In studies of the response function of state-of-the-art Si(Li) and HPGe detectors to low-energy (2-20 keV) mono-energetic x-rays, various characteristic features have been observed. To trace their origin we have studied the effect of the signal processing electronics on the evolution of the electronic signal, and measured the spectral shape of energetic electrons originating from the surfaces of Si and Ge crystals and front contact materials, using a high-energy range electrostatic electron spectrometer. From the measured electron spectra leaving the surfaces of the detector and front contact materials, and from the details of electron transport processes, the origin of the distinct features is identified and an approximate analytical form for the representation of the detector response function has been derived. It gives an excellent description of the response function and may replace the frequently applied Hypermet function. On the basis of this study, an explanation is given of the origin of the exponential tail and other various discrete structures on the low-energy side of the primary peak. The difference in low-energy side tailing between Si and HPGe detectors is explored. A detailed analysis of the so-called dead layer concept is given. Characteristic structures, 'kinks', are predicted in the spectra measured by solid-state detectors.