The Franz-Keldysh effect and free carrier dispersion effect in germanium

We calculated the changes of refractive index and absorption coefficient in Ge induced by the Franz-Keldysh (FK) effect and free carrier dispersion (FCD) effect, taking advantage of reported absorption spectra.The FK effect is weak near the indirect absorption edge of Ge. FCD effect can induce a much larger change of refractive index. In the wavelength range of 2-10 μm, theoretical formulas about dependences of the changes of absorption coefficient and refractive index on the change of carrier concentrations are presented. In addition, FCD effects in N-type and P-type Ge are compared.