Quantum size effect in thin-wire transport

A quantum transport theory for electric conductivity is presented for the condition that the de Broglie wavelength of a thermal electron becomes comparable to the transverse dimensions of a thin wire of rectangular cross section. The theoretical results, which include the effect of size quantization, are analyzed in the ultrathin limit (UTL). In the UTL the ratio of longitudinal resistivity to bulk resistivity is shown to be proportional to λD²A, where λD is the de Broglie wavelength and A is the area of cross section. The results for transverse resistivity are also given and discussed.