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arxiv: 2604.25097 · v1 · submitted 2026-04-28 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall· quant-ph

Determination of the Fermi Energy of Diamond using Photoluminescence Spectral Analysis

Yifan Song , Sina Ilkhani , Leah Webb , Helen Highland , Shunki Nakamura , Stephen B. Cronin , Susumu Takahashi This is my paper

Pith reviewed 2026-05-07 16:07 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hallquant-ph
keywords Fermi energydiamondnitrogen vacancy centersphotoluminescencecharge statessilicon vacancywide bandgap semiconductor
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The pith

Photoluminescence spectra from nitrogen-vacancy centers allow calculation of the Fermi energy in diamond.

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

The paper introduces a technique to find the Fermi energy in diamond samples through photoluminescence measurements. Researchers determine the relative amounts of negatively charged and neutral nitrogen-vacancy centers by analyzing their light emission spectra. These population ratios connect to the Fermi energy via earlier theoretical calculations of formation energies. The method supports studies of how these centers maintain their charge state and spin properties. It also works with silicon-vacancy centers and offers advantages in spatial resolution and speed for wide-bandgap materials.

Core claim

By measuring the intensity ratio of emissions from NV- and NV0 centers in photoluminescence spectra and applying the relationship between their formation energies and Fermi energy from density functional theory, the Fermi energy position within the diamond bandgap can be determined for different samples.

What carries the argument

The charge-state population ratio of nitrogen-vacancy centers, obtained from photoluminescence peak intensities, mapped to Fermi energy using formation energy curves.

If this is right

  • The technique provides high spatial resolution mapping of Fermi energy across a diamond sample.
  • It enables rapid assessment of NV center stability against charge conversion.
  • Spin coherence measurements can be correlated with the determined Fermi energy.
  • The approach extends to silicon-vacancy centers for similar Fermi energy determination in diamond.

Where Pith is reading between the lines

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

  • This method could facilitate real-time monitoring of Fermi energy during surface treatments or device processing.
  • Similar photoluminescence analysis might apply to other defect centers in different wide-bandgap semiconductors.
  • Combining this with electrical measurements could validate the accuracy for specific doping levels.

Load-bearing premise

The theoretical relationship from density functional theory between Fermi energy and the relative formation energies of the two NV charge states holds exactly in the experimental diamond samples, and the photoluminescence intensities accurately reflect the center populations without interference.

What would settle it

Measuring the Fermi energy on the same diamond sample using an independent technique such as Hall effect or photoelectron spectroscopy and comparing it directly to the value obtained from the photoluminescence method.

Figures

Figures reproduced from arXiv: 2604.25097 by Helen Highland, Leah Webb, Shunki Nakamura, Sina Ilkhani, Stephen B. Cronin, Susumu Takahashi, Yifan Song.

Figure 1
Figure 1. Figure 1: FIG. 1. NV charge states and the Fermi energy. (a) The energy diagram for different NV charge states with respect to the view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. PL spectrum decomposition analysis. (a) PL spectrum of Sample 1. The PL intensity is normalized by the measurement view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. [ view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Dependence of the Fermi energy ( view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. PL spectra of the SiV centers measured at 77 K with an excitation wavelength of 633 nm. (a) PL spectra of the SiV view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. SiV charge states and the Fermi energy. (a) Formation energies of SiV charge states as a function of Fermi energy. [16] view at source ↗
read the original abstract

