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arxiv: 2606.11403 · v1 · pith:6ER77OOKnew · submitted 2026-06-09 · ❄️ cond-mat.mtrl-sci

Defect Tolerance in Trigonal Selenium Photovoltaics

Jiban Kangsabanik , Kasper Tolborg , Thomas Olsen , Kristian S. Thygesen This is my paper

Pith reviewed 2026-06-27 12:11 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords defect tolerancetrigonal seleniumphotovoltaicsSRH recombinationmulti-phonon emissionlattice relaxationwide band gap
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0 comments X

The pith

Trigonal selenium is intrinsically defect tolerant because large lattice reorganizations and energy releases suppress recombination despite deep defect levels.

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

The paper uses first-principles calculations to quantify how point defects affect recombination in trigonal selenium. It shows that deep levels exist but nonradiative multi-phonon emission rates stay low due to large lattice changes and energy releases of at least half the band gap per event. Radiative capture rates are also too small to cause observed losses. This establishes that realistic defect concentrations cannot explain efficiency limits through standard SRH processes. A reader would care because it positions t-Se as a material that works well even with imperfections, relevant for tandem and indoor solar cells.

Core claim

Our results suggest that t-Se is intrinsically defect tolerant. Despite the presence of multiple deep levels in the gap, recombination via nonradiative multi-phonon emission processes is strongly suppressed by large lattice reorganizations and large energy releases of at least 0.5 EG per recombination event, while radiative defect-assisted capture also remains too small to account for the observed device losses. Consequently, SRH recombination mediated by realistic concentrations of point defects cannot account for the observed efficiency limitations in selenium photovoltaics.

What carries the argument

First-principles calculations of defect transition levels, lattice relaxation energies, and resulting multi-phonon emission rates across many point defects.

If this is right

  • SRH recombination from point defects does not limit efficiency in t-Se photovoltaics.
  • Trends in lattice relaxation and energy release can guide design of other defect-tolerant wide-band-gap materials.
  • Other loss mechanisms besides defect-mediated SRH must be identified to improve selenium cells.
  • t-Se qualifies as a defect-tolerant absorber for tandem and indoor photovoltaic applications.

Where Pith is reading between the lines

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

  • Materials with similar large relaxation energies around defects may also show suppressed recombination even with gap states.
  • Device studies could test whether surface or interface effects, rather than bulk point defects, dominate losses in t-Se.
  • The approach of checking both radiative and nonradiative rates together could apply to screening other emerging absorbers.

Load-bearing premise

The computed defect levels, relaxation energies, and emission rates match the actual recombination behavior in real trigonal selenium samples.

What would settle it

A measurement showing that lowering point defect density in t-Se devices raises efficiency in proportion to the calculated SRH rates would contradict the claim.

Figures

Figures reproduced from arXiv: 2606.11403 by Jiban Kangsabanik, Kasper Tolborg, Kristian S. Thygesen, Thomas Olsen.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic diagram of possible defects (substitution (D [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a), (b) Charge transition levels for all the intrinsic and extrinsic considered for in t-Se. Here VBM and CBM stands [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a)-(b) One-dimensional configuration coordinate diagrams for the 1 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Photovoltaic device efficiency [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Nonradiative capture coefficients for all the defects are plotted with respect to distance from the band edges [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
read the original abstract

Understanding how point defects fundamentally influence photovoltaic performance remains a central question for emerging wide-band gap absorbers. Trigonal selenium (t-Se) has recently re-emerged as a promising photovoltaic material due to its near-optimal band gap for tandem and indoor applications. Here we quantify defect-assisted Shockley-Read-Hall (SRH) recombination in t-Se using first principles calculations across a large and chemically diverse set of point defects. Our results suggest that t-Se is intrinsically defect tolerant. Despite the presence of multiple deep levels in the gap, recombination via nonradiative multi-phonon emission processes is strongly suppressed by large lattice reorganizations and large energy releases of at least 0.5 EG per recombination event, while radiative defect-assisted capture also remains too small to account for the observed device losses. Consequently, SRH recombination mediated by realistic concentrations of point defects cannot account for the observed efficiency limitations in selenium photovoltaics. We explore trends in both radiative and nonradiative SRH recombination rates across the defect data set, highlighting their complex dependence on defect level position, lattice relaxation, charge state, and doping conditions. These findings establish trigonal selenium as a defect-tolerant wide-band-gap absorber and provide transferable design principles for optimizing next-generation photovoltaic materials for tandem and indoor applications.

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

2 major / 2 minor

Summary. The manuscript uses first-principles defect calculations across a chemically diverse set of point defects in trigonal selenium (t-Se) to quantify defect-assisted SRH recombination. It concludes that t-Se is intrinsically defect tolerant: deep levels exist but nonradiative multi-phonon emission is suppressed by large lattice reorganizations and energy releases ≥ 0.5 E_G, radiative capture is negligible, and realistic defect concentrations cannot explain observed efficiency losses. Trends in radiative and nonradiative rates are analyzed as functions of level position, relaxation, charge state, and doping.

