If there is a foreign atom embedded in the metal or semiconductor, a so-called impurity, the electrons that move freely through the solid are scattered by the deviating potential of the impurity. During the scattering process the initial state wave vector k i of the electron wave function is scattered to a final state wave vector k f. Because the electron gas is a Fermi gas only electrons with energies near the Fermi level can participate in the scattering process because there must be empty final states for the scattered states to jump to. Electrons that are too far below the Fermi energy E F can't jump to unoccupied states. The states around the Fermi level that can be scattered occupy a limited range of k -values or wavelengths. So only electrons within a limited wavelength range near the Fermi energy are scattered resulting in a density modulation around the impurity of the form