# On the extraction of resistivity and area of nanoscale interconnect lines by temperature-dependent resistance measurements

## TL;DR

This paper critically examines the TCR method for nanoscale interconnects, highlighting its limitations due to size effects, surface roughness, and barrier layers, and proposes modifications for more accurate resistivity and area extraction.

## Contribution

The study refines the TCR method to account for surface roughness and barrier layers, improving accuracy in nanoscale interconnect characterization.

## Key findings

- TCR deviates from bulk values due to size effects and surface roughness.
- The modified TCR method yields the harmonic average of cross-sectional area.
- Barrier layers cause overestimation of the conductor area when neglected.

## Abstract

Several issues concerning the applicability of the temperature coefficient of the resistivity (TCR) method to scaled interconnect lines are discussed. The central approximation of the TCR method, the substitution of the interconnect wire TCR by the bulk TCR becomes doubtful when the resistivity of the conductor metal is strongly increased by finite size effects. Semiclassical calculations for thin films show that the TCR deviates from bulk values when the surface roughness scattering contribution to the total resistivity becomes significant with respect to grain boundary scattering, an effect that might become even more important in nanowires due to their larger surface-to-volume ration. In addition, the TCR method is redeveloped to account for line width roughness. It is shown that for rough wires, the TCR method yields the harmonic average of the cross-sectional area as well as, to first order, the accurate value of the resistivity at the extracted area. Finally, the effect of a conductive barrier or liner layer on the TCR method is discussed. It is shown that the liner or barrier parallel conductance can only be neglected when it is lower than about 5 to 10% of the total conductance. It is furthermore shown that neglecting the liner/barrier parallel conductance leads mainly to an overestimation of the cross-sectional area of the center conductor whereas its resistivity is less affected.