The file is already merged — a single workbook **Book1** with 15 power columns (5→100 µW) and an energy axis in eV (range 1.196–1.606 eV). Suggested fit window: **1.23–1.45 eV**.

Now running the validated pipeline: despike (mandatory before any fit), then the Lorentzian-based power-law analysis.



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

## Pipeline
1. **Merged spectra** — file already contained one workbook (`Book1`) with 15 power columns (5–100 µW), energy axis in eV.
2. **Despike** — removed **130 cosmic-ray spikes** (σ=4) before fitting.
3. **Lorentzian fit** on all 15 spectra in the 1.23–1.45 eV window → all converged to **HIGH** quality (R² = 0.887–0.984).
4. **Allometric fit** ($I = a\cdot P^{b}$) on the intensity panel; trend fit on the peak-position panel.

## Per-power results (Lorentzian fit)

| Power (µW) | Intensity (counts) | $x_c$ (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. $b \approx 1$ → intensity scales **linearly** with power (unsaturated, excitonic regime; no visible Auger/saturation up to 100 µW).
- **Peak position vs power**: monotonic **blueshift** from 1.3206 → 1.3356 eV (+15 meV), fitted trend slope ≈ **5.0 meV/decade**. (The position shift is a saturating blueshift, so it's reported as a log-slope rather than a strict $x_c = a\cdot P^{b}$, since $x_c$ does not extrapolate to zero.)

📥 **Full results:** [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261