Finite size effects in stress analysis of interconnect structures

Abstract

Conventional formulations of thermal stress evolution in interconnect structures usually ignore the interface integrity between the various levels. In this letter we present thermal and residual stress versus temperature data from simple copper thin-film structures on silicon. The results indicate that interconnection models which assume fully elastic behavior and perfectly bonded interfaces may yield inaccurate predictions of the thermo-mechanical response for feature sizes smaller than 10μm.

Applicability range of Stoney’s formula and modified formulas for a film/substrate bilayer

“…Both experiment and theoretical analyses show that the interfacial slip greatly influences the stress distribution inside the layer. 20,25 Therefore, the deflection and curvature of the bilayer are affected. The interface layer models including the shear-lag model 26 and lap-shear model 27,28 can be used to model the nonideal case by allowing interfacial slip.…”

Effect of Compliant Interface on the Curvature and Stress of Micron-Size Film-Substrate Composite Structure

“…All these above will reduce the overall interface adhesion for sure [5]. Both experiment and theoretical analysis show that the analysis of rigid interface model errors more and more when the size of film-substrate composite shrinks in micron order [1,2].…”

“…2 --Ec/i=2X1O0 parameters ( i.e. Eo, Go and 77) [1,2], so the thickness of 0~~~~~~-0.03 both the film and substrate is changed in Fig. 3 to show the effect of layer dimensions.…”

“…As the material properties of film and substrate such as Young's modulus, lattice parameters, coefficients of thermal expansion may be different and also due to the stress build-up during fabrication and processing, the stress inside the film and substrate can be different and result in the deflection of composite structure to relax stress [8]. The following Stoney's 1909 formula [9] serves the cornerstone of relating the stress/force inside film to the curvature of a composite structure 6f cst = 2 hs Es (1) Kst is the curvature and f is the force per unit length inside film (when the film is very thin, f is the surface stress [10]). …”

“…The rigid interface model (also called ideal interface [1,2], perfectly bonded interface [3] or coherent interface [4]), which allows no interfacial slip is a strong constraint condition because the strains inside two solid phases separated by an interface can be independent [4]. During the fabrication and processing of film-substrate layered structures, such as chemical vapour deposition, wafer bonding, sputtering, doping/diffusion, implantation, thermal annealing process, heteroepitaxial film growth etc., defects like dislocation, twin, cavities etc appear.…”