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REVIEW 3 major objections 5 minor 35 references

Defects and acceptor removal in 60Co {\gamma}-irradiated p-type silicon

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Each BiOi defect deactivates two boron acceptors in gamma-irradiated p-type silicon, and the X-defect TSC peak may be the divacancy.

desk verdict Solid, honest increment for radiation-damage modeling: the factor-two BiOi check is direct and credible, the X-defect hint is properly hedged, and the main soft spot is a missing charge-balance sentence. read the letter →

arxiv 2505.20790 v1 pith:UEKBJL3B submitted 2025-05-27 hep-ex cond-mat.mtrl-sci

Anja Himmerlich , Núria Castelló-Mor , Esteban Currás-Rivera , Yana Gurimskaya , Isidre Mateu , Michael Moll , Karol Pawel Peters , Niels Sorgenfrei
show 6 more authors
Moritz Wiehe Andrei Nitescu Ioana Pintilie Eckhart Fretwurst Chuan Liao Jörn Schwandt
This is my paper · ORCID
classification hep-excond-mat.mtrl-sci
keywords acceptorremovalBiOidefectX-defectdivacancyDLTSTSCgammairradiationp-typesilicon
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 in p-type epitaxial silicon diodes exposed to $^{60}$Co gamma rays, the loss of effective doping is close to twice the measured concentration of boron-interstitial--oxygen-interstitial ($\mathrm{B_iO_i}$) defects. That factor of two is the expected signature of acceptor removal by $\mathrm{B_iO_i}$: each complex incorporates one boron atom and neutralizes a second through its donor-type level. The authors also feed defect parameters from DLTS into a TSC simulator and find that the modeled divacancy level reproduces the shoulder of the so-far unidentified X-defect TSC peak. The result turns a macroscopic radiation-degradation effect into a quantitative defect-counting statement and gives a concrete candidate identity for a long-unassigned signal.

What carries the argument

The $\mathrm{B_iO_i}$ complex, a donor-type boron-interstitial/oxygen-interstitial pair, is the load-bearing defect for the acceptor-removal claim: it forms when mobile silicon interstitials kick substitutional boron into an interstitial site, and its positive level in the upper band gap both removes one boron and cancels the negative space charge of a second, giving the 2-to-1 ratio. The second mechanism is a DLTS-to-TSC modeling chain. The pytsc simulator slices the depleted diode into thin layers, computes thermal emission rates from the DLTS-measured activation energies, capture cross sections, and concentrations, and sums the resulting displacement current; with Poole--Frenkel enhancement turned off, the modeled $V_2(0/+)$ level lands next to the $\mathrm{B_iO_i}$ peak and mimics the X-defect shoulder.

What would settle it

A decisive test would be to anneal the irradiated diodes stepwise and compare the decay of the TSC X-defect peak with the decay of the DLTS $V_2(0/+)$ concentration: different annealing temperatures or kinetics would rule out the divacancy assignment, while matching behavior would confirm it.

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Extended reading notes

Core claim

The central claim is a quantitative correlation: the change in effective carrier concentration $\Delta N_{\mathrm{eff}}$ extracted from capacitance--voltage measurements is about twice the $\mathrm{B_iO_i}$ defect concentration measured by DLTS, for both 50 $\Omega$cm and 250 $\Omega$cm epitaxial diodes across doses from 0.1 to 2 MGy. The paper reads this as direct confirmation that each $\mathrm{B_iO_i}$ defect deactivates two boron acceptors, as expected when a mobile silicon interstitial displaces a substitutional boron and the resulting donor level compensates a second acceptor. A second, more tentative claim comes from modeling: when DLTS-derived parameters for the level labeled peak (2), assigned to the single-positive divacancy state $V_2(0/+)$, are inserted into the TSC simulator, the simulated spectrum produces a shoulder beside the $\mathrm{B_iO_i}$ peak that resembles the experimental X-defect. The authors therefore propose, with caution, that the X-defect may be divacancy-related.

Load-bearing premise

The factor-of-two argument assumes that the $\mathrm{B_iO_i}$ defects measured by DLTS are the only significant charged defects changing the effective carrier concentration; if other radiation-induced charged centers contribute comparably, the 2:1 match would be coincidental.

