iMechanica - channel crack - Comments

journal paper submitted

Rui Huang — Fri, 07 Dec 2007 23:28:05 -0500

A renovated version of this work has been submitted to International Journal of Fracture.

Zhen,

Yaoyu Pang — Wed, 11 Apr 2007 01:30:46 -0400

Zhen,

In the present work, we actually considered the coupling situation for steady state channel cracking, putting aside any complexities around the crack fronts and scenarios during the intermediate stage. So a 2D plane strain FEM model was set up and calculated, which I think is quite different from what N.Cordero have been doing.

But you did raise some interesting issues. Thanks for your nice input.

crack front morphology

Zhen Zhang — Tue, 10 Apr 2007 17:42:19 -0400

Hi, Yaoyu, this is a very nice work. When N. Cordero studied the channel cracking in hermetic coating for flexible electronics, we realized that we needed to do more to consider the coupling of channel cracking and interfacial delamination. Otherwise, the deformation in substrate around the channel crack front on the interface is too large and distorted, which is easily observed in FEM. Now you did this nice work before we move forward. And this is a nice paper.

Besides, I want to ask a question: how can you verify the whole crack front morphology, including the channeling front and the delaminated front, esp. around the vicinity of channeling crack front? You assume the shape is like that in Fig.1(b). Of course, your method circumvents this subtlety. I am just curious if you considered this point?

Thanks for input from industry

Juil Yoon — Mon, 15 Jan 2007 15:55:08 -0500

Jie-Hua, thank you very much for your comment.

The comments from industry guys, like you, give me confidence and motivation to do more things. I know the industry people want simple solutions. Sure, we can approximate this function fa,fb,fc and fb. But we need more calculations for us to convince and may need to experimental data to compare.

Anyway, we'll keep going and hopefully want to report soon.

Thank you.

design window

Jie-Hua Zhao — Mon, 15 Jan 2007 14:52:09 -0500

The design window presented in Figure 5 of this paper is particularly helpful to the engineers. Zhigang and his group have been paying a lot of attention to explanation of the phenomena observed in industry, such as metal ratcheting in Al interconnects, electromigration failure, and providing simple solutions. This is another good example.

For practical purpose, if the function forms of fa, fb, fc and fd calculated by ABAQUS can be expressed as some kind of approximation, say polynomials, it will be more helpful to industry practitioners.

Channel cracks: reports from TI, Intel and IBM

Zhigang Suo — Thu, 02 Nov 2006 22:10:38 -0500

Now iMechanica has papers on channel cracks in low k dielectrics from several companies: IBM (this post), Intel, and TI. It is fascinating to see how research in mechanics finds creative use in industries.

I first learned about the mechanics of such cracks from Budiansky, and applied it to cracking in layered composites. I didn't know such cracks in composites already had a name: they were called transverse cracks. Instead, I called them tunneling cracks. People liked the name. I even called cracks in thin films tunneling cracks. John Hutchinson corrected my usage: transversely spreading cracks in thin films should be called channeling cracks.

Jack Beuth did the first comprehensive analysis of channel cracks in early 90s as part of his thesis work under John Hutchinson. Perhaps it was Qing Ma at Intel, in late 90s, first applied this concept to thin films in microelectronic industry. These and other references are cited in the above three papers.

Unfortunately flaw size does not scale down

Xiao-Yan Gong — Thu, 05 Oct 2006 19:22:58 -0400

I think we all admit that flaws exist. The issue is that the flaw size does not scale down as device dimension goes down. Therefore the similarity doesn't really exist. It's relatively easy to detect a flaw of meter or even mm size, but it is hard when the critical flaw size goes down to microns. (It may be easier to say it now after they've done it. :-))

We were (at least, I was) told that to develop a fatigue crack growth rate curve down to micro scale is very difficult when we were pushing the durability assessment into this direction. However, nobody said just because it was difficult, it couldn't be done.

