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

## Power-dependent PL analysis — Lorentzian fits + allometric fits

**Pipeline:** despike (σ=4, 130 cosmic-ray spikes removed across 15 spectra) → Lorentzian fit of each spectrum in the window **1.23–1.45 eV** → per-power extraction of peak position $x_c$ and peak intensity → allometric fit $y = a\,P^{\,b}$ on both panels.

All 15 powers (5–100 µW) converged at **HIGH tier** (R² = 0.887–0.984, median 0.981).

**Per-power peaks (Lorentzian):**

| P (µW) | Intensity (cts) | x_c (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 |
| 40 | 694.6 | 1.3315 | 59.3 | 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 panel** $I = a\,P^{b}$: $a = 16.28 \pm 1.81$, $b = 1.0048 \pm 0.0261$, R² = 0.995 → **~linear (excitonic)** behavior.
- **Peak-position panel**: $x_c$ shifts from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — a monotonic **blueshift** (~5 meV/decade), consistent with exciton–exciton interaction / band filling at higher excitation.

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

RESULT: b = 1.00 ± 0.03