An evaluation of Fuchs-Sondheimer and Mayadas-Shatzkes models below 14nm node wide lines

The applicability of the Fuchs-Sondheimer and Mayadas-Shatzkes scattering models below the 14nm node with wide interconnect trenches of variable aspect ratio is investigated. The aspect ratio of these lines was varied between 1.2, 1.8, and 2.5; and the grain structure was concurrently manipulated. As the vertical dimension varied from greater than and less than the mean free path in Cu (39nm) at 21°C, the experiment found that the current approximation to the Fuchs-Sondheimer equation requires adjustment to the leading coefficient. Further, parameter fitting leads to the conclusion that specularity in these samples has a negative value of -0.2. The negative specularity is explained by surface roughness. The Mayadas-Shatzkes model retains its applicability and fits the data with a reflectivity of 0.16-0.17.