The file is a single workbook (`Book1`) with all 15 power levels (5–100 µW) already as columns against an energy axis (eV). Nothing to merge or subtract — the spectra are already consolidated. Suggested fit window: **1.23–1.45 eV**.

Pipeline: despike (mandatory) → Lorentzian fit per power → extract intensity & xc → allometric fit. Starting with cosmic-ray removal.



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

## Pipeline executed
1. **Despike** (σ=4): removed 130 cosmic-ray spikes across all 15 powers, written back.
2. **Lorentzian fit** on every spectrum (window 1.23–1.45 eV) → extracted peak intensity and center *xc* per power.
3. **Allometric fit** $I = a\cdot P^{b}$ on the intensity panel + trend fit on the *xc* panel.

All 15 spectra converged in the **HIGH tier** (R² = 0.887–0.984, median 0.981; SNR 7.6–24). No Si reference folder existed, so no background subtraction was applied.

## 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 fits

**Intensity vs power** — $I = a\cdot P^{b}$:
- $a = 16.28 \pm 1.81$
- **$b = 1.0048 \pm 0.0261$**, R² = 0.995
- Interpretation: essentially **linear** ($b \approx 1$) → excitonic regime, no saturation/Auger nonlinearity over 5–100 µW.

**Peak position vs power** — monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), a total shift of ~15 meV (~5.0 meV per decade of power); fitted trend overlaid on the right panel.

📥 Full per-point data: [power_fit_results.csv]([file link removed])

The reported exponent is the intensity allometric coefficient (the standard PL power-law exponent).

RESULT: b = 1.0048 ± 0.0261