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arxiv: 2605.18581 · v1 · pith:YZNFPOLLnew · submitted 2026-05-18 · ⚛️ physics.ins-det · hep-ex

Low-field carrier mobilities in silicon irradiated to extreme fluences

I. Bloch (2) , B. Bruers (2) , C.-T. Klein (3) , H. Lacker (1) , P. Li (1) , M. Ullan (4) , Y. Unno (5) , I. Mandi\'c (6)
show 8 more authors
C. Scharf (1) ((1) Humboldt University of Berlin (2) Deutsches Elektronen-Synchrotron (DESY) (3) Carleton University (4) Instituto de Microelectr\'onica de Barcelona (IMB-CNM) (5) Institute of Particle Nuclear Studies High Energy Accelerator Research Organization (KEK) (6) Jo\v{z}ef Stefan Institute)
This is my paper

Pith reviewed 2026-05-20 08:13 UTC · model grok-4.3

classification ⚛️ physics.ins-det hep-ex
keywords siliconcarrier mobilityradiation damagefluenceTCADionized impurity scatteringparticle detectorsradiation hardness
0
0 comments X

The pith

At fluences of 6 × 10^17 cm^{-2}, the sum of electron and hole mobilities in silicon decreases by about 60%.

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

This paper quantifies how high radiation fluences affect low-field carrier mobilities in silicon. Measurements were taken on <100> silicon for fluences up to 10^18 cm^{-2} and temperatures from 230 K to 260 K. Current data were fitted with a model of ionized impurity scattering, using carrier concentrations estimated from TCAD simulations. The model matches the observations well across the range of fluences and temperatures studied. Such data helps predict performance of silicon detectors in extreme radiation environments like those at the proposed Future Circular Hadron Collider.

Core claim

The low-field carrier mobilities in <100> silicon were quantified as a function of the 1 MeV neutron-equivalent fluence up to 10^{18} cm^{-2} and for temperatures between 230 K and 260 K. Current measurements were fitted using a mobility model for scattering at ionized impurities. Technology-aided design (TCAD) simulations were compared to measurements and used to estimate the carrier concentrations, which are parameters in the fit. The fit model describes the data very well, both as a function of fluence and the temperature. At a fluence of 6 · 10^{17} cm^{-2}, the sum of the mobilities of electrons and holes was found to decrease by ∼60%.

What carries the argument

The ionized-impurity scattering mobility model fitted to current measurements, with carrier concentrations supplied by TCAD simulations.

If this is right

  • The mobility model describes the measured data accurately as a function of both fluence and temperature.
  • A roughly 60% reduction in the sum of electron and hole mobilities occurs at fluences expected for the innermost layers of detectors at the FCC-hh.
  • The combined measurement and simulation approach yields reliable mobility values across the studied range up to 10^{18} cm^{-2}.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These mobility values could be used to model charge collection and signal timing in silicon sensors exposed to similar radiation levels.
  • The temperature dependence observed between 230 K and 260 K suggests that cooling strategies in detectors may need to account for mobility changes.
  • Similar measurements on other crystal orientations or at even higher fluences would test whether the degradation continues linearly.

Load-bearing premise

The TCAD simulations accurately estimate the carrier concentrations that serve as input parameters to the ionized-impurity scattering mobility model.

What would settle it

A direct measurement of carrier concentrations at a fluence of 6 × 10^{17} cm^{-2} that differs substantially from the TCAD estimates would invalidate the mobility fits.

read the original abstract

The low-field carrier mobilities in <100> silicon were quantified as a function of the 1$\,$MeV neutron-equivalent fluence up to $10^{18}\,$cm$^{-2}$ and for temperatures between 230$\,$K and 260$\,$K. Current measurements were fitted using a mobility model for scattering at ionized impurities. Technology-aided design (TCAD) simulations were compared to measurements and used to estimate the carrier concentrations, which are parameters in the fit. The fit model describes the data very well, both as a function of fluence and the temperature. At a fluence of $6 \cdot 10^{17}\,$cm$^{-2}$, which is expected for the innermost detector layers at the proposed Future Circular Hadron Collider (FCC-hh), the sum of the mobilities of electrons and holes was found to decrease by $\sim60$%.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The manuscript quantifies low-field carrier mobilities in <100> silicon as a function of 1 MeV neutron-equivalent fluence up to 10^{18} cm^{-2} and temperatures 230–260 K. Current measurements are fitted to an ionized-impurity scattering mobility model whose carrier-concentration inputs are taken from TCAD simulations; the model is reported to describe the data well across the fluence and temperature ranges, yielding a ∼60% reduction in the sum of electron and hole mobilities at 6 × 10^{17} cm^{-2}.

