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

## Lorentzian power-dependent PL analysis

Pipeline: inspect → **despike** (130 cosmic-ray spikes removed, σ=4, written back) → **Lorentzian fit** on all 15 spectra (integration window 1.23–1.45 eV) → allometric fit I = a·P^b. All 15 columns converged to **HIGH tier** (R² 0.887–0.984), so every point is included in both panels.

**Per-power Lorentzian results:**

| Power (µW) | Intensity (counts) | x_c (eV) | FWHM (meV) | R² |
|---|---|---|---|---|
| 5 | 98.8 | 1.32062 | 62.4 | 0.887 |
| 10 | 189.9 | 1.32437 | 64.4 | 0.950 |
| 15 | 267.9 | 1.32636 | 64.1 | 0.958 |
| 20 | 353.8 | 1.32783 | 62.7 | 0.968 |
| 25 | 425.2 | 1.32905 | 61.7 | 0.973 |
| 30 | 516.0 | 1.32998 | 61.3 | 0.975 |
| 35 | 564.8 | 1.33044 | 60.8 | 0.978 |
| 40 | 694.6 | 1.33152 | 59.3 | 0.981 |
| 45 | 738.5 | 1.33179 | 59.1 | 0.981 |
| 50 | 818.3 | 1.33279 | 59.0 | 0.981 |
| 60 | 935.9 | 1.33317 | 58.0 | 0.982 |
| 70 | 1140.4 | 1.33430 | 57.1 | 0.983 |
| 80 | 1264.7 | 1.33446 | 56.3 | 0.983 |
| 90 | 1538.0 | 1.33509 | 55.3 | 0.984 |
| 100 | 1714.6 | 1.33562 | 54.4 | 0.984 |

**Allometric fit — intensity (left panel), I = a·P^b:**
- a = 16.28 ± 1.81, **b = 1.0048 ± 0.0261**, R² = 0.995 (n = 15)
- Interpretation: essentially linear (b ≈ 1) → excitonic, single-particle regime (no biexciton saturation over this range).

**Peak-position trend (right panel):** x_c blueshifts monotonically from 1.3206 eV (5 µW) to 1.3356 eV (100 µW) — a total blueshift of ~15 meV, i.e. ≈ 5.0 meV per decade of power. FWHM narrows slightly from ~62 to ~54 meV with increasing power.

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

RESULT: b = 1.005 ± 0.026