Substrate-Influenced Thermo-Mechanical Fatigue of Copper Metallizations: Limits of Stoney’s Equation

Abstract

Rapid progress in the reduction of substrate thickness for silicon-based microelectronics leads to a significant reduction of the device bending stiffness and the need to address its implication for the thermo-mechanical fatigue behavior of metallization layers. Results on 5 µm thick Cu films reveal a strong substrate thickness-dependent microstructural evolution. Substrates with hs = 323 and 220 µm showed that the Cu microstructure exhibits accelerated grain growth and surface roughening. Moreover, curvature-strain data indicates that Stoney’s simplified curvature-stress relation is not valid for thin substrates with regard to the expected strains, but can be addressed using more sophisticated plate bending theories.

Warpage Behavior on Silicon Semiconductor Device: The Impact of Thick Copper Metallization

“…Two analytical approaches aimed to predict stress and warpage are described in this section. Stoney's equation [22,27,28] are commonly used as reference. This formula is developed for "membrane-like" geometries made by two materials, such as the system made by semiconductor wafer and ECD metal, in which one layer (in our case, ECD Cu) is much thinner than other.…”

Novel Approach for Assessing Cyclic Thermomechanical Behavior of Multilayered Structures

“…Even though no physical contact, e.g., with an indenter is made, this kind of experimental setup is called "thermomechanical" throughout literature. [7][8][9][10] Using a beam geometry and expanding on an elastic 2D model, the resulting stack curvature at the examined temperature enables to assess the internal stress and strain state of the respective layers. [11] The gathered information provides an understanding of maximum stress differences at interfaces as well as possible elastic-plastic responses of the material system, which, in the case of the presented experiments, is a well-known combination of Si, WTi, and Cu which is frequently used in microelectronic applications as substrate, diffusion barrier, and metallization layer, respectively.…”

“…Bigl et al investigated the thermomechanical high-cycle fatigue properties starting with the Cu film and extending their attention to the entire material system (also refer to Sample A therein). [8,9,23,24] Furthermore, the WTi layer has been examined regarding its residual stresses and thermal stability. [10,20,25] More recently, attention was placed on the properties of the interfaces, especially during fracture toughness experiments and cyclic heating.…”

“…and twin boundary migration. [8] Thousands of short pulses using either an infrared furnace, [12] ultrasonic resonance, [29] or resistive heating of a polycrystalline Si layer [30] were utilized for these experiments. Using only three cycles in the work herein presented, we want to understand the origins of the governing deformation mechanisms, which we presume lie in the internal stress-strain states.…”

“…Even though no physical contact, e.g., with an indenter is made, this kind of experimental setup is called “thermomechanical” throughout literature. [ 7–10 ] Using a beam geometry and expanding on an elastic 2D model, the resulting stack curvature at the examined temperature enables to assess the internal stress and strain state of the respective layers. [ 11 ]…”