The file is a single merged workbook **Book1** with column A as energy (eV) and 15 power columns (5 µW → 100 µW). No separate Si/reference folder exists, so the data is already merged. Suggested fit range: 1.23–1.45 eV.

Per protocol, I'll despike first (mandatory before any fit), then run the Lorentzian power-dependence fit.



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

## Power-dependent PL analysis — Book1 (Lorentzian fits)

All 15 power spectra (5 → 100 µW) were despiked first (130 cosmic-ray spikes removed), then each was fitted with a **Lorentzian** over 1.23–1.45 eV. Every column reached the **HIGH** tier (R² = 0.887–0.984, median 0.981), so no rescue/raw-peak fallbacks were needed.

**Peak position & intensity per power:**

| Power (µW) | xc (eV) | FWHM (meV) | Intensity (a.u.) | R² |
|---|---|---|---|---|
| 5 | 1.3206 | 62.4 | 98.8 | 0.887 |
| 10 | 1.3244 | 64.4 | 189.9 | 0.950 |
| 20 | 1.3278 | 62.7 | 353.8 | 0.968 |
| 30 | 1.3300 | 61.3 | 516.0 | 0.975 |
| 40 | 1.3315 | 59.3 | 694.6 | 0.981 |
| 50 | 1.3328 | 59.0 | 818.3 | 0.981 |
| 60 | 1.3332 | 58.0 | 935.9 | 0.982 |
| 70 | 1.3343 | 57.1 | 1140.4 | 0.983 |
| 80 | 1.3345 | 56.3 | 1264.7 | 0.983 |
| 90 | 1.3351 | 55.3 | 1538.0 | 0.984 |
| 100 | 1.3356 | 54.4 | 1714.6 | 0.984 |

(15 µW = 1.3264 eV / 267.9; 35 µW = 1.3304 eV / 564.8; 45 µW = 1.3318 eV / 738.5 — see CSV for the full set.)

**Allometric fit on intensity (I = a·Pᵇ):**
- $b = 1.0048 \pm 0.0261$, $a = 16.28 \pm 1.81$, R² = 0.995
- Interpretation: **~linear (excitonic)** — intensity scales essentially proportionally to excitation power across the whole range.

**Allometric/trend fit on peak position (xc vs P):**
- A monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), i.e. ≈ 15 meV total, ≈ 5.0 meV per decade of power — consistent with band-filling / band-gap renormalization at higher carrier density.

📥 Full data + fits: [power_fit_results.csv]([file link removed])

RESULT: b = 1.005 ± 0.026