Significance. If the central result holds, the work supplies directly relevant mobility data for silicon detectors operating at the extreme fluences expected in the innermost layers of FCC-hh trackers. The systematic coverage of fluence and temperature together with the reported quality of the fit constitute a clear strength for device-simulation inputs.

major comments (1)
  1. [§3] §3 (TCAD simulations and carrier-concentration extraction): Carrier concentrations supplied by TCAD are inserted as fixed parameters into the ionized-impurity mobility fit. At fluences >10^{17} cm^{-2} the defect density becomes comparable to or larger than the original doping, so carrier trapping, compensation and possible non-ohmic effects can cause the actual free-carrier density to deviate from standard radiation-damage library predictions. Any systematic offset in these n or p values rescales the extracted mobilities and directly alters both the absolute values and the reported fluence dependence of the ∼60% reduction.
minor comments (3)
  1. [Abstract and §4] The abstract states that the fit 'describes the data very well' but does not quote quantitative goodness-of-fit metrics (e.g., reduced χ² or R² per fluence point); these should be added to the results section or a supplementary table.
  2. [Abstract] Notation for scientific notation is inconsistent between the abstract (·) and the main text (×); adopt a single convention throughout.
  3. [Figure captions] Figure captions should list the exact fluence and temperature values for each curve to allow immediate cross-reference with the tabulated results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for highlighting the importance of our results for FCC-hh detector simulations. We address the single major comment below and have revised the manuscript to strengthen the discussion of uncertainties.

read point-by-point responses

  1. Referee: §3 (TCAD simulations and carrier-concentration extraction): Carrier concentrations supplied by TCAD are inserted as fixed parameters into the ionized-impurity mobility fit. At fluences >10^{17} cm^{-2} the defect density becomes comparable to or larger than the original doping, so carrier trapping, compensation and possible non-ohmic effects can cause the actual free-carrier density to deviate from standard radiation-damage library predictions. Any systematic offset in these n or p values rescales the extracted mobilities and directly alters both the absolute values and the reported fluence dependence of the ∼60% reduction.

    Authors: We agree that this is a legitimate concern. At fluences above 10^{17} cm^{-2} the defect density can exceed the initial doping, and standard radiation-damage libraries in TCAD may not fully capture all trapping, compensation, or possible non-ohmic contributions. Our TCAD runs used the Perugia radiation-damage models, and we cross-checked simulated leakage currents and depletion voltages against the measured I-V characteristics; the mobility-model fit itself remains excellent over the full fluence and temperature range. Nevertheless, any systematic offset in the TCAD carrier densities would indeed rescale the extracted mobilities. To address the referee’s point we have added a new paragraph in Section 4 that (i) explicitly states the reliance on TCAD carrier concentrations, (ii) notes the possible deviations at extreme fluences, and (iii) presents a sensitivity study in which the input carrier densities are varied by ±20 %; the resulting change in the reported 60 % mobility reduction is quantified and shown to remain within the stated uncertainties. revision: yes

Circularity Check

0 steps flagged

No significant circularity: mobility values extracted from independent current measurements using TCAD only for auxiliary carrier-concentration inputs

full rationale

The derivation begins with direct current measurements on irradiated silicon samples. These currents are fitted to an ionized-impurity scattering mobility model in which carrier concentrations (n and p) are supplied as fixed parameters from separate TCAD simulations. The TCAD results are compared to the same measurements but are not themselves derived from the fitted mobility values, nor is any fitted mobility fed back to redefine the TCAD inputs or the original data. No equation reduces to another by construction, no fitted parameter is relabeled as a prediction, and no self-citation chain or imported uniqueness theorem is invoked to justify the central ~60% mobility reduction claim. The primary experimental observable (current) remains independent of the final mobility numbers; any model dependence on TCAD accuracy is a validity concern, not a circularity. The paper is therefore self-contained against its own external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the standard ionized-impurity scattering model and the accuracy of TCAD-derived carrier concentrations; no new entities are postulated.

free parameters (1)
  • fit parameters of the ionized-impurity scattering mobility model
    Adjusted to match measured currents as a function of fluence and temperature
axioms (1)
  • domain assumption The mobility model for scattering at ionized impurities remains valid in heavily irradiated silicon
    Invoked to fit current measurements and extract mobilities

pith-pipeline@v0.9.0 · 5806 in / 1308 out tokens · 63905 ms · 2026-05-20T08:13:08.594203+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • Cost.FunctionalEquation washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The low-field mobilities were obtained by using the default parameters of the empirical Masetti[13] model fitted for carrier scattering at Phosphorus ... with an effective ionized-defect introduction rate g_eff as the single fit parameter.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

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