It is shown for the first time that electron-electron scattering of slow electrons with an energy of 10–50 eV at the surface of some metals is mainly an event of binary scattering of particles with conserved total momentum and energy, while analogous scattering at the surface of a semiconductor (n-Si) and an insulator (MgO) is a multiparticle event. A model is proposed, in which the electron subsystem of a solid is characterized by short-range order. Each electron is at the center of a spherical cell and surrounded by nearest neighbors (electrons) with a coordination number of 12. The overlap of the fields of charges gives rise to a negative potential U c (r) ≈ U c , which is virtually constant along the coordinate and contains spherical cells with a central field U(r) of individual charges. The value of constant negative potential U c depends on the extent of electron screening, which is high for metals and low for semiconductors and insulators. In metals, scattering governed by the binary mechanism may take place (i.e., scattering of a primary electron in the central field of an electron of the metal); this is ensured by a relatively small value of constant potential U c . The electron subsystem of the metal behaves as a Fermi gas of weakly interacting quasiparticles. Electron screening in semiconductors and insulators is insignificant, and constant negative potential U c is an order of magnitude higher than the analogous potential in metals. Slow primary electrons are scattered in the total field of many charges before they reach the central field of an individual electron. The electron subsystem of a semiconductor and an insulator in the excitation range studied here behaves as an ensemble of strongly interacting particles.