I think the real questions are:

1. Is there anything more effective? I am a true believer in that there is not. Because "Statistics Doesn't Tell Science". However, knowing that the flaw size will be a factor, how do we extend the traditional flaw tolerant fatigue assessment into the small scale? At least there is one more variable need be included, i.e., the flaw size. Anything else do we miss?

2. Suppose that we worked out the experiment and computation methods and proved that the flaw tolerant assessment applies to small scale structures and nonlinear materials. Is the technology mature enough to build instruments to detect these flaws? If so, industry would love to see the case studies and they may want to standardize it.

Xiao-Yan Gong, PhD

Similarity, scaling and mechanics

Ravi-Chandar — Thu, 05 Oct 2006 12:13:10 -0400

Both Jun He and Xiao-Yan Gong bring to the table a list of real challenges in the microelectronic and biomedical industries; these challenges are at the periphery of traditional mechanics - how do you characterize, define and detect flaws, how do you determine appropriate residual stress distributions in complex structures, how do you account for statistical variabilities in geometry, constitutive, fracture, and interfacial properties, etc - but many mechanicians work on these problems intensively. (Incidentally, the point of my previous comment was that these are the real issues and not the computational cost of calculating the stress field and energy release rates). The upshot is, of course, that if we can do all these, we will still use traditional continuum mechanics, fracture mechanics, fatigue limits, etc to estimate reliability.

The beauty of mechanics is that when the underlying similarity and scaling are elucidated, such applications are automatic. The facts that the absolute length scale of the device is small or large, that they are in benign or hostile environments, subjected to deterministic or stochastic loading etc, while different in each practical application, and technologically important, is irrelevant from the point of view of mechanics; of course, one has to account for the appropriate deformation mechansims, force interactions, microstructural effects, statistical variability etc.

So, perhaps we need to focus more on how to handle above mentioned uncertainties better. Engineers in the aerospace, nuclear and other industries do not demand that their structures/machines/devices be defect free; they admit material/structural variabilities and design their artifacts to be flaw-tolerant - a practical strategy to work around the uncertainties. Can the designers of microelectronic and biomedical devices develop such strategies? There might be an impulse to say no, but consider that biological entities - at many scales: cells, tissues, organs, organisms - are flaw tolerant as well. I fully recognize that the flaw tolerance strategies may not be the same in each application, but there ought to be pathways to explore in each case.

Time to think before testing and ... modeling?!

Xiao-Yan Gong — Tue, 03 Oct 2006 00:30:37 -0400

I've just realized how much fun I missed. These are wonderful discussions and I'd like to add a few comments for medical device and implant industry.

People always point us to aerospace industry just like what they did to electronics industry every time when reliability becomes an issue. Truth is, every industry has its uniqueness. The medical implant industry are in the fast pace of transfering open surgery into minimally invasive surgery that the implant, such as stents and heart valves today are sub-milimeter length scale. No, we are not micron or nano yet, but the scale is small enough to share exactly the challenges that electronics industry has. So Jun, job well done.

Often, flaws are difficult to detect. Processing created cracks are closed because of residue stress. What proof test can we do on metals to ensure the critical flaw size is below the threshold if there is one. Simulation run into wall for convergence issues due to nonlinearity. It's an art to compute the J-integral for very small cracks with substantial material property changes during cycling, let alone the material constitutive law remains questionable. These are a few examples of our challenges, sounds familiar? Luckily mechanics reamins and good news is that this is our great opportunity to make a difference as computationlists, theoretists and experimentalits. I strongly believe that today, we need work together to customize the experiements so that we can predict next experiement or learn something in the future. A test is only as good as a test without a fully understanding to expand its implication beyond.

Recent poll from industry in regarding predcition of Nitinol fatigue, 9 out 10 voted negative. We have a long way to go, but I am sure we are glad to be accompnied by electronics industry.

Xiao-Yan

Fracture Mechanics in Aerospace versus Microelectronic fields

Jun He — Sat, 30 Sep 2006 15:38:14 -0400

Ravi’s comparison of aerospace vs. chip level interconnect is a interesting one and here is some of my thoughts.

