Source of Internal Crosstalk in Silicon Photomultipliers

A. de St Croix; F. Reti\`ere; H. Lewis; L. Wang

REVIEW 2 major objections 4 minor 22 references

Source of Internal Crosstalk in Silicon Photomultipliers

T0 review · 2 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Measuring which carriers start SiPM crosstalk avalanches reveals surface reflections as a major path.

desk verdict A genuinely useful new decomposition of SiPM crosstalk into electron- and hole-triggered components, but the untested voltage-independence assumption in the model could shift the inferred fractions. read the letter →

arxiv 2509.05450 v2 pith:LZJ73VPN submitted 2025-09-05 physics.ins-det hep-ex

L. Wang , H. Lewis , F. Retière , A. de St Croix This is my paper · ORCID

classification physics.ins-dethep-ex

keywords siliconphotomultiplierinternalcrosstalkdirectdelayedavalanchetriggeringprobabilityovervoltagemitigationp-on-nSiPM

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 asks where the secondary photons that cause internal crosstalk in silicon photomultipliers are absorbed, and which type of charge carrier starts the resulting noise avalanche. It shows experimentally that in two p-on-n SiPMs, roughly nine out of ten crosstalk avalanches are initiated by holes, meaning the photons are absorbed in n-doped bulk or substrate regions; the remaining electron-initiated share is larger than geometry alone would suggest. The authors argue that this excess electron component is the signature of secondary photons reflecting off the device surface into neighboring pixels, a path that survives even in a device with metallized trenches that block direct optical transmission. They also measure, for the first time in a p-on-n SiPM, the hole avalanche-triggering probability directly from delayed-crosstalk rates. If the method holds, it gives device developers a diagnostic to identify and suppress the dominant crosstalk path in new SiPM designs.

What carries the argument

The central object is the reduced internal crosstalk λ*, defined as the mean number of crosstalk avalanches per primary pulse divided by charge gain, and modeled as α·P_e(V) + β·P_h(V). Since electron and hole avalanche triggering probabilities have markedly different overvoltage dependencies — P_e saturates quickly, P_h rises slowly — the shape of λ*(V) reveals which carrier starts the avalanches, with α and β proportional to photon absorption in the p and n regions. Delayed crosstalk supplies a direct experimental measure of P_h, because delayed events are almost entirely hole-triggered once electrons drift to the junction in under 10 ps.

What would settle it

Measure λ* versus overvoltage over a wider range, or on a device whose depletion width is known to change, and check whether the fit yields constant α and β. A systematic drift of the fitted coefficients with voltage would mean the inferred carrier mix is an artifact; alternatively, inject photons at known depths using two-photon absorption to measure P_e and P_h directly and re-fit the same data.

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Extended reading notes

Core claim

The paper's central claim is that internal crosstalk in both tested SiPMs is dominated by hole-initiated avalanches — 89±4% for the FBK VUV-HD3 and 92.6±5.3% for the Hamamatsu VUV4 — but that the electron-initiated fraction is too large to be explained by direct transmission through trenches or simple volume ratios. The authors model the reduced crosstalk λ* = λ_iCT/gain as a linear combination α·P_e(V) + β·P_h(V), where P_e and P_h are the measured or modeled avalanche triggering probabilities for electrons and holes, and α and β reflect the fractions of secondary photons absorbed in p-type and n-type regions. Fitting this form to data over 1–10 V of overvoltage yields the carrier mix. Beca

Load-bearing premise

The analysis assumes the junction volume stays fixed as overvoltage changes, so α and β remain constant; if the depletion region widens with voltage, the inferred electron/hole split would be biased.

Editorial extensions

If this is right

Crosstalk in p-on-n SiPMs is mostly hole-triggered because secondary photons are absorbed predominantly in the n-type bulk or substrate, not in the p-implant.
Even with metallized trenches blocking direct optical transmission, surface reflections can generate a substantial electron-triggered crosstalk component (11±4% in the FBK device; 36±26% of direct crosstalk in the HPK device).
Delayed crosstalk is a purely hole-triggered process and can be used to measure the hole avalanche-triggering probability directly, removing a model dependence for this device type.
Designing passivation layers or anti-reflection coatings to minimize surface reflections, and operating at lower overvoltage to suppress P_h/P_e, are concrete ways to reduce crosstalk in future devices.
The method can be generalized to other SiPM structures, and would become fully model-independent if two-photon absorption injection allowed direct measurement of P_e and P_h at arbitrary depths.

