Carrier effective mass from a reflectivity minimum ($m^{\ast }=n{e}^2{\lambda }_{\min }^2/[4{\pi }^2{ϵ}_0{c}^2({ϵ}_b-1)]$)

For a weakly absorbing doped semiconductor with one dominant carrier species and approximately constant background dielectric function ${ϵ}_b>1$, the Drude model gives a normal-incidence reflectivity minimum near ${ϵ}_r=1$. Thus ${\omega }_{pc}^2=({ϵ}_b-1){\omega }_{\min }^2$, with ${\omega }_{pc}^2=n{e}^2/({ϵ}_0{m}^{\ast })$ and ${\omega }_{\min }=2\pi c/{\lambda }_{\min }$. Eliminating the plasma frequency proves the displayed mass estimate. The real-dielectric zero instead has ${\omega }_0\simeq {\omega }_{pc}/\sqrt{{ϵ}_b}$ 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.