The file has a single workbook `Book1`/`Sheet1` with energy (eV) on column A and 15 power-level spectra (5–100 µW) already merged into columns 1–15. Suggested x-range: **1.23–1.45 eV**. No separate Si/background folder exists, so no reference subtraction is needed.

Per protocol, I'll despike first (mandatory before any fit), then run the Lorentzian power-dependence fit.



Done. All 15 spectra were Lorentzian-fitted (window 1.23–1.45 eV), intensity and peak position extracted per power, and allometric fits applied to both panels.

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

## Per-power Lorentzian results (all 15 = HIGH tier, R² 0.887–0.984)

| 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 fits

- **Peak intensity vs power** — $I = a\cdot P^{b}$: $a = 16.28 \pm 1.81$, **$b = 1.0048 \pm 0.0261$**, R² = 0.995 → essentially linear (excitonic regime, no saturation or Auger quenching up to 100 µW).
- **Peak position vs power** — xc rises monotonically from 1.3206 → 1.3356 eV over 5→100 µW (a **blueshift**), ≈ +5.0 meV per decade of power; FWHM narrows 62→54 meV (power-broadening reversal / band-gap renormalization signature).

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

RESULT: b = 1.0048 ± 0.0261