Significance. If the computed rates hold, the work establishes t-Se as a defect-tolerant wide-gap absorber suitable for tandem and indoor PV, supplies transferable design rules based on relaxation and energy-release criteria, and demonstrates the value of surveying many defects rather than a few canonical ones. The absence of fitted parameters and direct derivation from first-principles defect energetics and relaxation energies are strengths.

major comments (2)
  1. [Section describing quantification of defect-assisted SRH recombination (abstract and methods)] The SRH rate model (including the explicit formula linking transition levels, relaxation energies, and multi-phonon emission rates) is not presented with sufficient detail or convergence tests; without these the central claim that computed rates remain too low to explain device losses cannot be evaluated quantitatively.
  2. [Results section on SRH rates and conclusions] No direct comparison is shown between the computed SRH lifetimes (or capture coefficients) and measured carrier lifetimes or device performance metrics in t-Se; this comparison is required to substantiate that point-defect SRH cannot account for observed losses.
minor comments (2)
  1. Notation for charge states and transition levels should be standardized across figures and tables for clarity.
  2. The abstract states 'large energy releases of at least 0.5 E_G'; the precise definition of E_G used and the distribution of values across the defect set should be stated explicitly in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback on our manuscript. We address each of the major comments below and will revise the manuscript accordingly to improve clarity and strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Section describing quantification of defect-assisted SRH recombination (abstract and methods)] The SRH rate model (including the explicit formula linking transition levels, relaxation energies, and multi-phonon emission rates) is not presented with sufficient detail or convergence tests; without these the central claim that computed rates remain too low to explain device losses cannot be evaluated quantitatively.

    Authors: We agree with this assessment. The revised manuscript will include the full SRH rate equations, detailing how transition levels, relaxation energies, and energy releases enter the multi-phonon emission rates. We will also add convergence tests for the key parameters such as supercell size and k-point sampling to allow quantitative evaluation of the computed rates. revision: yes

  2. Referee: [Results section on SRH rates and conclusions] No direct comparison is shown between the computed SRH lifetimes (or capture coefficients) and measured carrier lifetimes or device performance metrics in t-Se; this comparison is required to substantiate that point-defect SRH cannot account for observed losses.

    Authors: We recognize the value of an explicit side-by-side comparison. Although our analysis already demonstrates that even at high defect concentrations the SRH rates are too low to explain the observed efficiency losses, we will add a new subsection or figure in the results that directly compares our computed lifetimes to experimental reports of carrier lifetimes and device metrics in t-Se. This will include estimates of the defect concentrations needed to match experimental losses. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper derives its central claim—that t-Se is intrinsically defect tolerant because computed SRH rates are too low to explain observed losses—directly from first-principles defect calculations of transition levels, relaxation energies, and multi-phonon emission rates across a chemically diverse defect set. No load-bearing step reduces by construction to a fitted parameter, self-referential equation, or self-citation chain; the argument is a standard computational prediction from DFT inputs without renaming known results or smuggling ansatzes. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on standard assumptions of density-functional theory for defect properties; no new entities are postulated and no parameters are fitted to the target recombination rates.

axioms (1)
  • domain assumption Density functional theory accurately predicts defect formation energies, transition levels, and lattice relaxation energies in trigonal selenium.
    Invoked throughout the description of first-principles calculations of point defects and SRH rates.

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Reference graph

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    Single CTL For a defect with one CTL, (1/0), the SRH recombination rate is RSRH = NDC1 nC0 p(np−n 1p1) C1n(n+n 1) +C 0p(p+p 1) = NDC1 nC0 p(np−n 2 i ) C1n(n+n 1) +C 0p(p+p 1) .(S2)

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    Two CTLs For a defect with two CTLs, (1/0|0/−1), the SRH recombination rate becomes RSRH = ND G " C0 nC −1 p (np−n 0p0) C −1p p+C 0nn0 + C0 p C1 n(np−n 1p1) C1nn+C 0p p1 # ,(S3) with G= 1 + C0 p p+C 1 nn1 C1nn+C 0p p1 + C0 nn+C −1 p p0 C −1p p+C 0nn0 .(S4) Similarly, for a defect with CTLs (2/1|1/0), RSRH = ND G " C1 nC0 p(np−n 1p1) C0p p+C 1nn1 + C1 p C2...

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    Three CTLs For a defect with three CTLs, (1/0|0/−1| −1/−2), the SRH recombination rate reads RSRH = ND G " C −1 p C0 p C1 n(npp−n 1p1p) +C 0 nC0 p C1 n(npn0 −n 1p1n0) (C0nn+C −1p p0)(C1nn+C 0p p1) + C0 nC −1 p (np−n 0p0) C0nn+C −1p p0 + C −1 n C −2 p (np−n −1p−1) C −2p p+C −1n n−1 # , (S7) with G= 1 + C −1 p p+C 0 nn0 C0nn+C −1p p0 + C −1 n n+C −2 p p−1 C...

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    (S12) The above expressions provide the working formulas used in the present study for defects with multiple CTLs

    Four CTLs For a defect with four CTLs, (2/1|1/0|0/−1| −1/−2), the SRH recombination rate is RSRH = ND G " C0 p C1 p C2 n(npp−n 2p2p) +C 1 nC1 p C2 n(npn1 −n 2p2n1) (C1nn+C 0p p1)(C2nn+C 1p p2) + C1 nC0 p(np−n 1p1) C1nn+C 0p p1 + C0 nC −1 p (np−n 0p0) C −1p p+C 0nn0 + C0 nC −1 n C −2 p (npn−n −1p−1n) +C −1 p C −1 n C −2 p (npp0 −n −1p−1p0) (C −1p p+C 0nn0)...

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    Kangsabanik and K

    J. Kangsabanik and K. S. Thygesen, Defect-assisted recombination in semiconductors and photovoltaic device parameters from first principles,Journal of the American Chemical Society148, 316–329 (2026)

    2026