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

## Results

**Lorentzian fits** were performed on all 15 power levels (5–100 µW) in the window 1.23–1.45 eV. All 15 spectra achieved **HIGH-tier** quality (R² = 0.887–0.984, median 0.981).

### Per-power extracted values

| Power (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 |
| 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(P) panel

$$I = a \cdot P^{\,b}$$

- **a** = 16.28 ± 1.81
- **b** = 1.0048 ± 0.0261
- R² = 0.9951 (15 points)
- Interpretation: **~linear (excitonic)** regime — intensity scales proportionally with pump power.

### Peak-position trend — xc(P) panel

- xc shifts from **1.3206 eV** (5 µW) to **1.3356 eV** (100 µW): a net **blueshift of ≈ 15 meV**.
- Slope: **+5.0 meV per decade** of power.
- FWHM narrows from 62 → 54 meV over the same range, consistent with reduced thermal broadening at higher excitation.

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

RESULT: b = 1.0048 ± 0.0261