Evaluation of via density and low-k Young's modulus influence on mechanical performance of advanced node multi-level Back-End-Of-Line

• Exploration of 4D BEOL design space (consisting of different via densities and low-k Young's modulus)
• Determining the influence of different design parameters (via densities and low-k Young's modulus) on design performance
• Determining peel stresses in different via layers using orthogonal polynomials
• Introduction of distance norms as value functions for optimal design selection

Utilizing Design Of Experiments (DOE) and a decision making procedure, the mechanical performance of different advanced node Back-End-Of-Line (BEOL) configurations is evaluated, where the average peel stress in metal vias is considered as the critical parameter, and is identified with mechanical performance. The goal is to guide the design of the BEOL in its conceptual phase, with respect to the via densities and low-k Young's modulus. The first section of the paper discusses an exploration of the design space X, using the orthogonal method as a selected DOE with which 16 different BEOL configurations are evaluated. The DOE is used to generate regression equations which allow to evaluate the influence of individual design parameters on mechanical performance. Low-k Young's modulus was proved to have dominant effect on reducing the stresses in the vias, and while the influence of the via density is lower, it is still possible to reduce the stresses by increasing the via density. In the second part, a decision making procedure is introduced, with the objective of choosing the optimal design out of a number of existing designs. Designs that are defined in the design space are mapped to the attribute space Y, and to the metric space M, which allows for comparison of individual designs in respect to the stress levels in different BEOL via layers. In this part, all designs are sorted in the metric space, and are ready to be evaluated. Finally, different distance norms (metrics) are introduced as value functions to evaluate individual designs. Based on these norms, an optimal design with high low-k Young's modulus and via 0 density has been identified, along with a number of other designs which show good mechanical performance.