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

📥 **Results:** [power_fit_results.csv]([file link removed])

## Done — Lorentzian cascade fit + allometric analysis (15 powers, 5→100 µW)

Data was already merged (one workbook, one column per power); no Si reference present. Despiked (25 spikes removed) before fitting. Each spectrum was fitted with a **Lorentzian** in the window 1.23–1.45 eV; all 15 converged to **HIGH** tier (R² 0.887–0.984, median 0.981; SNR 7.6–24).

**Per-power extracted values (from the Lorentzian fits):**

| Power (µW) | Intensity (counts) | xc (eV) | FWHM (meV) |
|---:|---:|---:|---:|
| 5 | 98.8 | 1.3206 | 62.4 |
| 10 | 189.9 | 1.3244 | 64.4 |
| 15 | 267.9 | 1.3264 | 64.1 |
| 20 | 353.8 | 1.3278 | 62.7 |
| 25 | 425.2 | 1.3290 | 61.7 |
| 30 | 516.0 | 1.3300 | 61.3 |
| 35 | 564.8 | 1.3304 | 60.8 |
| 40 | 694.6 | 1.3315 | 59.3 |
| 45 | 738.5 | 1.3318 | 59.1 |
| 50 | 818.3 | 1.3328 | 59.0 |
| 60 | 935.9 | 1.3332 | 58.0 |
| 70 | 1140.4 | 1.3343 | 57.1 |
| 80 | 1264.7 | 1.3345 | 56.3 |
| 90 | 1538.0 | 1.3351 | 55.3 |
| 100 | 1714.6 | 1.3356 | 54.4 |

**Allometric fit — Intensity vs Power (left panel), $I = a\,P^{b}$:**
- $a = 16.28 \pm 1.81$
- **$b = 1.0048 \pm 0.0261$**, $R^2 = 0.995$
- Interpretation: **~linear (excitonic)** — $b$ is consistent with 1 within uncertainty, i.e. no saturation or bimolecular quenching over this range.

**Peak position vs Power (right panel):**
- Monotonic **blueshift**: xc rises from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), a total shift of ~15 meV.
- Drift rate ≈ **5.0 meV/decade**; the peak also narrows (FWHM 62.4 → 54.4 meV) as power increases.

RESULT: b = 1.0048 ± 0.0261