Electrical current in nanoelectronic devices

In ultra-small electronic devices of the next generations the semiclassical model of electron motion in a periodical lattice between collisions turns out to be inadequate because the electron spread has magnitude order of the size of the ultra-small electronic device. In this Letter we consider the basic conceptual framework regarding how the length scale of the electrical device influences the transport behavior of the electrons between collisions and the electrical current. By taking into account the interference effects we obtain a very basic model for electrons transport, where the density current peak is given as function on the ratio between the thermal de Broglie wavelength and the lattice period. This result could be also useful in order to understand the basic effect of the insulator/metal transition.