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# Chip-package interaction and interfacial delamination

In flip-chip package, the mismatch of thermal expansion coefficients between the silicon die and packaging substrate induces concentrated stress field around the edges and corners of silicon die during assembly, testing and services. The concentrated stresses result in delamination on many interfaces on several levels of structures, in various length scales from tens of nanometers to hundreds of micrometers. A major challenge to model flip-chip packages is the huge variation of length scales, the complexity of microstructures, and diverse materials properties. In this paper, we simplify the structure to be silicon/substrate with wedge configuration, and neglect the small local features of integrated circuits. This macroscopic analysis on package level is generic with whatever small local features, as long as the physical processes of interest occur in the region where the concentrated stress field due to chip-packaging interaction dominates. Because it is the same driving force that motivates all of the flaws. Therefore, the different interface cracks with same size and same orientation but on different interfaces should have similar energy release rates provided that the cracks are much smaller than the macroscopic length. We calculate the energy release rate and the mode angle of crack on the chip-package interface based on the asymptotic linear elastic stress field. In a large range of crack length, the asymptotic solution agrees with finite element calculation very well. We discuss the simplified model and results in context of real applications. In addition, we find that the relation of energy release rate *G* and crack length *a* is not power-law since local mode mixity is dependent of crack length *a*. Therefore, the curve of *G~a* can be wavy and hardly goes to zero even if crack length *a* goes to atomically small. The local mode mixity plays an important role in crack behavior.

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## Comments

## mode mixity w/ and w/o fillet

Zhen,

We consider the packages defective if we don't see proper formation of underfill fillet after underfill dispense, which speaks for the vital role of fillet to the reliability of flip chips.

Apparently the strength of singularity is totally different at die corner in cases of w/ and w/o fillet. In presence of corner defects, w/o fillet, the crack is almost dictated by the opening mode, with fillet the mode is rapidly shifting to shear mode. As you correctly pointed out, the fillet makes the crack much harder to grow.

Charlie

## How about a chip-package corner in 3D?

Dear Zhen,

With interest I read your paper. I find the combination of analytical solutions and numerical modeling very powerful for understanding the basic mechanics in chip-package interactions. We have done many ABAQUS calculations of similar problems, for which I often find it difficult to draw any physical conclusions due to the complexity of the model. Now I think I have a clue to make the calculation more meaningful. For that I thank you.

As powerful as it is, I see one limitation of this work, that is, the 2D consideration. At most, the 2D model simulates the behavior at the edge of the chip, far away from the chip corner, where delamination failure is most likely to occur. I suspect a 3D configuration is required for the stress field near the real corner. Is it possible to develop an asymptotic solution in this case? If yes, it would be very useful, I think.

RH

## 3D corner singularity can be approximated by 2D edge singularity

Dear Rui,

Thank you very much for your interest.

As you pointed out, the delamination failure is most likely to occur at 3D corner, not only for chip-package structure, but also for others, e.g. SiN square pads on strained silicon. In order to avert the complexity of 3D corner singularities, we considered the 2D plain strain problems in our study. But, the 3D corner is more critical than 2D edge and therefore deserves attention. Dunn et al. (JMPS, 2001) had an asymptotic solution for the perfectly 3D corner. Here, we propose a 2D approximate solution for the 3D corner based on the following arguments. Since in practice, the 3D corner is formed by the perpendicular edges of pads on the substrate, and usually rounded with a radius. So it is not a perfectly sharp 3D corner. For example, in SiN pad on strained silicon, the rounded radius is much larger than atomic scale, e.g., 40 nm rounded radius for a 500 nm thick SiN pad in Kammler et al. (APL, 2005). The local stress state close to the root of 3D bimaterial interface is still in plain strain state (maybe this is a vague statement, but at least this is a good approximation). Hence, the singular stress expression of 2D plain strain problem still applies, except that the stress intensity factors need to be modified to include the effects of the stress overlapping from two adjacent edges. Then, the remaining complexity is from the 3D FEM calculation and the curve fitting.

## 2D vs 3D

Zhen:

Very good point. I agree that the 2D solution could serve as a good approximation for rounded 3D corners. In this case, I believe the applicable area of the 2D plane strain solution would be limited by the rounded radius. For a 40 nm rounded corner, this area must be very small. Remember, we still have to take out the area really close to the corner for the k-annulus.

Thank you for the pointer to Dunn et al.'s paper. I should definitely check that out.

RH

## Cohesive Zone Elements

Dear Friend,

I saw your Dissertation and papers and I think that my PhD topic is very similar to yours. Actually I am doing my PhD in Germany at Fraunhofer Institut and my PhD is supported by Robert BOSCH company.

I wnated to ask, If you have any experience about cohesive zone elements. Do you know how you can bring thermal diffusion between to materials in interface?

stay Happy

Hossein Shirangi

## I wish I knew.

Dear Hossein,

Thank you very much for your interest. I am so happy that we have the same interests.

In the problems I considered, there was no coupling of thermal conduction and mechanical failures yet. The only experience with cohesive zone element was described in my thesis, chapter 3. If there is any chance, I would like to do some in the problems you mentioned here.

Zhen

## Interfacial heat transport

Hi Hossein,

Similar as the mechanical cohesive model, what you need is a relation between the heat flux

J, the temperture difference Δθ, and the displacement difference Δx.More serious studies would require well designed experiments. However, as you are asking about the cohesive zone element, I assume that you only need a hand-waving model. Here is one:

If we still assume a linear kinetic law, say

J=kΔθ, but takekas a function of Δx. Physically, we know that k→∞ when Δx=0, and k=0 when Δx>x0, wherex0 is the distance over which the cohesive force is taken to be 0. A simple guess of the functional form would be k = k0 * (x0/Δx- 1), when Δx<x0 and k=0 when Δx>x0. But such singular form might not be usefull in numerical calculation. I would suggest using the form (for Δx<x0)k = A * (

x0 - Δx)nwhere A is a big enough number and n is the index you can tune.

## thanx Wei

Hi Wei,

thanx for your kind answer. It seems that u know alot abou cohesive zone elements.

stay Happy and regards from Germany

Hossein

## a very good idea

Hi, Wei,

Thank you very much for your comment. This is a very good thought. Simple and easy to implement, but also capture the physics. You are always excellent.

Thanks a lot.

Zhen