The file contains one workbook (`Book1`) with 15 power-level columns (5–100 µW) and an energy axis in eV. No separate Si reference folder exists, so no background merge is needed. Suggested x-range: **1.23–1.45 eV**.

**Step 1 — Despike (mandatory before any fit):**



130 cosmic-ray spikes removed across all 15 columns. Data written back.

**Step 2 — Lorentzian fit + allometric (power-law) analysis:**



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

## Results — Lorentzian Power-Dependence Analysis

**Profile:** Lorentzian | **Window:** 1.23–1.45 eV | **Points:** 15/15 (all HIGH tier)

### Allometric fit: $I = a \cdot P^{b}$

| Parameter | Value |
|-----------|-------|
| $a$ | 16.28 ± 1.81 |
| $b$ | **1.005 ± 0.026** |
| $R^2$ | 0.995 |
| Interpretation | ~linear (excitonic regime) |

### Per-power extracted values

| Power (µW) | Intensity (counts) | $x_c$ (eV) | FWHM (meV) | $R^2$ | Tier |
|---|---|---|---|---|---|
| 5 | 98.8 | 1.3206 | 62.4 | 0.887 | HIGH |
| 10 | 189.9 | 1.3244 | 64.4 | 0.950 | HIGH |
| 15 | 267.9 | 1.3264 | 64.1 | 0.958 | HIGH |
| 20 | 353.8 | 1.3278 | 62.7 | 0.968 | HIGH |
| 25 | 425.2 | 1.3290 | 61.7 | 0.973 | HIGH |
| 30 | 516.0 | 1.3300 | 61.3 | 0.975 | HIGH |
| 35 | 564.8 | 1.3304 | 60.8 | 0.978 | HIGH |
| 40 | 694.6 | 1.3315 | 59.3 | 0.981 | HIGH |
| 45 | 738.5 | 1.3318 | 59.1 | 0.981 | HIGH |
| 50 | 818.3 | 1.3328 | 59.0 | 0.981 | HIGH |
| 60 | 935.9 | 1.3332 | 58.0 | 0.982 | HIGH |
| 70 | 1140.4 | 1.3343 | 57.1 | 0.983 | HIGH |
| 80 | 1264.7 | 1.3345 | 56.3 | 0.983 | HIGH |
| 90 | 1538.0 | 1.3351 | 55.3 | 0.984 | HIGH |
| 100 | 1714.6 | 1.3356 | 54.4 | 0.984 | HIGH |

### Key observations
- **Intensity scales linearly** with excitation power ($b ≈ 1.0$), characteristic of the excitonic (non-saturating) regime.
- **Peak position blueshifts** by ~15 meV from 5 → 100 µW (~5 meV/decade), consistent with band-filling or screening effects at higher carrier density.
- **FWHM narrows** slightly with power (64 → 54 meV), indicating improved spectral definition at higher SNR.

📥 [Download full results CSV]([file link removed])

RESULT: b = 1.005 ± 0.026