A comprehensive ellipsometric study was performed on Fe$_{1-x}$Co$_{x}$Si single crystals in the spectral range from 0.01 eV to 6.2 eV. Direct and indirect band gaps of 73 meV and 10 meV, respectively, were observed in FeSi at 7 K. One of four infrared-active phonons that is energetically close to the direct absorption edge is coupled both to the electrons and to the low-energy phonon. This is evident from asymmetry in the phonon line shape and a reduction of its frequency when the absorption edge shifts across the phonon energy due to the temperature dependence of the direct band gap. As the temperature increases, the indirect gap changes sign, which manifests as a transition from a semiconductor to a semimetal. The corresponding gain of the spectral weight at low energies was recovered within an energy range of several eV. The present findings strongly support the model indicating that Fe$_{1-x}$Co$_{x}$Si can be well described in an itinerant picture, taking into account self-energy corrections.
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