The file contains a single workbook **Book1** with 15 power-level spectra (columns 1–15: 5→100 µW) on an energy axis (eV). No separate Si/reference folder exists, so the data is already consolidated — no merge step needed. Suggested fit window: 1.23–1.45 eV.

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



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

## Lorentzian power-dependence analysis — Book1 (5→100 µW, 15 spectra)

Fit window **1.23–1.45 eV**, Lorentzian profile, despiked (130 spikes removed) before fitting. All 15 columns converged at **HIGH tier** (R² = 0.887–0.984, median 0.981; SNR 7.6–24.0).

### Per-power extraction (Lorentzian fit)

| P (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** — $I = a\cdot P^{b}$:
- $a = 16.28 \pm 1.81$
- **$b = 1.0048 \pm 0.0261$** (R² = 0.995, 15 pts)
- Interpretation: **~linear (excitonic)** — intensity scales ∝ P with no saturation or Auger-dominated sub-linear regime across 5–100 µW.

**Peak position vs power** — xc shifts monotonically to higher energy (**blueshift**) from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), a total of **+15 meV**, i.e. ≈ **5.0 meV/decade**. The dependence is very weak (near-flat), so a power-law exponent on xc would be ≪1; the dominant, well-determined allometric parameter is the intensity exponent above.

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

RESULT: b = 1.0048 ± 0.0261