File inspected. Structure: single workbook **Book1**, x-axis in column A (eV, 1.196–1.606), with 15 power columns (5→100 µW). Data is already merged into per-power columns — no Si/background folder present, so no subtraction needed. Suggested fit window: **x = 1.23–1.45 eV**.

Pipeline: despike (mandatory) → Lorentzian fits → intensity & xc extraction → two allometric plots.




Lorentzian fits converged on **all 15 spectra** (HIGH tier, R² = 0.887–0.984). The allometric intensity fit returned **I = a·P^b with b = 1.0048 ± 0.0261** (R² = 0.995, "~linear/excitonic"). Both panels (intensity vs power, xc vs power) are plotted. Now completing the allometric fit on the xc-vs-power panel.







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

**Pipeline:** despike (130 spikes removed, σ=4) → Lorentzian fit on all 15 spectra (window 1.23–1.45 eV) → intensity & xc extraction → two allometric plots. All 15 fits converged at HIGH tier (R² = 0.887–0.984).

### Per-power Lorentzian results
| Power (µW) | Intensity (a.u.) | 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 fits
- **Intensity vs power — I = a·P^b:** **b = 1.0048 ± 0.0261**, a = 16.28 ± 1.81, R² = 0.995 (15 points). Essentially linear → stable excitonic emission, no saturation or bi-exciton quenching in this range.
- **Peak position (xc) vs power:** weak **blueshift** from 1.3206 → 1.3356 eV (Δ ≈ 15 meV over 5→100 µW), ≈ 5.0 meV/decade. The allometric (log–log) slope is near-zero (**b_xc ≈ 0.004**), i.e. the peak energy is nearly power-independent / mildly saturating. *(Derived from the fitted centers; the server's `power_law_table` is PLE-oriented, so this panel is characterized by the fit trend rather than a separate nonlinear regression.)*

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

RESULT: b = 1.0048 ± 0.0261