Technology and reliability constrained future copper interconnects. I. Resistance modeling

Abstract

A realistic assessment of future interconnect performance is addressed, specifically, by modeling copper (Cu) wire effective resistivity in the light of technological and reliability constraints. The scaling-induced rise in resistance in the future may be significantly exacerbated due to an increase in Cu resistivity itself, through both electron surface scattering and diffusion barrier effect. The impact of these effects on resistivity is modeled under various technological conditions and constraints. These constraints include the interconnect operation temperature, the effect of copper-diffusion barrier thickness and its deposition technology, and the quality of interconnect/barrier interface. Reliable effective resistivity trends are established at various tiers of interconnects, namely, at the local, semiglobal, and global levels. Detailed implications of the effect of resistivity trends on performance are addressed in the second part of this work.

A Maxwell Garnett Model for Dielectric Mixtures Containing Conducting Particles at Optical Frequencies

“…And the remainder have an average characteristic dimension of b i = l+d 2 , which can lead to some decrease of conductivity. Thus, the coefficient Λ may be even smaller than is given in the tables in [8], if the surface roughness and grain size of metal inclusion are taken into account [9][10][11]. For our computations, we assume that a reasonable value is Λ = 0.8, corresponding to a 20% decrease in conductivity.…”

Dependence of resistivity on surface profile in nanoscale metal films and wires

“…These approaches assume a ratio p of carrier collisions with the surface reflect specularly, while 1−p scatter diffusely. Such theories can be fit to experiment with p as a free parameter, but do not provide insight into how to improve conductivity.More recently, surface roughness scattering has raised the attention of researchers in industry [5,6,7], and quantum mechanical approaches to surface scattering calculations have been proposed. The two primary approaches include the Kubo linear response theory of Tesanović et al [8] and Trivedi and Ashcroft [9], and the diagrammatic Keldysh formalism of Meyerovich and collaborators [10,11,12].…”

Studies of two-dimensional h-BN and MoS2 for potential diffusion barrier application in copper interconnect technology

“…However, all of these barrier materials are at least one order of magnitude more resistive than Cu itself. 4 Thus, to lower the overall line resistance, it is essential to maximize the Cu volume in its damascene trench, which requires the thickness of the barrier material to be reduced as much as possible. Conversely, it has been found that conventional barrier materials lose their capability of blocking Cu diffusion when their thicknesses are scaled below~3 nm, as illustrated in Fig.…”