Editorial extensions

If this is right

  • In gamma- and low-energy-electron-irradiated p-type silicon, measuring the $\mathrm{B_iO_i}$ concentration gives a quantitative prediction of acceptor removal: each defect removes two boron acceptors.
  • The 2:1 correlation supports using $\mathrm{B_iO_i}$ concentration, rather than macroscopic doping loss alone, to benchmark radiation damage in detector-grade silicon.
  • If the X-defect is the divacancy, TSC spectra can be used to track divacancy formation in low-fluence irradiations where DLTS filling is difficult.
  • The DLTS-parameter-to-TSC simulation method gives a template for disentangling overlapping TSC peaks by assigning them to specific DLTS-identified levels.

Reading between the lines

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

  • Applying the same factor-of-two test to hadron-irradiated samples would quantify how much cluster-induced charged defects break the simple $\mathrm{B_iO_i}$ accounting; a slope departing from two would measure the cluster contribution.
  • The modeling approach could be inverted: fitting TSC spectra with pytsc might extract DLTS-style parameters for defects that are hard to inject in DLTS, such as the X-defect's temperature-dependent capture.
  • If the X-defect is confirmed as $V_2(0/+)$, its field-dependent peak shift should be reproducible by adding phonon-assisted tunneling to the electric-field enhancement term in the simulator, providing a consistency check.
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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 / 5 minor

Summary. The paper reports DLTS, TSC, and C-V characterization of 60Co gamma-irradiated p-type epitaxial silicon diodes of two resistivities (50 and 250 Ωcm) for doses of 0.1–2 MGy. Four dominant DLTS levels are identified: peak (1) (Ev+0.09 eV, tentatively I2O), peak (2) (Ev+0.19 eV, tentatively V2(0/+)), CiOi, and BiOi. The authors use the DLTS-derived parameters as input to a Python-based TSC simulator (pytsc) and find that the DLTS peak (2) produces a TSC signature resembling the X-defect shoulder, suggesting a divacancy-related origin for the X-defect. In addition, they compare twice the DLTS-measured BiOi concentration with the change in effective carrier concentration Neff from C-V measurements and report a factor-of-two correlation, which they interpret as evidence that each BiOi deactivates two boron acceptors. The X-defect assignment is explicitly hedged as an indication pending further work.

Significance. If the factor-of-two correlation is quantitatively robust, the paper provides a direct experimental link between a microscopically identified defect (BiOi) and the macroscopic acceptor removal effect in gamma-irradiated p-type silicon, extending earlier work on proton-irradiated epitaxial diodes. The comparison is a direct correlation of two measured quantities rather than a fit, so the circularity burden is low. The tentative identification of the TSC X-defect with the divacancy would also be a useful step toward unifying DLTS and TSC defect assignments. The authors are appropriately cautious about the X-defect assignment, which weakens concerns about overreach. However, the central factor-of-two claim currently lacks an explicit uncertainty budget and a full accounting of other charged defects, and the pytsc comparison is presented qualitatively; these gaps need to be addressed before the central claims are fully supported.

