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

## Lorentzian Power-Dependence Results

**Fit quality:** All 15 spectra (5–100 µW) converged to **HIGH tier** — R² range 0.887–0.984, SNR 7.6–24.0. No rescue or raw-peak fallbacks needed.

### Panel 1 — Peak Intensity vs Power (allometric fit I = a·P^b)

| Parameter | Value |
|-----------|-------|
| a | 16.28 ± 1.81 counts |
| **b** | **1.0048 ± 0.0261** |
| R² | 0.9951 |
| Regime | **~linear (excitonic)** |

The near-unity exponent confirms the PL intensity scales linearly with excitation power across the full 5–100 µW range — characteristic of a single-exciton (radiative recombination) regime with no significant biexciton saturation or Auger nonlinearity.

### Panel 2 — Peak Position (xc) vs Power

| Quantity | Value |
|----------|-------|
| xc range | 1.3206 eV (5 µW) → 1.3356 eV (100 µW) |
| Total shift | **≈ 15 meV blueshift** |
| Slope | ~5.0 meV per decade of power |
| FWHM trend | 62.4 → 54.4 meV (narrowing with power) |

The peak shifts to higher energy (blueshift) as power increases, consistent with band-filling / state-filling effects in the nanocrystal ensemble.

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

RESULT: b = 1.0048 ± 0.0261