File structure is clear: a single workbook `Book1` with an energy axis (eV) and 15 power columns (5–100 µW), already merged per power. No Si reference folder exists, so no background subtraction is needed. Suggested fit range is 1.23–1.45 eV.

Per protocol, I must despike before any fit.



Despiking removed 130 cosmic-ray spikes across all 15 power columns; cleaned data written back. The main PL peak sits near 1.33 eV, well inside the 1.23–1.45 eV window.

Now running the Lorentzian power-law fit (per-power Lorentzian profiles + allometric fits on both intensity and peak position vs power).



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

## Power-dependent PL analysis — `powerdep_manuscript.opj`

**Pipeline:** inspected → despiked (130 cosmic-ray spikes removed, σ=4, written back) → per-power Lorentzian fits over 1.23–1.45 eV → allometric fits. All 15 power levels (5–100 µW) landed in the **HIGH** tier (per-spectrum Lorentzian R² = 0.887–0.984, median 0.981; SNR 7.6–24). No Si reference folder existed, so no background subtraction was applied.

**Per-power extracted quantities (Lorentzian fit):**

| P (µW) | Intensity (counts) | x_c (eV) | FWHM (meV) |
|---|---|---|---|
| 5 | 98.8 | 1.3206 | 62.4 |
| 20 | 353.8 | 1.3278 | 62.7 |
| 50 | 818.3 | 1.3328 | 59.0 |
| 100 | 1714.6 | 1.3356 | 54.4 |

(Full table of all 15 points in the CSV below.)

**Allometric fit — intensity vs power** (left panel, $I = a\,P^{b}$):
- $a = 16.28 \pm 1.81$
- **$b = 1.0048 \pm 0.0261$**, R² = 0.995 → essentially linear (excitonic, non-saturating) emission across 5–100 µW.

**Peak position vs power** (right panel): $x_c$ shifts from 1.3206 eV at 5 µW to 1.3356 eV at 100 µW — a **blueshift** of ≈ 15 meV total (~5 meV/decade), consistent with band filling / many-body effects. The server reports this as a monotonic trend rather than a power-law (allometric) relation, since $x_c$ does not follow a $P^{b}$ scaling.

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

RESULT: b = 1.0048 ± 0.0261