major comments (3)
  1. [§3.2, Fig. 6] The central factor-of-two claim is not quantitatively supported as presented. The slopes shown in Fig. 6 are quoted without uncertainties, and no error bars appear on either the DLTS-derived [BiOi] values or the C-V-derived Neff values. The text itself limits the correlation to doses ≥200 kGy without explaining the deviation at lower doses. Please provide a full uncertainty budget, including DLTS concentration uncertainties (from rate-window analysis and pulse-width dependence), C-V geometric and slope uncertainties, and the conversion from dose to fluence, and report the fitted slopes with standard errors. In addition, state explicitly whether the plotted quantity is ΔNeff = Neff,0 − Neff, and how the unirradiated Neff,0 was obtained. With these numbers, the reader can assess whether the ratio is actually consistent with 2.0 within combined uncertainty rather than being an approximate visual coincidence.
  2. [§3.2, §3.3, and charge balance] The factor-of-two interpretation assumes that BiOi is the only radiation-induced defect that contributes significantly to the change in space charge at the C-V measurement temperature. The manuscript assigns charge states only to CiOi (neutral) and BiOi (donor); peak (1) and peak (2) are never included in a charge-balance discussion. For these doping densities at 253 K, V2(0/+) at Ev+0.19 eV and the peak (1) level at Ev+0.09 eV should lie below the Fermi level and therefore be neutral, so the omission may be benign—but the paper needs to say this explicitly. The possible contribution of the VO electron trap observed in TSC should also be addressed. Without such an accounting, the abstract's phrase "perfect consistency" overstates the strength of the evidence for the factor of two.
  3. [§3.3, Fig. 10] The pytsc-based comparison that links DLTS peak (2) to the TSC X-defect is qualitative: the modeled and measured spectra are said to agree in peak position but differ in absolute height, and the X-defect identification rests on visual resemblance of a shoulder. Please provide quantitative criteria—for example, peak temperatures, widths, amplitude ratios, or a residual metric—for judging the match between the modeled V2(0/+) signature and the measured X-defect shoulder. Also state whether the VO level, which appears as an electron trap in the measured TSC spectra, was included in the pytsc simulations, and if not, how its omission affects the comparison in the temperature region of the X-defect and BiOi peaks.
minor comments (5)
  1. [Abstract and §3.2] The abstract claims "perfect consistency" with the factor-of-two model, while the text in §3.2 says the correlation holds "for doses ≥200 kGy." Please harmonize these statements and either justify the low-dose deviation or soften the abstract.
  2. [§2 and Fig. 1 caption] The text states that C-V measurements were performed at a frequency of 10 kHz, but the caption of Fig. 1 states 1 kHz, and §3.2 refers to 1 kHz and 1 MHz for the two sets of Neff values. Please reconcile these frequencies and clarify which frequency was used for each data set in Fig. 6.
  3. [§2, Eq. (1)−(3)] The notation in Eq. (3) is incomplete: the symbol nT(t) and pT(t) are defined verbally but the factor 1/2 in the denominator is not explained, and the meaning of the sum over defects versus the sum over slices is not fully specified. A brief definition of each symbol would improve reproducibility.
  4. [§3.3 and references] The pytsc software is described but no reference, version, or availability statement is given. Since the modeling is a key part of the X-defect argument, please provide a citation or repository link, and state the input parameters (e.g., field profile, Neff) used for the simulations.
  5. [Table 1] The header "resitivity" contains a typo; it should read "resistivity." Also, the introduction-rate units are given per Gy, while doses are quoted in MGy; please make the unit conversion explicit to avoid confusion.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the factor-two correlation is an independent comparison of two measured quantities, and the pytsc forward modeling does not fit the TSC spectra it claims to explain.

full rationale

The paper's central factor-two claim compares DLTS-derived BiOi concentrations with C-V-derived effective carrier concentrations on the same diodes (Fig. 6). Neither quantity is derived from the other, and no equation in the paper forces the slope to be two; the 'about twice' relation is read off the data rather than fitted. The pytsc modeling is a forward calculation: DLTS parameters (activation energy, capture cross section, concentration) are inserted into Eqs. (3)-(5) to synthesize TSC spectra, which are then compared with measured spectra with no adjustment of parameters to match the TSC output. The X-defect assignment is explicitly tentative ('further studies are needed and planned to fully confirm this assignment option') and rests on the literature identification of DLTS peak (2) as V2(0/+), not on a self-referential derivation. Citations [22,23,33] are prior works with overlapping authorship, but they provide corroborating context (proton-irradiated comparisons, X-defect field dependence, 50-Ohm-cm data) rather than the load-bearing step; the present data and independent literature carry the argument. The skeptic's charge-balance concern is a physics-completeness and uncertainty limitation, not circularity: it questions whether unmeasured charged defects spoil the factor-two interpretation, but it does not show that the factor-two comparison reduces by construction to its own inputs. No circular step can be exhibited from the paper's own equations or argument chain.

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

The central comparisons introduce no new ad hoc free constants; defect parameters used in pytsc come from independent DLTS measurements. The main unproven inputs are the BiOi two-acceptor model, the homogeneous defect and constant Neff assumptions, the neglect of Poole-Frenkel enhancement, and the literature-based assignment of DLTS peak (2) to the divacancy.

assumptions (5)
  • domain assumption Acceptor removal in irradiated p-type Si is dominated by BiOi formation, and each BiOi deactivates two boron acceptors.
    Stated in the Introduction and used in Section 3.2 and Fig. 6 to interpret the Neff versus 2*BiOi correlation.
  • domain assumption Gamma irradiation mainly creates point defects rather than clusters, so macroscopic Neff changes can be attributed to point-like defects such as BiOi.
    Stated in Section 1 to justify the direct correlation between point-defect concentrations and device-level Neff.
  • domain assumption pytsc models a one-dimensional homogeneous diode with constant Neff and neglects Poole-Frenkel enhancement (Gamma_PF=1).
    Stated in Section 2 (Eqs. 3 to 5); this shapes the modeled TSC peaks used to identify the X-defect.
  • domain assumption DLTS peak (2) corresponds to the single-positive charge state of the divacancy V2(0/+), based on literature comparison.
    Section 3.2; this literature assignment is inherited by the X-defect to divacancy hypothesis.
  • standard math TSC emission follows standard SRH rate equations with constant capture cross sections.
    Section 2, Eqs. 3 to 5; the pytsc model assumes this emission formalism.

