The Effect of Scattering of Phonons, Size and Grain Boundary on Electrical Properties for Ruthenium Nano Metals

The study examines the impact of thickness on the electrical resistance of Ruthenium at room temperature. By applying the Fuchs-Sondheier and Mayadas Shatzkces models, the study establishes a linear relationship between thickness and grain boundary scattering. The M.S. model is crucial in calculating the size impact, accounting for all types of scattering affecting grain boundaries. On the other hand, the F.S. model focuses on explaining conduction electron scattering on material surfaces, particularly on tiny grains. The study's equation, derived from these two models, considers surface scattering and metal resistance to determine an experimental thickness that depends on metal resistivity. The Boltzmann Equation can be utilized to solve this equation. The study highlights the significance of Ruthenium as a common component of electrical and electronic circuits in producing electronic chips due to its excellent electrical conductivity.