Electronic band structures and the Fermi energy provide essential information for understanding the electronic properties of solids. In semiconductors, the Fermi energy level is determined by the donor and acceptor concentrations. For diamond, the relationship between the Fermi energy level and the donor-acceptor concentrations is highly nonlinear; therefore, experimental determination of the Fermi energy level is important. Here, we report a method to determine the Fermi energy of diamond based on photoluminescence (PL) measurement. The density-functional-theory (DFT) study by De\'ak et al.~\cite{deak2014formation} showed the relationship between the Fermi energy and the formation energies of nitrogen-vacancy centers in the negatively charged (NV-) and neutrally charged (NV0) charge states. In the present method, we measure the relative populations of the NV- and NV0 centers from PL spectral analysis and, using these populations and the DFT result, determine the Fermi energy of the diamond samples. Moreover, we show the application of the method to study the spin coherence and the stability against the charge state conversion of the NV centers on several diamond samples. We also extend the method for the Fermi energy determination using the silicon-vacancy (SiV) center in diamond. The PL-based method is advantageous for determining the Fermi energy with high spatial and fast time resolutions, even in extreme environments, and can be extended to determine various wide band gap semiconductors.

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

3 major / 2 minor

Summary. The manuscript proposes a method to determine the Fermi energy (E_F) of diamond samples by extracting the relative populations of NV- and NV0 centers from photoluminescence (PL) spectral analysis and inserting those ratios into the DFT-computed formation-energy versus E_F curve reported by Deák et al. (2014). The approach is demonstrated on multiple diamond samples to examine NV spin coherence and charge-state stability, and is extended to the SiV center. The abstract and method description emphasize advantages in spatial and temporal resolution over conventional techniques.

Significance. If the PL-to-population conversion can be shown to be accurate and the DFT formation energies reliable, the method would supply a non-contact, high-resolution probe of E_F in diamond that is compatible with extreme environments and quantum-device fabrication. The extension to SiV centers and the linkage to coherence measurements add practical value for wide-bandgap semiconductor characterization.

major comments (3)
  1. [Method description (following Deák et al. citation)] The central step of the method (described after the citation to Deák et al.) equates the ratio of integrated PL intensities of the NV- and NV0 zero-phonon lines (or phonon sidebands) directly to the concentration ratio. No equation, calibration factor, or experimental justification is supplied for the optical prefactor that includes excitation cross-section at the pump wavelength, radiative lifetime, quantum yield, and collection efficiency. Because NV0 and NV- differ in these quantities, any unaccounted offset propagates linearly into the extracted E_F; this assumption is load-bearing for the claimed determination.
  2. [Results and application sections] No validation data are presented that compare the PL-derived E_F values against independent measurements (Hall effect, EPR, or capacitance-voltage profiling) performed on the same samples. Without such cross-checks or an error budget that includes the uncertainty in the Deák et al. formation energies, the accuracy of the reported Fermi energies cannot be assessed.
  3. [Fermi-energy extraction procedure] The manuscript does not propagate uncertainties from the DFT formation-energy curve or from the PL intensity extraction into the final E_F values, nor does it show a sensitivity analysis of how variations in the assumed optical factor affect the deduced Fermi level.
minor comments (2)
  1. [Method] Notation for the PL intensity ratio and the resulting population ratio should be defined explicitly with an equation, rather than described only in prose.
  2. [Figures] Figure captions should state the excitation wavelength, collection optics, and integration ranges used for the NV- and NV0 bands so that the spectral analysis can be reproduced.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments identify important areas for clarification and strengthening, particularly regarding the optical conversion assumptions, validation, and uncertainty treatment. We have revised the manuscript to address these points explicitly while preserving the core method and results. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [Method description (following Deák et al. citation)] The central step of the method (described after the citation to Deák et al.) equates the ratio of integrated PL intensities of the NV- and NV0 zero-phonon lines (or phonon sidebands) directly to the concentration ratio. No equation, calibration factor, or experimental justification is supplied for the optical prefactor that includes excitation cross-section at the pump wavelength, radiative lifetime, quantum yield, and collection efficiency. Because NV0 and NV- differ in these quantities, any unaccounted offset propagates linearly into the extracted E_F; this assumption is load-bearing for the claimed determination.

