The file is a single merged workbook (Book1/Sheet1): column A = energy axis (eV, 1.196–1.606 eV) plus 15 power columns (5 µW → 100 µW). No Si/reference folder exists, so no background subtraction is needed. Suggested fit window is 1.23–1.45 eV.

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



Despiking complete — 130 cosmic-ray spikes removed across all 15 power columns (cleaned data written back). Now running the Lorentzian power-dependence fit over the 1.23–1.45 eV window, which fits each spectrum, extracts intensity + peak position per power, plots both vs power, and performs the allometric (power-law) fit.



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

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

**Pipeline:** inspect → despike (σ=4, 130 spikes removed, written back) → Lorentzian+slope fit per spectrum over **1.23–1.45 eV** → extract intensity & peak position → allometric fit.

All 15 power levels (5–100 µW) converged at **HIGH tier** (R² = 0.887–0.984, median 0.981; SNR 7.6–24.0). No points rejected.

### Per-power extraction (Lorentzian fit)

| Power (µW) | Intensity (a.u.) | 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 → **~linear (excitonic)** regime

**Peak position vs power** — monotonic **blueshift** from 1.3206 → 1.3356 eV (≈ +15 meV total), ≈ 5.0 meV/decade of power, saturating toward high power (typical band-filling / exciton–exciton interaction signature).

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

RESULT: b = 1.0048 ± 0.0261