Arrhenius Fitting Lab — choose the window, extract the energy

Synthetic R(T) data from an illustrative semiconductor, plotted on Arrhenius axes. Drag the two handles to set the fitting window; the straight-line fit reports an apparent activation energy — meaningful only when the window sits inside a single transport regime.

Model honesty: the dataset is synthetic — the same illustrative 1.12 eV-gap semiconductor with a 0.16 eV donor level (10¹⁵ cm⁻³) and T^−3/2 phonon mobility used in the companion overview, sampled at even temperature steps across −190 °C to 600 °C with Gaussian noise of 3% added to ln R. For this nearly uncompensated model, a window inside the freeze-out segment returns a slope near E_d/2 ≈ 0.07 eV (the small power-law prefactor shifts the fitted value slightly below the ideal E_d/2), a window inside the intrinsic segment returns a slope approaching E_g/2 = 0.56 eV (≈0.51–0.53 eV in the hottest windows, while the extrinsic contribution fades), and a window straddling the exhaustion plateau returns a physically meaningless mixture. The apparent energy is the fitted slope × k_B; the faint curve is the noise-free model. Regenerating the noise tests sensitivity to the imposed synthetic randomness only — systematic temperature offsets, contact drift and model bias are outside its reach. All values are illustrative teaching quantities, not data for any real material.