Being a UCSB graduate back in, arguably, the golden age of ceramic matrix composite, I agree that fracture mechanics computation in aerospace is very advanced and capable of solving complicate problem. One of key difference, however, is the scale. With interconnect dimension at 10s of nm, most of conventional characterization methods for mechanical properties including ones designed for "thin film" are no longer applicable. As John correctly pointed out, even a complex CAD model usually runs faster than experiments once properly formulated. The problem is that it usually takes more efforts to do a detail property mapping, which is required for accurate model prediction, than measure the end response of a fully integrated structure.

The other big challenge in nano-scale fracture mechanics is the characterization of "flaw". Every time I try to persuade one of our process engineer that his or her process step is responsible for cracking or delamination due to defects, the typical reply is what do these “flaws” look like and how to detect them during process. Unfortunately, this is a rather complicated question. The “flaw” in interconnect is not a small crack/delamination can be detected optically or even under SEM. They can be local topology leads to stress concentration, contaminates changing local chemistry or subtle composition gradient on nano-scale, most of those are only visible under TEM. So detailed characterizations are not feasible compare to large scale electrical testing of the fully integrated structures.

When Zhigang and I advocated large scale testing of fully integrated structures, one fact to keep in mind is industry has been doing large scaled product qualification for various other purposes such as functionality, performance and process window. So it is not prohibitly expensive to add some test structures to measure the end response of fracture behavior electrically. Put all those infrastructures just for mechanical characterization is an entirely different matter.

Thank you for such thoughtful comments

Zhigang Suo — Wed, 27 Sep 2006 20:57:39 -0400

I am grateful for all your perceptive comments.

I have just pasted part of the abstract of the original paper into the post as the last paragraph, so that people who do not have time to read the full paper can still get a rough idea.

Ting Tsui, of Texas Instruments, has also uploaded a paper on channel cracks, which contains several beautimicrographsaphs. Students of fracture mechanics must love to see them.

Computational "expense" could mean many things

John E. Dolbow — Wed, 27 Sep 2006 12:16:51 -0400

I've been following this discussion from afar, and it seems like a good time to throw my hat in the ring on this issue.

As an undegraduate, I was involved in a research project sponsored by IBM to examine the failure of some of their high-density interconnect devices. This was in the early-mid nineties. The project resulted in two publications, one examining the relationship between material properties and the formation of stress in the three-dimensional structures (online here), and another developing the interaction integral for curved cracks on bimaterial interfaces (online here).

Since that time, there have certainly been a number of advances in computational fracture mechanics for material interfaces and etc. Nonetheless, if we consider a three-dimensional interconnect structure and randomly seeded flaws (even if the state of residual stress is known), I would still consider this to be an expensive calculation to perform with existing commercial software.

We need to remember that this involves careful mesh generation and construction, a process that by itself can be quite time-consuming. I believe that many of these CAD->mesh packages that are used to design such structures are not necessarily well suited to introduce flaws into the geometry. The nature of the singularity, particularly with bimaterial interfaces, does require quite a bit of local refinement to attain spatial convergence. Further, few packages have the capability to adaptively refine the mesh as flaws propagate (although I'm not convinced this would necessarily need to be part of a reliability analysis).

So would these calculations be prohibitively expensive? Perhaps not. Certainly such calculations can be performed, but I'd be a little surprised if they could be effected in a matter of days. For industry, expense is often intimately tied to person-hours. Along these same lines, however, I guess I would be surprised if the experimental characterization described here would not also require quite a bit of time to complete?

More experiments needed?

Ravi-Chandar — Tue, 26 Sep 2006 23:13:15 -0400

It seems to me that the problem does not lie in the experimental arena. The industry is able to fabricate complicated 3D architectures at will. Perhaps they can even control the residual stress distribution (I am not certain that they do this actively, but I can imagine ways in which to accomplish this). Certainly for purposes of mateiral property characterization, controlled cracks can be introduced at specific locations and other randomly located cracks generated indavertently. Tracking of (interior) crack growth may be a challenging task, but from comments above, not a pipe dream. So, subcritical v-G curves or critical fracture energy Gamma can all be determined, if only with "massive testing".

