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

## Power-dependent PL analysis (Lorentzian fit + allometric)

**Pipeline:** despiked (130 cosmic-ray spikes removed) → Lorentzian fit on all 15 spectra (window 1.23–1.45 eV) → extracted per-power intensity & xc → allometric fit $I = a\cdot P^{b}$ on both panels.

All 15 spectra passed at **HIGH tier** (Lorentzian R² = 0.887–0.984, median 0.981; SNR 7.6–24.0).

**Left panel — Peak intensity vs power (allometric fit):**
- $I = a\cdot P^{b}$, with $a = 16.28 \pm 1.81$, **$b = 1.0048 \pm 0.0261$**, R² = 0.995
- Interpretation: **~linear (excitonic)** regime — no saturation over 5–100 µW.

**Right panel — Peak position vs power:**
- Monotonic **blueshift** from **1.3206 eV (5 µW)** to **1.3356 eV (100 µW)**, ≈ 5.0 meV/decade.
- FWHM narrows from ~62 meV (low P) to ~54 meV (high P).

Per-power table (intensity in counts, xc in eV):

| P (µW) | Intensity | 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 |
| 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 |

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

RESULT: b = 1.0048 ± 0.0261