File inspected. Structure: **Book1/Sheet1**, x-axis in **eV** (col A), 15 power columns (5–100 µW), already merged (one column per power, no Si folder). Suggested fit range: **1.23–1.45 eV**.

Pipeline: despike → Lorentzian fit all spectra → extract intensity & xc → allometric fits. Starting with the mandatory despike.



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

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

## Summary

Data was already merged (one column per power, Book1/Sheet1, eV axis). After removing **130 cosmic-ray spikes** (despike σ=4), a **Lorentzian + slope** profile was fitted to all 15 spectra over 1.23–1.45 eV. Every column converged to **HIGH tier** (R² = 0.887–0.984, median 0.981).

**Allometric fit — intensity vs power:** $I = a\,P^{b}$
- $a = 16.28 \pm 1.81$
- $b = 1.0048 \pm 0.0261$
- R² = 0.995 → **~linear (excitonic)** regime

**Peak-position trend — xc vs power:** monotonic **blueshift**, 1.3206 → 1.3356 eV, ≈ **+4.99 meV per decade** of power (band-gap renormalization / screening); FWHM narrows 62 → 54 meV.

### Per-power Lorentzian parameters

| 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 |

Note: the intensity panel carries the explicit allometric ($I=aP^b$) fit; the xc panel is fitted with the tool's trend model (per-decade slope), since the xc shift is weak and near-logarithmic rather than a clean power law. The reported `b` below is the intensity allometric exponent.

RESULT: b = 1.0048 ± 0.0261