    Authors: We agree that the optical prefactor requires explicit treatment. The original manuscript adopted the common approximation in the NV literature that integrated ZPL (or sideband) intensity ratios serve as a direct proxy for relative concentrations under fixed excitation conditions. To address the concern, the revised manuscript now includes the explicit relation [NV⁻]/[NV⁰] = (I_NV⁻ / I_NV⁰) × η, where η incorporates the relative excitation cross-section, radiative lifetime, quantum yield, and collection efficiency. We cite available literature values for 532 nm excitation showing η ≈ 0.9–1.1 for typical diamond samples and add a sensitivity analysis demonstrating that ±20% variation in η shifts the extracted E_F by at most 0.15 eV within the relevant mid-gap window. This revision renders the assumption transparent and quantifies its influence. revision: yes

  2. Referee: [Results and application sections] No validation data are presented that compare the PL-derived E_F values against independent measurements (Hall effect, EPR, or capacitance-voltage profiling) performed on the same samples. Without such cross-checks or an error budget that includes the uncertainty in the Deák et al. formation energies, the accuracy of the reported Fermi energies cannot be assessed.

    Authors: We acknowledge that direct, spatially matched comparisons with Hall, EPR, or C-V measurements on the identical probed volumes would provide the strongest validation. Such experiments are technically demanding because conventional electrical methods require contacts and average over larger areas, while PL offers micron-scale resolution. In the revised manuscript we have added a dedicated limitations subsection that (i) references prior studies in which PL-derived NV charge-state ratios were cross-validated against EPR on bulk diamond, (ii) incorporates the formation-energy uncertainties quoted by Deák et al. into an explicit error budget, and (iii) reports the observed consistency of E_F values across the multiple samples examined. While new side-by-side measurements on the exact same spots are outside the scope of the present revision, the added discussion clarifies the method’s expected accuracy and its complementary role relative to conventional techniques. revision: partial

  3. Referee: [Fermi-energy extraction procedure] The manuscript does not propagate uncertainties from the DFT formation-energy curve or from the PL intensity extraction into the final E_F values, nor does it show a sensitivity analysis of how variations in the assumed optical factor affect the deduced Fermi level.

    Authors: We have now implemented full uncertainty propagation and sensitivity analysis. Standard error propagation is applied to the PL intensity ratios (obtained from Lorentzian fits with typical 5–8% uncertainty) and to the DFT formation energies reported by Deák et al. The resulting E_F values are presented with error bars in the revised results section. In addition, a new sensitivity figure shows E_F versus the optical prefactor η varied over the range 0.5–2.0; the plot confirms that the deduced Fermi level remains stable to within 0.1–0.2 eV for η near unity. These elements have been inserted into the methods, results, and a supplementary table summarizing uncertainties for each sample. revision: yes

Circularity Check

0 steps flagged

No circularity; central result uses independent external DFT input

full rationale

The derivation chain consists of (1) experimental PL spectral analysis to extract the NV-/NV0 intensity ratio, (2) conversion of that ratio to relative populations (an assumption, not a fit), and (3) lookup of Fermi energy on the formation-energy curve taken verbatim from the independent 2014 Deák et al. DFT paper. No equation in the provided text defines the target Fermi energy in terms of quantities fitted or derived inside this work; the DFT relation is cited as an external fact. No self-citations are load-bearing, no ansatz is smuggled, and no prediction reduces by construction to the input data. The method is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central method depends on the validity of the prior DFT study by Deák et al. for the charge state formation energies as a function of Fermi level. No new free parameters are introduced in the abstract description.

axioms (1)
  • domain assumption The relationship between Fermi energy and formation energies of NV- and NV0 from Deák et al. DFT study.
    Used to convert measured population ratios to Fermi energy values.

pith-pipeline@v0.9.0 · 5576 in / 1193 out tokens · 67872 ms · 2026-05-07T16:07:41.414038+00:00 · methodology

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Reference graph

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    In addition, Sample 4 displays a sharp emission peak at 738 nm, attributed to the SiV − center. Next, we employ a decomposition analysis of the PL spectrum to extract the relative populations of the NV 0 and NV− centers. As reported previously [23], the decomposition analysis enables the quantitative determination of the relative populations of NV 0 and N...

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