The file has one workbook (`Book1`) with all 15 power columns already merged into a single sheet (5–100 µW), x-axis in eV. No separate Si/reference folder exists, so the data is already in the merged form needed. Now I'll despike (mandatory before any fit), then run the Lorentzian + allometric analysis.



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

## Pipeline completed

**Data:** 15 merged power spectra (5–100 µW) in `Book1`, x-axis in eV. Despiked first (130 cosmic-ray spikes removed, σ=4), then Lorentzian-fitted each spectrum over 1.23–1.45 eV. All 15 fits converged to the **HIGH** tier (R² = 0.887–0.984, median 0.981; FWHM 54–64 meV).

### Per-power results (Lorentzian fit)

| Power (µW) | Intensity (counts) | xc (eV) |
|---|---|---|
| 5 | 98.8 | 1.3206 |
| 10 | 189.9 | 1.3244 |
| 15 | 267.9 | 1.3264 |
| 20 | 353.8 | 1.3278 |
| 25 | 425.2 | 1.3290 |
| 30 | 516.0 | 1.3300 |
| 35 | 564.8 | 1.3304 |
| 40 | 694.6 | 1.3315 |
| 45 | 738.5 | 1.3318 |
| 50 | 818.3 | 1.3328 |
| 60 | 935.9 | 1.3332 |
| 70 | 1140.4 | 1.3343 |
| 80 | 1264.7 | 1.3345 |
| 90 | 1538.0 | 1.3351 |
| 100 | 1714.6 | 1.3356 |

### Allometric fit — intensity panel (left)
$$I = a \cdot P^{b}$$
- $a = 16.28 \pm 1.81$
- $b = 1.0048 \pm 0.0261$
- $R^2 = 0.995$ (n = 15)

$b \approx 1$ → **linear (excitonic)** scaling: intensity grows proportionally with excitation power, with no super-linear gain (which would signal defect/trap filling) or sub-linear quenching.

### Peak-position panel (right)
The peak **blueshifts** monotonically with power: from **1.3206 eV** (5 µW) to **1.3356 eV** (100 µW), a total shift of **+15.0 meV**, i.e. ≈ **5.0 meV/decade**. The fit curve is overlaid on the panel. (Note: the allometric exponent $b$ reported below is the intensity-scaling exponent — the standard allometric PL quantity — since a raw $x_c = aP^b$ fit is dominated by the ~1.32 eV offset rather than the small shift.)

📥 Full data + fit parameters: [power_fit_results.csv]([file link removed])

RESULT: b = 1.0048 ± 0.0261