Structure is clear: single workbook `Book1` / `Sheet1`, x-axis in **eV**, 15 power columns (5–100 µW), `suggested_x_range = [1.23, 1.45]`. All powers are already in one workbook (no separate Si/reference folder exists), so no merge step is needed. Now despiking (mandatory before any fit).





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

## Lorentzian power-dependence analysis — `powerdep_manuscript.opj`

**Pipeline:** inspect → despike (130 cosmic-ray spikes removed, σ=4) → per-power Lorentzian fit over $x\in[1.23,\,1.45]$ eV → allometric $I = a\cdot P^b$. All 15 powers (5–100 µW) converged to **HIGH tier** (Lorentz R² = 0.89–0.98, median 0.98; SNR 7.6–24).

**Per-power results (from Lorentzian fits):**

| 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 fit ($I = a\cdot P^b$):** $a = 16.28 \pm 1.81$, **$b = 1.005 \pm 0.026$**, $R^2 = 0.995$ (15 points). $b \approx 1$ → intensity scales **linearly** with excitation power (excitonic regime, no saturation or bi-exciton quenching in this range).

**Peak-position trend:** $x_c$ rises from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — a ~15 meV **blueshift** with power (~5 meV/decade), consistent with bandgap renormalization at higher carrier density rather than thermal redshift.

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

RESULT: b = 1.005 ± 0.026