The file contains one workbook **Book1** with the energy axis (col A, ~1.196–1.606 eV) and 15 power-level columns already merged (5→100 µW). No Si/reference folder exists, so no background subtraction is needed. Suggested fit window: **1.23–1.45 eV**.

Per protocol, I must despike before any fit. Doing that now.



Despike complete — 130 cosmic-ray spikes removed across all 15 columns and written back. A clear PL peak sits near ~1.33 eV. Now running the Lorentzian power-dependence fit (Lorentzian profile per your request), extracting both intensity and xc per power, with both panels and the allometric fit.



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

Done. Despiked (130 spikes removed), then Lorentzian-fitted all 15 merged power spectra in the 1.23–1.45 eV window. Every column converged to **HIGH tier** (R² = 0.887–0.984). Per-power results:

| 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 |

**Allometric fit — intensity vs power** (left panel, $I = a\,P^{b}$):
- **b = 1.0048 ± 0.0261**, a = 16.28 ± 1.81, R² = 0.995 → **~linear (excitonic)** regime; no evidence of bimolecular/triplet recombination over 5–100 µW.

**Trend fit — peak position vs power** (right panel):
- Monotonic **blueshift** from 1.3206 eV (5 µW) to 1.3356 eV (100 µW), ≈ **5.0 meV per decade** of power, with FWHM narrowing 62→54 meV. Note: a strict allometric power-law ($y=a\,x^b$) is not a physical model for an absolute energy axis (it would force xc→0 as P→0), so the xc panel carries a smooth trend fit rather than a dimensionless exponent — hence the single well-defined allometric exponent below is the intensity one.

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

RESULT: b = 1.0048 ± 0.0261