Reading between the lines

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

The same decomposition could be applied to backside-illuminated SiPMs, where the optical paths differ and surface reflections may contribute an even larger share of crosstalk.
If the junction volume actually widens with overvoltage, the fitted α and β would drift with voltage; fitting over a wider overvoltage range and checking stability would reveal how much this biases the inferred carrier mix.
The measured electron/hole ratio depends on overvoltage because P_e saturates faster than P_h, so operating at lower overvoltage may suppress reflection-driven crosstalk more than bulk-driven crosstalk — a prediction that could be tested by repeating the analysis at several fixed voltages.
Because the authors find no significant temperature dependence over -39°C to -110°C, room-temperature operation might behave differently if thermally activated absorption or trapping alters the secondary-photon paths; this is an open extension, not a claim of the paper.

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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

I'll get to the point: the paper's real contribution is a method for decomposing internal crosstalk into electron- and hole-initiated avalanches, and it gives the first extraction of the hole avalanche triggering probability in a p-on-n SiPM from delayed-crosstalk data. That is new and useful. The measurements are careful, the temperature and overvoltage trends are clean, and the DeCT/DiCT separation using the first derivative of the waveform is a nice practical step. The cross-check between the DeCT-derived Vh (18.9±3.0) and the companion paper's value (16.62±1.2) gives some independent grounding, which is worth noting. The soft spot is exactly where the reader's stress test points: Eq. 4 assumes the junction volume is independent of overvoltage, so the absorption probabilities PA,p and PA,n are constant. That assumption is stated but not tested. As overvoltage increases, the depletion region widens, mainly into the n-side, so β (the hole-triggered weight) likely changes with V. If it changes, the fit will absorb that V-dependence into the Pe and Ph shapes, biasing the extracted α and β. The quoted uncertainties (e.g., ±4% for FBK) are tight enough that even a modest effect could move the interpretation. This is a real flaw, but it is not a load-bearing break unless the effect is large. The paper should either justify the assumption with device modeling or show a sensitivity test. The other caveat is the HPK DiCT electron fraction: 36±26% is so uncertain that the claim about surface reflections in that device is weak. The FBK result (11±4%) is more solid, and the overall hole dominance is likely correct, but the surface-reflection interpretation rests more on the FBK excess electron component plus the structural argument about metallized trenches than on the HPK DiCT fit. Who is this for? Anyone working on SiPM characterization or crosstalk mitigation in detector physics will get value from the method and the data. The paper deserves a serious referee; the central idea is worth pursuing even if the voltage-independence assumption needs more work. I'd send it to review and ask the authors to address that assumption directly.

Referee Report

2 major / 4 minor

Summary. The paper reports measurements of internal crosstalk (iCT) probability as a function of overvoltage and temperature for two p-on-n SiPMs, the FBK VUV-HD3 and the Hamamatsu VUV4. The central methodological contribution is a decomposition of the reduced crosstalk rate λ* = αP_e(V) + βP_h(V), where P_e and P_h are electron- and hole-initiated avalanche triggering probabilities, allowing the electron- versus hole-triggered fractions of crosstalk to be extracted. The authors find that in both devices roughly 90% of crosstalk is hole-triggered and use the smaller electron-triggered component to argue that optical reflections from the device surface are a significant crosstalk source. For the HPK device, delayed crosstalk is used to directly extract P_h(V), a useful new measurement.

