Infrared Absorption in n-Type Silicon

The absorption by free carriers in $n$-type silicon has been studied in a spectral region from 1 to 45 microns for samples of various impurity and carrier concentrations. In all samples measured the absorption consists of a band between 1.5 and 5 microns in addition to an absorption which rises smoothly with wavelength. The absorption band is found to be proportional to the carrier concentration in samples doped with different donor impurities. It is suggested that the band is associated with the excitation of carriers to a higher lying energy band. The behavior of the smoothly rising portion of the absorption curve is in agreement with the Fan and Fr\"ohlich theory of free-carrier absorption. Quantitative agreement is obtained with a value of $0.3m$ for the effective mass.