Influence of indenter tip diameter and film thickness on flat indentations into elastic-plastic films by means of the finite element method


The modern trend towards thinner gadgets and therefore thinner materials has presented new challenges, more so, during material fabrication and testing. Specifically, the mechanical robustness of Back End Of Line (BEOL) bond pad stacks has been greatly affected as a result of utilization of porous low-k materials and reduction of the material layer-size thickness. This translates into an increased risk of fracture in the embedded silicon oxide layers especially during electrical wafer testing and wire bonding. Subsequently, fracture is followed by metal migration into the oxide cracks which eventually lead to electrical product failure in field applications. Therefore, in order to avoid such failure, it is imperative that further research be undertaken in order to figure out how input geometrical parameters, namely the indenter tip radius and the film thickness, affect the imprint depth.

Recently, Dresden University of Technology scientists: Professor Cornelia Breitkopf and Angel Ochoa Brezmesa (PhD candidate) from the Institute of Energy Technology at Faculty of Mechanical Engineering investigated finite element models of an imprinting scenario of a flat cylindrical indenter into a thin aluminum elastic-plastic film on a rigid substrate. In doing so, they purposed to unearth how the diameter of the indenter tip and the film thickness affect the imprint depth, as it would present vital information for the correct assessment of mechanical reliability of BEOL structures during wafer testing. Their work is currently published in the research journal, Thin Solid Films.

In brief, the research method employed commenced with finite element analysis of a model of an imprinting scenario of a flat indenter tip into a thin metallic elastic-plastic film on a rigid substrate. Here, they considered solely flat cylindrical indenter tips to ensure analytical simplicity. Next, they assessed the influence of the indenter tip diameter and film thickness on the load-displacement curves. Lastly, they compared the performance of the finite element model they had utilized with previous experimental models used by other researchers.

The authors observed that the ratio of the indenter tip radius(a) to layer thickness(t) clearly affected the normalized indentation depth, when departing from the condition a ≫ t. They also noted that indentations characterized by large ratios of indenter tip radius to layer thickness behaved in a stiffer way in comparison to indentations with lower ratios. This attribute was found to lead to lower imprint depths for the same applied pressure.

In summary, Breitkopf-Brezmesa study presented a thorough review of existing analytical studies regarding flat indentations in thin films on rigid substrates. In general, it was seen that the results obtained from their study, could enable prediction of the effect of needle tip diameter and thickness of the indented pads on the imprint depth. Altogether, Dresden University of Technology researchers presented a fast-forward step in the enhancement of prediction capability of the mechanical reliability during wafer testing and wire bonding that could lead to higher mechanical robustness of BEOL structures.


Angel Ochoa Brezmes, Cornelia Breitkopf. Influence of indenter tip diameter and film thickness on flat indentations into elastic-plastic films by means of the finite element method. Thin Solid Films, volume 653 (2018) page 49–56.

Go To Thin Solid Films

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