File inspected. Key findings:
- **Single workbook** `Book1`/`Sheet1` — all 15 power spectra already merged as columns (5→100 µW), X-axis in **eV**.
- No separate Si/reference folder present → no background subtraction step; `power_fit` handles residual baseline internally via its slope term.
- Suggested fit range: **1.23–1.45 eV** (dominant peak).

Data is already in one merged workbook, so I'll skip merge and go straight to despike (mandatory before any fit).






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

## Power-dependent PL analysis — `powerdep_manuscript.opj`

**Pipeline:** inspect → (data already merged into one workbook, 15 power columns) → despike (σ=4, **130 spikes removed**) → Lorentzian fit on all 15 spectra → allometric fits.

### Per-power Lorentzian results (window 1.23–1.45 eV)
All 15 spectra converged at **HIGH tier** (R² = 0.887–0.984, median 0.981; SNR 7.6–24).

| P (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 |
| 20 | 353.8 | 1.3278 | 62.7 | 0.968 |
| 30 | 516.0 | 1.3300 | 61.3 | 0.975 |
| 50 | 818.3 | 1.3328 | 59.0 | 0.981 |
| 70 | 1140.4 | 1.3343 | 57.1 | 0.983 |
| 100 | 1714.6 | 1.3356 | 54.4 | 0.984 |

*(full 15-point table in the CSV below)*

### Allometric fits
- **Intensity I(P)** — $I = a\,P^{\,b}$: **a = 16.28 ± 1.81 counts**, **b = 1.0048 ± 0.0261**, R² = 0.995 → **~linear (excitonic)** regime, no saturation over 5–100 µW.
- **Peak position xc(P)** — monotonic **blueshift** from 1.3206 → 1.3356 eV (+15.0 meV), slope ≈ **5.0 meV/decade**; consistent with bandgap renormalization / reduced screening at higher excitation.

📥 [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261