Color Centers in Crystals
Stokes shift, quantum defect and absorption of colour centres (NV⁻ in diamond, F₂ and F₂⁺ in LiF) from their absorption and emission band maxima, cross-section and density.
Choosing a centre fills its band maxima at room temperature and its absorption cross-section at 532.0 nm. Edit any value for another centre.
Stokes Shift
0.420 eV
3389 cm⁻¹, 135.8 nm
Quantum Defect
19.3 %
1 − λ_abs/λ_em: energy left as heat per photon at unit quantum yield
Zero-Phonon Line
637.5 nm
between the band maxima
Absorption Coefficient α
31.00 cm⁻¹
σN at the cross-section's wavelength
Optical Density
0.6732
αd/ln 10
Transmitted
21.22 %
e^(−αd), no surface reflections
Preset Centres
| Centre | Absorption (nm) | ZPL (nm) | Emission (nm) | Stokes (eV) | σ_a (×10⁻¹⁷ cm²) |
|---|---|---|---|---|---|
| NV⁻ (diamond) | 568.7 | 637.5 | 704.5 | 0.420 | 3.1 at 532.0 nm |
| F₂ (LiF) | 443.0 | — | 678.0 | 0.970 | — |
| F₂⁺ (LiF) | 645.0 | — | 910.0 | 0.560 | — |
Model
ΔE = hc(1/λ_abs − 1/λ_em)
quantum defect = 1 − λ_abs/λ_em
α = σN; OD = αd/ln 10; T = e^(−αd)
The lattice relaxes after absorption, so a centre emits at lower energy than it absorbs: the Stokes shift between the band maxima. In the linear coupling model it is about 2Sħω, with S the Huang–Rhys factor and ħω the phonon energy, but that holds only approximately. Band maxima only; band shapes, their temperature dependence and the quantum yield are not modelled.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Stokes shift ΔE = hc(1/λ_abs − 1/λ_em) between room-temperature band maxima and quantum defect 1 − λ_abs/λ_em; α = σN, T = e^(−αd) without surface reflections. Band shapes, the Huang–Rhys factor (ΔE ≈ 2Sħω only approximately) and quantum yields are not modelled. Only NV⁻ has a cited cross-section (532 nm).
- Doherty M. W., Manson N. B., Delaney P., Jelezko F., Wrachtrup J., Hollenberg L. C. L. (2013). The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45. Table 9: NV⁻ absorption 2.180 eV, ZPL 1.945 eV, emission 1.760 eV (Davies & Hamer 1976). doi:10.1016/j.physrep.2013.02.001
- Wee T.-L. et al. (2007). Two-photon excited fluorescence of nitrogen-vacancy centers in proton-irradiated type Ib diamond. J. Phys. Chem. A 111, 9379–9386. NV⁻ σ = (3.1 ± 0.8)e-17 cm² at 532 nm. doi:10.1021/jp073938o
- Baldacchini G. (2002). Colored LiF: an optical material for all seasons. J. Lumin. 100, 333–343. F₂ 443 → 678 nm and F₂⁺ 645 → 910 nm, as tabulated in Guerrero Perez M. et al., arXiv:2412.21060 (2024), Table I. doi:10.1016/S0022-2313(02)00460-X
- de Jong M., Seijo L., Meijerink A., Rabouw F. T. (2015). Resolving the ambiguity in the relation between Stokes shift and Huang–Rhys parameter. Phys. Chem. Chem. Phys. 17, 16959–16969. doi:10.1039/C5CP02093J