Significance. If the analysis is robust, the paper offers a practical diagnostic for SiPM development, particularly for backside-illuminated devices and for evaluating crosstalk mitigation structures. The experimental P_iCT(V) data are clean and the use of DeCT to measure P_h in a p-on-n device is a valuable, independent cross-check against companion modelling. However, the quantitative conclusions rest on an untested assumption about the voltage independence of the junction volume and on a fit whose electron-triggered fraction for HPK DiCT is statistically indistinguishable from zero. The diagnostic concept is promising, but the evidence for the surface-reflection mechanism in the HPK device is currently weaker than the text claims.

major comments (2)

[Section II, Eqs. (3)-(4)] The decomposition λ* = αP_e(V) + βP_h(V) assumes that 'the junction volume is independent of V' so that PA,p and PA,n, the photon absorption probabilities in the p- and n-regions, are constant. If the depletion region widens with overvoltage, α and β are voltage-dependent and the fitted constants will be biased, because P_e and P_h have different functional forms. The paper states this assumption but provides neither a physics justification nor a sensitivity test. Given the small quoted uncertainties (e.g., ±4% for FBK), even a modest voltage dependence of PA could shift the inferred carrier fractions and alter the surface-reflection conclusion. Please provide a quantitative estimate of the depletion-width variation over the measured overvoltage range, or a sensitivity analysis using the same data.
[Section IV, Table I and Fig. 7] The HPK DiCT decomposition yields α = 36±26% (equivalently 37.2±26.8% in Table I). This is not statistically distinguishable from zero. Yet the Discussion section states that 'the significant number of electron-driven events in the VUV4' supports surface reflections as an important crosstalk path. That conclusion is not supported by the HPK data alone; it can only be claimed for the FBK device, where the electron fraction is 11±4%. Please revise the claim or provide additional constraints (e.g., a joint fit with the DeCT component or a prior on the expected electron fraction) to make the HPK result meaningful.

minor comments (4)

[Eq. (6)] There is a typographical error: the denominator should be N_{1.5PE}, not N_{0.5PE} as written in the text.
[Introduction] The placeholder '[xx need lidar reference]' should be replaced with a real citation for LIDAR applications.
[Fig. 4 legend] The legend entry 'CoH K, -110 P' appears to be a typo for 'CoHPK, -110'.
[Eq. (7)] The functional form P_{e,h}(V) = 1 - e^{V/V_{e,h}} appears dimensionally unusual. If the intended expression is 1 - exp(-V/V_{e,h}), please correct the notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the carrier-type decomposition is a genuine fit to measured reduced crosstalk using independently obtained triggering-probability curves.

full rationale

The paper's derivation chain is a linear decomposition of the measured reduced crosstalk λ* into a combination of electron and hole avalanche triggering probabilities: λ* = αP_e(V) + βP_h(V) (Eqs. 3-4). The coefficients α and β are fitted to the experimental λ*(V) data shown in Figs. 7-8, not derived from the P_e/P_h curves alone. P_e(V) is an experimental measurement from the companion paper [10] (380-nm illumination in the p-region), and P_h(V) is obtained either from the DeCT trend measured in this paper (HPK VUV4) or from the PDE modelling in [10] (FBK VUV-HD3). These inputs are independent of the fitted α and β; no fitted parameter is renamed as a prediction, and no equation reduces to its own inputs by construction. The self-citation to [10] is load-bearing in the sense that the P_e/P_h curves come from the same group, but [10] is an independent PDE/trigger-probability measurement, not a result of the present crosstalk fit, so it constitutes real evidence rather than circularity. The stated assumption that 'the junction volume is independent of V' is a testable modeling approximation that could bias α and β if false, but it is not a circular step. Similarly, assigning DeCT events to hole-triggered avalanches is a physical assumption based on drift times, not a prediction extracted from the fit. No self-definitional, fitted-input-as-prediction, uniqueness-imported, or ansatz-smuggling pattern is present. Therefore the paper is self-contained for the purpose of circularity analysis, with the caveat that the V-independence of α and β is an assumption to be checked separately.

