= Carrier effective mass from a reflectivity minimum
{title2=$m^*=ne^2\lambda_{\min}^2/[4\pi^2\epsilon_0c^2(\epsilon_b-1)]$}
For a weakly absorbing doped semiconductor with one dominant carrier species and approximately constant background dielectric function $\epsilon_b>1$, the <Drude model> gives a normal-incidence reflectivity minimum near $\epsilon_r=1$. Thus $\omega_{pc}^2=(\epsilon_b-1)\omega_{\min}^2$, with $\omega_{pc}^2=ne^2/(\epsilon_0m^*)$ and $\omega_{\min}=2\pi c/\lambda_{\min}$. Eliminating the plasma frequency proves the displayed mass estimate. The real-dielectric zero instead has $\omega_0\simeq\omega_{pc}/\sqrt{\epsilon_b}$ and is the nearby screened plasma edge, so its wavelength requires a different denominator. With appreciable loss, fit the full complex <Fresnel equations> rather than identifying the minimum with an exactly real dielectric value.
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