 V without breakdown after irradiation.
    Stated as key in the abstract and Section 5; existing measurements show sensors can hold high bias, but breakdown risk at very high fluence and high field is not demonstrated.

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Cite this review

Pith. "Pith review of Tracking particles at fluences 5-10 $\cdot$1E16 $n_{eq}$/cm$^2$." pith.science (2026). https://pith.science/paper/H3RF2HGC

@misc{pith2026190811605,
  author       = {Pith},
  title        = {Pith review of: Tracking particles at fluences 5-10 $\cdot$1E16 $n_eq$/cm$^2$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H3RF2HGC}},
  note         = {Machine review of arXiv:1908.11605}
}
abstract

This paper presents the possibility of using very thin Low Gain Avalanche Diodes (LGAD) ($25 - 50\mu$m thick) as tracking detector at future hadron colliders, where particle fluence will be above $10^{16}\; n_{eq}/cm^2$. In the present design, silicon sensors at the High-Luminosity LHC will be 100- 200 $\mu$m thick, generating, before irradiation, signals of 1-2 fC. This contribution shows how very thin LGAD can provide signals of the same magnitude via the interplay of gain in the gain layer and gain in the bulk up to fluences above $10^{16}\; n_{eq}/cm^2$: up to fluences of 0.1-0.3$\cdot 10^{16}\; n_{eq}/cm^2$, thin LGADs maintain a gain of $\sim$ 5-10 while at higher fluences the increased bias voltage will trigger the onset of multiplication in the bulk, providing the same gain as previously obtained in the gain layer. Key to this idea is the possibility of a reliable, high-density LGAD design able to hold large bias voltages ($\sim$ 500V).

Figures

Figures reproduced from arXiv: 1908.11605 by the authors.

Figure 1
Figure 1. Spatial distribution of the damaged produced by a 1 MeV neutron in Silicon. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Probability as a function of particle fluence of hitting a square of 1 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Depletion voltage after a fluence of 1 · 1017 neq/cm2 as a function of sensor thickness assuming a standard g = 0.02 or a saturated g = 0.01 value of the acceptor creation coefficient. as predicted to be after a fluence of ∼ 1 · 1016 neq/cm2 , charge collection efficiency in a 50 µm thick sensor is still almost 80%. Regardless of the advantages listed above, thin sensors (20 - 30 µm) are not suitable for operation s… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Thin sensors with internal gain and 3D sensors manage to break the proportionality between [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 5
Figure 5. Figure 5: The picture shows the electric fields of 3 different sensors: high resistivity, low resistivity and [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: Interplay of the scattering length λ and the mean path needed for impact ionization α(E)−1 . 6 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 7
Figure 7. Figure 7: The picture shows the electric fields of a thin LGAD when (i) new , (ii) after a fluence of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]
Figure 8
Figure 8. Figure 8: Left side: In the current LGAD design, the gain is terminated using junction termination [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Sketch of the proposed sensor for particle tracking at very high fluences. [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

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Reference graph

Works this paper leans on

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