(Invited) Comparison of Empirical Models for Broadband Insertion Losses in TSV-Interconnects

Abstract

The reliability of through silicon via (TSV)-interconnects depends on various factors including integration schemes, manufacturing process (construction materials, wafer-scale homogeneity, thermal budget) and operating conditions. The magnitude of the frequency-dependent $S_{21}$ microwave scattering parameter quantifies insertion losses in TSV-interconnects. The insertion loss depends on the instantaneous electrical characteristics of the device under test. We attribute insertion loss (which affects device reliability) to reorientation of electrically active defects, cracks, voids, dielectric constant variation, and water molecules affected by heat. We model insertion losses with equivalent circuit models of varying complexity. We compare results determined with global and local models fit to low-frequency and high-frequency subsets of the full spectrum. We estimate model parameters with a stochastic optimization implementation of the Levenberg-Marquadt method. To illustrate the relevance of this methodology, for TSV-interconnects from two different providers, we quantify how estimated model parameters vary with thermal cycles for TSV-interconnects fabricated at particular wafer locations.