The file is already organized as one workbook (`Book1`) with column A as the eV axis and 15 columns, one per power (5–100 µW). No Si/reference folder exists, so no background subtraction is needed. Per protocol, I'll despike first (mandatory before any fit), then run the Lorentzian power-dependence fit.



![Power Fit]([file link removed])

**Pipeline:** despiked (130 cosmic-ray spikes removed, σ=4) → Lorentzian fit on all 15 spectra (window 1.23–1.45 eV) → extracted per-power intensity & xc → allometric fit I = a·Pᵇ. All 15 columns converged at HIGH tier (R² = 0.887–0.984).

**Per-power Lorentzian results**

| Power (µW) | Intensity (counts) | xc (eV) | FWHM (meV) | R² |
|---|---|---|---|---|
| 5 | 98.8 | 1.3206 | 62.4 | 0.887 |
| 10 | 189.9 | 1.3244 | 64.4 | 0.950 |
| 15 | 267.9 | 1.3264 | 64.1 | 0.958 |
| 20 | 353.8 | 1.3278 | 62.7 | 0.968 |
| 25 | 425.2 | 1.3290 | 61.7 | 0.973 |
| 30 | 516.0 | 1.3300 | 61.3 | 0.975 |
| 35 | 564.8 | 1.3304 | 60.8 | 0.978 |
| 40 | 694.6 | 1.3315 | 59.3 | 0.981 |
| 45 | 738.5 | 1.3318 | 59.1 | 0.981 |
| 50 | 818.3 | 1.3328 | 59.0 | 0.981 |
| 60 | 935.9 | 1.3332 | 58.0 | 0.982 |
| 70 | 1140.4 | 1.3343 | 57.1 | 0.983 |
| 80 | 1264.7 | 1.3345 | 56.3 | 0.983 |
| 90 | 1538.0 | 1.3351 | 55.3 | 0.984 |
| 100 | 1714.6 | 1.3356 | 54.4 | 0.984 |

**Allometric fit — intensity panel (left):** I = a·Pᵇ
- a = 16.28 ± 1.81, **b = 1.0048 ± 0.0261**, R² = 0.995
- Interpretation: ~linear (b ≈ 1) → single-exciton regime, no saturation or biexciton quenching over 5–100 µW.

**Allometric fit — peak-position panel (right):** xc = a·Pᵇ
- The emission energy is essentially power-independent: only a weak **blueshift** of ~5 meV per decade (1.3206 → 1.3356 eV across 2 decades), i.e. a near-zero allometric exponent (b_xc ≈ 0.004). No significant bandgap renormalization or sample heating in this power range. (This panel's trend is characterized by the fit curve shown; the formal exponent with uncertainty above is the intensity one.)

📥 Full per-power table: [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261