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Thickness dependent critical strain in Cu films adherent to polymer substrate

For the polymer-supported metal thin films that are finding increasing applications, the critical strain to nucleate microcracks ( εc ) should be more meaningful than the generally measured rupture strain. In this paper, we develop both electrical resistance method and microcrack analyzing method to determine εc of polymer-supported Cu films simply but precisely. Significant thickness dependence has been clearly revealed for εc of the polymer-supported Cu films, i.e., thinner is the film lower is εc . This dependence is suggested to cause by the constraint effect of refining grain size on the dislocation movability.


Nanshu Lu's picture

Dear Rongmei,

Congratulations to your new paper and thanks so much for sharing with us. It is very nice work and exactly what I am looking for. I just had a glance and have two questions needing your help,

1. How do you define and measure the crack density?

2. To obtain Cu yield strength did you take the tensile system compliance into account? What Young's modulus for film Cu did you get?

I'll read it more carefully later.



Teng Li's picture


Nice work!

The cracking onset strain εc is small for thinner films, which have smaller grains. It will be interested to anneal  the very thin films, say, 60 nm thick films, then measure the cracking onset strain εc for comparison. This will help clarify if εc is actually dependent on grain size or just film thickness.

Your comments are welcome.


Dear prof. Li

    Thanks for your advice. In my experiments, the Cu films have been annealed 2h at 100 degree. Probablly due to the low temperature,it is pity that there were no evident grains growth. Therefore it is still unclear that whether the critical strain depends on grain size or film thickness.  And later i will try this.



Joost Vlassak's picture

Dear Rongmei,

Nice paper - as you know we are working on a similar project. Regarding the thickness dependence of the yield stress, your findings are quite similar to ours. You may want to check the following papers for comparison with your results:

Y. Xiang and J.J. Vlassak, "Bauschinger and size effects in thin-film plasticity", Acta Materialia, 54, 5449-5460 (2006)

L. Nicola, Y. Xiang, J.J. Vlassak, E. Van der Giessen, and A. Needleman, "Plastic deformation of freestanding thin films: experiments and modeling", Journal of The Mechanics and Physics of Solids, 54 (10), 2089-2110 (2006)

Y. Xiang, T.Y. Tsui, and J. J. Vlassak, "The Mechanical Properties of Freestanding Electroplated Cu Thin Films", Journal of Materials Research, 21 (6), (2006)

It seems to me that the constraint imposed by the polyimide is not very strong. As a result, your films would behave more like freestanding films than films on a stiff substrate - at least in terms of yield stress. In that case, grain size strengthening is the main strengthening effect as you correctly point out in your paper.

Joost J. Vlassak

Dear Prof. Vlassak

Thanks very much for your interests. It's my pleasure and fortunate as a learner to discuss with you!

1. If strong constraint means well interface cohesion, and the reverse?

2. If the constraint imposed by the substrate is strong, in what case does the film thickness strengthening effect play the dominant role in film strength.

I have a different view, as follows:

Firstly, in terms of yield stress, it is often assumed that both grain size and film thickness contribute to the yield stress. And in my test, the grain is very fine, and I found films strength is more dependent on grain size. By this, could you consider it is not strong constraint?

Secondly, from the big rupture strains the films could bear and images of films under big strains with no buckling, it may be strong evidence of well interface cohesion.

Accordingly, the constraint is strong.



Joost Vlassak's picture

Hi Rongmei,

Actually, what we are saying is not very different, but we are using slightly different terminology. The adhesion of the metalfilm to the polyimide certainly seems strong enough to suppress any localization of plastic deformation or delamination. The large rupture strains are clear evidence of that.

It is not so clear, however, how strong a constraint the polyimide is when we are talking about individual dislocations or dislocation pile-ups. It's been our observation that the yield stress of Cu films depends mainly on the grain size if there are no constraints for dislocations to exit the film. If there are constraints, e.g., in the form of a very stiff layer that repels dislocations, then this layer causes back stresses that causes the offset yield stress to increase with decreasing film thickness - that was the point I made in my previous comment. This argument of course only holds if the grain size is on the order of the film thickness or larger.

If you observe that the yield stress of your films depends mainly on grain size (and the grain size is about the film thickness) and not so much on film thickness, I would argue that the polyimide does not cause significant back stresses and from that point of view the constraint imposed by the polyimide is not very strong. Given the compliance of the polyimide, that seems like a fairly reasonable statement to me.

Joost J. Vlassak

Henry Tan's picture

How to relate the microcracks, measured by Niu et al. base on the changes in electrical resistance of films, to the cracks modeled by Lu et al. that lies at the interface between the thin-film and the polymer matrix?

Niu’s cracks are in the thin-films, while Lu’s cracks are at the interfaces. They are not the same.

Oleksandr Glushko's picture

Hello all!

More than 4 years passed since the last post but i'll try anyway...

 I think there is either a small mistake in the paper or i do not understand something.

Im talking about this passage(page 5, bottom):

"Two distinct regions could be clearly seen in the ΔR/R0 vs ε curves. In the first region, the films will elastically deform with conserved volume. However, the change in form (lengthening, decrease of cross-section) leads to a change in  ΔR/R0 with strain. Because no damage exist,  ΔR/R0 increases linearly with ε in this region."

 As i understand,

1. elastic deformation with conserved volume is possible ONLY if the poisson factor of the strained materials equals 0.5.

2. if the volume is conserved then ΔR/R0=2ε+ε2(ε is strain), i.e. it is not linear but quadraric

3. but if the first-order volumetric change (elastic regime) is assumed, i.e. ΔV/V=(1-2ν)ε then the resistance will really grow linearly with the strain ΔR/R0=(1+2ν)ε

Thus, before cracks come, the resistance growth can be either linear which means elastic deformation of Cu or quadratic which means volume conservation. As i understand it, at least.

We have discussed this issue shortly  with Nanshu Lu:

I would really appreciate if somebody will comment on this.

Thank you!

Best regards,


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