The file is already merged — a single workbook **Book1** with the energy axis (col A) and 15 power columns (5 µW → 100 µW). Suggested x-range is [1.23, 1.45] eV.

Let me check the exact tool signatures I'll need before running the pipeline.




Data is already merged into **Book1** (energy axis + 15 power columns, 5–100 µW). My pipeline: despike → Lorentzian batch fit → extract intensity & xc per power → two plots with allometric fits.

Starting with the mandatory despike (σ=4, write-back):



Despike complete: 130 cosmic-ray spikes removed across all 15 power columns and written back. The dominant PL peak sits near ~1.32 eV.

Now running the Lorentzian fit on all 15 spectra over the suggested window [1.23, 1.45] eV:



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

| P (µW) | xc (eV) | Amplitude A | R² |
|---|---|---|---|
| 5 | 1.3190 | 10.87 | 0.890 |
| 10 | 1.3244 | 21.79 | 0.950 |
| 15 | 1.3264 | 30.65 | 0.958 |
| 20 | 1.3278 | 38.65 | 0.968 |
| 25 | 1.3291 | 47.46 | 0.973 |
| 30 | 1.3300 | 57.65 | 0.976 |
| 35 | 1.3305 | 64.50 | 0.978 |
| 40 | 1.3316 | 76.20 | 0.982 |
| 45 | 1.3319 | 82.15 | 0.982 |
| 50 | 1.3329 | 91.99 | 0.983 |
| 60 | 1.3332 | 108.96 | 0.984 |
| 70 | 1.3343 | 127.50 | 0.986 |
| 80 | 1.3345 | 144.27 | 0.987 |
| 90 | 1.3352 | 164.37 | 0.988 |
| 100 | 1.3357 | 188.15 | 0.989 |

Now running the power-dependent analysis (Lorentzian profile, locked demo params) to build the I(P) and xc(P) panels with the allometric fit:



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

**Pipeline executed:** merged spectra (Book1, 15 powers 5–100 µW) → despiked (σ=4, 130 spikes removed) → Lorentzian fit on all 15 spectra (window 1.23–1.45 eV, R² = 0.89–0.99) → extracted peak intensity and xc per power → allometric fits.

**Per-power Lorentzian results** (intensity = fitted peak height above wing baseline; xc = peak center):

| P (µW) | Intensity (cnt) | xc (eV) | FWHM (meV) |
|---|---|---|---|
| 5 | 98.8 | 1.3206 | 62.4 |
| 10 | 189.9 | 1.3244 | 64.4 |
| 20 | 353.8 | 1.3278 | 62.7 |
| 30 | 516.0 | 1.3300 | 61.3 |
| 50 | 818.3 | 1.3328 | 59.0 |
| 70 | 1140.4 | 1.3343 | 57.1 |
| 100 | 1714.6 | 1.3356 | 54.4 |

**① Intensity vs power — allometric fit I = a·P^b** (left panel, log–log):
- **b = 1.0048 ± 0.0261**, a = 16.28 ± 1.81, R² = 0.995
- Interpretation: **~linear (excitonic)** — PL intensity scales proportionally with excitation power, no saturation or biexciton/quasiparticle effects in this range.

**② Peak position vs power** (right panel):
- xc shifts from 1.3206 → 1.3356 eV, a weak **blueshift of ~15 meV** total, ≈ **5 meV/decade**, that visibly **saturates** (sub-linear, logarithmic-like approach to a plateau).
- Note: a strict allometric form xc = c·P^d is *not* a physically appropriate model here — it forces xc → 0 as P → 0, whereas the data are nearly flat and saturating. The effective exponent would be tiny (d ≈ 0.004, i.e. essentially zero), so I report the trend/rate rather than a spurious power-law coefficient.

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

RESULT: b = 1.0048 ± 0.0261