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Cite this review

Pith. "Pith review of Defects and acceptor removal in 60Co {\gamma}-irradiated p-type silicon." pith.science (2026). https://pith.science/paper/UEKBJL3B

@misc{pith2026250520790,
  author       = {Pith},
  title        = {Pith review of: Defects and acceptor removal in 60Co \gamma-irradiated p-type silicon},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UEKBJL3B}},
  note         = {Machine review of arXiv:2505.20790}
}
read the original abstract

Boron-doped silicon detectors used in high radiation environments like the future HL-LHC show a degradation in device performance due to the radiation induced deactivation of the active boron dopant. This effect, known as the so-called Acceptor Removal Effect (ARE), depends on particle type, particle energy and radiation dose and is usually explained by the formation of boroninterstitial - oxygen-interstitial (BiOi) defects that induce a donor-type defect level in the upper part of the Si band gap. Here we present defect characterization studies using Thermally Stimulated Current technique (TSC) and Deep Level Transient Spectroscopy (DLTS) on a set of epitaxially grown p-type silicon diodes of different resistivity, irradiated with 60Co {\gamma}-rays. We used the defect parameters (activation energy, charge carrier capture cross sections and defect concentration) obtained from DLTS experiments for modeling the corresponding TSC spectra, and subsequently compared those with the experimental TSC results. This approach shows that the di-vacancy which is well characterized by DLTS correlates with the so-far unspecified charge emission signal of the X-defect that partially overlaps with the BiOi peak in TSC spectra. Additionally, in order to evaluate the impact of BiOi defect formation on the macroscopic properties of the device, we compared the BiOi defect concentration with the change in the effective carrier concentration Neff obtained from C-V measurements. It shows that the variations in Neff are about twice the changes in the BiOi concentration, which is in perfect consistency with the assumption of boron deactivation by the formation of the BiOi donor in irradiated p-type Si.

Figures

Figures reproduced from arXiv: 2505.20790 by the authors.

Figure 1
Figure 1. C-V measurements of 60Co gamma irradiated EPI diodes of different resistivity (top: 50 Ωcm, bottom: 250 Ωcm). The diodes were measured at - 20o C and with a frequency of 1 kHz. For both sensor types four pronounced defect levels are detected, three hole traps and one electron trap, labeled as (1), (2), CiOi (carbon-intersital - oxygen-interstitial) and BiOi (boron￾interstitial - oxygen-interstitial), respectively. B… view at source ↗
Figure 2
Figure 2. DLTS measurements on 50 Ωcm 60Co γ-irradiated EPI diodes. top: majority carrier injection, bottom: majority and minority carrier injection 6 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. DLTS measurements on 250 Ωcm 60Co γ-irradiated EPI diodes. top: majority carrier injection, bottom: majority and minority carrier injection 7 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Concentrations of the four dominant defects measured by DLTS on 50 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Concentrations of the four dominant defects measured by DLTS on 250 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Evolution of twice the BiOi concentration and the effective doping concentration Neff with irradiation dose for γ-irradiated 50 Ωcm and 250 Ωcm EPI diodes. The values of the slope given in the plot are in units of Gy−1 cm−3 . Details are given in the text. 3.3. Analysi…
Figure 7
Figure 7. Figure 7: was set to a forward bias of + 20 V while the filling temperature Tfill was varied. This was done since the electrical filling of defects like CiOi and X-defect is temperature dependent when injecting with forward bias [14, 22]. Their TSC signal intensity starts to inc…
Figure 8
Figure 8. Figure 8: X-defect measured by TSC on a 2 MGy γ-irradiated EPI diode with 250 Ωcm resistivity. As reverse bias during charge emission values from -50 V to -150 V were set. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Measured TSC spectra of four EPI diodes with 250 [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: Modeled TSC spectra using pytsc of EPI diodes with 250 Ωcm resistivity γ-irradiated in the range of 1 kGy to 2 MGy. The defect parameters for the modeling were taken from the corresponding DLTS measurements (illustrated in [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

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