We have carried out an in-depth investigation on the reflectivity R　and phase shift φ of a novel semiconductor mirror, which can be applied in the far-infrared (FIR) spectral range. By fitting FIR reflection spectra of the GaAs material with different doping concentrations, empirical formulas are obtained for the doping concentration-dependent carrier relaxation time τ of n-GaAs and p-GaAs. The effects of structure and material parameters on the reflectivity and the phase shift of the mirror are analytically studied on the　basis of the deduced formulas. All the related parameters of the mirror are further optimized, and the corresponding wavelength selectivity is calculated according to the highest absorption in the detector cavity. The experimental FIR reflection result confirms the theoretical simulation, revealing the unique properties of this mirror, which establishes the basis of optimum designing of various FIR mirrors.