I have the structure: one workbook (`Book1`) with the energy axis in column A and one already-merged spectrum per power (5–100 µW, columns 1–15). Suggested fit range is 1.23–1.45 eV. No Si/reference folder present, so no background subtraction is needed.

First, mandatory despiking before any fit:



Despiking removed 130 cosmic-ray spikes across all 15 power columns; cleaned data written back. The main exciton sits near ~1.32 eV, well inside the 1.23–1.45 eV window.

Now running the Lorentzian power-dependence analysis (Lorentzian fit on every spectrum → extract intensity + xc per power → allometric fits):



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

All 15 merged power spectra (5–100 µW) were despiked (130 cosmic-ray spikes removed) and fitted with a **Lorentzian** profile over 1.23–1.45 eV. Every fit converged at HIGH quality (R² = 0.887–0.984, median 0.981).

**Extracted per power** (Lorentzian):

| 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 (left = intensity, right = peak position):**

- **Intensity** — $I = a\,P^{b}$: $a = 16.28 \pm 1.81$, $b = 1.0048 \pm 0.0261$, $R^2 = 0.995$ (n = 15). Essentially **linear** ($b \approx 1$) → excitonic, no saturation or Auger quenching across 5–100 µW.
- **Peak position** — $x_c = a'\,P^{b'}$: saturating power-law (blueshift) from 1.3206 eV (5 µW) to 1.3356 eV (100 µW); the server characterizes the trend as **+4.99 meV per decade** of power (equivalent allometric exponent $b' \approx 0.0016$). FWHM narrows 62.4 → 54.4 meV with increasing power.

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

RESULT: b = 1.0048 ± 0.0261