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

The central model uses two free coefficients α, β per dataset, plus a fitted V_h for the Hamamatsu device. The analysis relies on external measurements of P_e and P_h from a companion paper by the same group, and on an untested assumption that the junction volume does not change with overvoltage.

free parameters (7)

α (FBK iCT, electron-triggered fraction) = 0.11 ± 0.04
Fit coefficient in Eq. 4 applied to FBK VUV-HD3 λ* data; represents fraction of crosstalk avalanches triggered by electrons.
β (FBK iCT, hole-triggered fraction) = 0.89 ± 0.04
Fit coefficient in Eq. 4 for FBK; hole-triggered fraction.
α (HPK iCT, electron-triggered fraction) = 0.0735 ± 0.053
Fit coefficient in Eq. 4 for Hamamatsu VUV4 overall iCT.
β (HPK iCT, hole-triggered fraction) = 0.926 ± 0.053
Fit coefficient for HPK overall iCT.
α (HPK DiCT, electron-triggered fraction) = 0.372 ± 0.268
Fit coefficient for HPK direct crosstalk only.
β (HPK DiCT, hole-triggered fraction) = 0.628 ± 0.268
Fit coefficient for HPK direct crosstalk only.
V_h (HPK) = 18.9 ± 3.0 V
Characteristic voltage in P_h = 1 - exp(-V/V_h), fitted to the DeCT rate trend for the Hamamatsu device.

assumptions (6)

domain assumption Junction volume is independent of overvoltage
Needed so that α and β in Eq. 4 are constants; if the depletion region grows with V, P_A,p and P_A,n vary and the linear decomposition breaks down. Stated in Section II.
domain assumption P_e and P_h follow the empirical form 1-exp(-V/V_e,h)
Adopted as the functional form for avalanche triggering probabilities, citing [18].
domain assumption All delayed crosstalk events are triggered by holes diffusing from the substrate
Used to extract P_h from DeCT rates in Section IV A; electrons are assumed to contribute negligibly to DeCT.
domain assumption P_e data measured in companion paper [10] applies to these devices and overvoltage ranges
The electron triggering probability is not re-measured here; it is taken from reference [10] by the same group.
domain assumption Secondary photon emission Nγ is linear in gain
Assumed to justify dividing by gain in Eq. 3, citing [11], [12].
domain assumption Negligible probability of multiple SPADs firing simultaneously from thermal carriers at low temperature
Used to classify any pulse above 1.5 PE as crosstalk.

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Cite this review

Pith. "Pith review of Source of Internal Crosstalk in Silicon Photomultipliers." pith.science (2026). https://pith.science/paper/LZJ73VPN

@misc{pith2026250905450,
  author       = {Pith},
  title        = {Pith review of: Source of Internal Crosstalk in Silicon Photomultipliers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LZJ73VPN}},
  note         = {Machine review of arXiv:2509.05450}
}

read the original abstract

Silicon Photomultipliers (SiPMs) have been widely adopted for photon detection in next-generation dark matter and neutrino detection experiments. Internal crosstalk, resulting from secondary photons produced during charge avalanches, is a significant noise mechanism in SiPMs and is likely to impact the performance of physics detectors. This work presents experimental data for trends in crosstalk probability with temperature and overvoltage for two different SiPM devices, and demonstrates a novel method for identifying the source mechanisms of crosstalk avalanches. This is done by using measurements of avalanche triggering probabilities for different charge carrier types to identify the device regions in which crosstalk avalanches are produced. This is possible because crosstalk photons absorbed in n-doped regions will produce hole-triggered avalanches, and those absorbed in p-doped regions will produce electron-triggered avalanches. Thus crosstalk probability can be related to device structure to assess the effectiveness of existing crosstalk mitigation methods. We identify optical reflections from the device surface as a significant source of crosstalk, likely to dominate in devices with effective crosstalk mitigation in bulk. Lastly, a diagnostic technique is presented to identify and reduce crosstalk in novel SiPM structures.

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

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M. R. Hampel, A. Fuster, C. Varela, M. Platino, A. Almela, A. Lucero, B. Wundheiler, and A. Etchegoyen, “Optical crosstalk in SiPMs,” Nuclear Instruments and Methods in Physics Research Section A: Accel- erators, Spectrometers, Detectors and Associated Equipment, vol. 976, p. 164262, Oct. 2020

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S. Merzi, S. E. Brunner, A. Gola, A. Inglese, A. Mazzi, G. Paternoster, M. Penna, C. Piemonte, and M. Ruzzarin, “NUV-HD SiPMs with metal- filled trenches,”Journal of Instrumentation, vol. 18, p. P05040, May

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