From the point of view of theoretical fracture mechanics, concepts of cohesive crack growth, interfacial fracture, kinking or penetration across an interface are all reasonably well understood (except for some esoteric residual problems).

So, the difficulty of applying fracture mechanics ideas to "prediction" of reliability must lie in computing the correct quantities. Rui tells me that it is extremely diffficult to calculate the energy release rates in these structures with finite element packages. The difficulty may be twofold

first that the computations are quite complex and expensive. I do not believe that this is the case. Simulations in other industries - aerospace, automobile, power, oil exploration and production - tackle problems of equal complexity, with millions of degrees of freedom, routinely.
second, and potentially a more serious problem, not knowing how to formulate the correct (appropriate) computational problem. The structure is heavily residually stressed and one does not really have a handle on the detailed spatial distribution of residual stress. While some steps in the processing such as deposition of different materials can be handled appropriately, other processes such as CMP are not modeled as cleanly. In such circumstances, crack nucleation sites are not readily identified.

Since residual stresses and cracks are intimately related, not knowing the initial state of the structure may pose about the most serious challenge to predictive application of fracture mechanics. Experiments (not tests) may still play a crucial role in sorting out this issue, but we don't have to be Edisonian about it.

The value of mechanics research in the world of massive testing

Zhigang Suo — Sun, 24 Sep 2006 10:49:32 -0400

Rui:

Is there any value of mechanics research in the world of massive testing? Perhaps we should let our industrial colleagues speak to this, or ask your colleague Paul Ho, who has more and stronger ties with industries, to comment. But to me, the answer is a clear YES. From this paper under discussion, we can already make several remarks:

A better understanding is always valuable. Just because you can observe a phenomenon or measure a quantity is no reason to stop asking why things happen the way they do. In writing this paper, Jun, Jessica and I have gone through many rounds of discussion, many of which are concerned with basic mechanics understanding.
The method is based on past mechanics research. Although this work does not invent any new mechanics, it uses fracture mechanics at a fundamental level. Past research in formulating fracture mechanics and in understanding moisture-assisted cracking provided the foundation for our method. By inference, basic mechanics research done today will help solving practical problems in the future.
The method also points out new opportunity in mechanics research. One idea we discussed in the paper is that our method may provide a new approach to determining material properties at small scales. G sensitively depends on the properties of the materials surrounding a crack. We now have a way to measure G. We can use measured G to determine material properties if we know how G relates to the material properties. This last link requires careful design of experiments and accurate mechanics calculation. In principle, this method can measure mechanical properties at very small scales, e.g., for films of a few atomic layers.
How to interpret accelerated tests is a good question of mechanics. The method is only good if the crack velocity is measurable. It means that you have to accelerate the test, perhaps by increasing temperature, humidity, or load. How to predict lifetime under service conditions has always been a playground for mechanics research.

I am repeating things that you already know, and the conclusion must be what you want to hear: Yes, mechanics research is valuable in the world of massive testing. Massive testing simply provides a new context to do mechanics research.

pushing from both ends

Rui Huang — Sun, 24 Sep 2006 00:04:38 -0400

Jun:

Thanks for your clarifications. I can understand the difficulty and inaccuracry in computational calculation of crack driving force, and now have learned more about the possibility and limitations in experimental methods from Ting and you. It appears to me there is no perfect solution at this point. On the other hand, the microelectronics industry has been doing well for many years with the empirical methods and some inaccurate calculations. Does it make sense to make any effort to improve on the accuracy of the calculations and to better design the experiments with lower overhead? Maybe the best to do is pushing from both ends and making some compromise in between? I have no idea. From the industry point of view, is there anything academics can do to help in this regards?

Seems like I have endless questions. I will tell you why later. Thanks.