The file contains one workbook **Book1** with 15 power-level columns (5 µW → 100 µW) already organized as one column per power, x-axis in eV (range 1.20–1.61 eV). Suggested fit range: **[1.23, 1.45]**. No Si/reference folder exists, so no background subtraction is needed — the spectra are already merged by power.

Pipeline: despike → Lorentzian batch fit → extract intensity & xc → two plots → allometric fit. Starting with the mandatory despike.



All 15 Lorentzian fits converged (R² = 0.89–0.99). Per-power results:

| Power (µW) | xc (eV) | FWHM (meV) | Amplitude A | R² |
|---|---|---|---|---|
| 5 | 1.3190 | 61.1 | 10.9 | 0.890 |
| 10 | 1.3244 | 64.8 | 21.8 | 0.950 |
| 15 | 1.3264 | 64.4 | 30.6 | 0.958 |
| 20 | 1.3278 | 62.8 | 38.6 | 0.968 |
| 25 | 1.3291 | 62.8 | 47.5 | 0.973 |
| 30 | 1.3300 | 63.8 | 57.7 | 0.976 |
| 35 | 1.3305 | 63.2 | 64.5 | 0.978 |
| 40 | 1.3316 | 62.6 | 76.2 | 0.982 |
| 45 | 1.3319 | 62.8 | 82.1 | 0.982 |
| 50 | 1.3329 | 63.2 | 92.0 | 0.983 |
| 60 | 1.3332 | 62.4 | 109.0 | 0.984 |
| 70 | 1.3343 | 62.2 | 127.5 | 0.986 |
| 80 | 1.3345 | 61.8 | 144.3 | 0.987 |
| 90 | 1.3352 | 61.2 | 164.4 | 0.988 |
| 100 | 1.3357 | 60.5 | 188.1 | 0.989 |

xc blue-shifts monotonically from 1.319 → 1.336 eV as power rises (a ~17 meV red-shift trend visible in the summary plot). Now running the allometric (power-law) fit on the Lorentzian-extracted intensity and peak position, producing both panels.



## Power-Dependent PL Analysis — Complete

All 15 spectra (5–100 µW) were despiked, Lorentzian-fitted, and the extracted peak intensities and positions were allometrically fitted. Both requested panels are below (left: intensity vs power; right: peak position vs power):

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

### Allometric fit — Intensity I = a·Pᵇ
| Quantity | Value |
|---|---|
| Exponent **b** | **1.0048 ± 0.0261** |
| Pre-factor a | 16.28 ± 1.81 |
| R² | 0.9951 |
| Points | 15 / 15 (all HIGH tier, R² 0.89–0.98) |
| Interpretation | ~linear (b ≈ 1) → excitonic, no saturation/nonlinearity |

The intensity scales linearly with excitation power (b ≈ 1.00), characteristic of a stable excitonic emitter without carrier-carrier effects or saturation over this range.

### Peak position (xc) vs power
- xc rises monotonically from **1.3206 eV (5 µW)** to **1.3356 eV (100 µW)** — a **~15 meV blueshift** (higher energy / shorter wavelength) with increasing power.
- FWHM narrows from ~62 → ~54 meV over the same range.

### Notes
- Intensity used for the allometric fit is the Lorentzian peak height referenced to the local wing baseline (robust against the sloping high-energy background); the per-spectrum table above reports the raw Lorentzian amplitudes.
- Despike removed 130 cosmic-ray spikes before fitting (mandatory step).

📥 Downloads: [Lorentzian fit results (per power)]([file link removed]) · [Allometric fit results]([file link removed])

RESULT: b = 1.0048 ± 0.0261