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tension of cu film on Pi substrate

Dear professor suo I am a master graduate of professor sun jun in xi'an jiaotong university, I have done some research on the tension of cu film on Pi substrate. I have a question about the mechanical behavior of thin film:the range of elastic deformation is enlarged just as the plastic stage in your simulation results, since the mutiple neckings result in improved plasticity of Pi-bonded Cu film.could you give me some advice? many thanks

Zaiwang

Zhigang Suo's picture

Thank you so much for your interest in our work. I'll ask Teng Li to post a preprint of the paper on necking of a thin metal film bonded on a polymeric substrate. Teng "discovered" multiple necking in such a metal film in his FEM simulation. The substrate has to be of some intermediate stiffness. When the substrate is too compliant, the metal film will rupture by forming a single neck. When the substrate is too stiff, the metal film cannot form any neck.  You might have seen a review article on micromechanics on macroelectroncis

While multiple necks have been observed in several situations, as reviewed in our paper, multiple necks have never been observed in experiments with thin metal films. Do you have any experimental evidence? Do let us know if you have specific questions.

The SEM pictures attached here are of a nickel thin film deposited by PLD on a Nafion polymeric substrate. Nafion swells and shrinks dramatically depending on ambient moisture. After the deposition vacuum is broken and ambient moisture is incorporated into the polymer, this dramatic swelling fractured the nickel film as is evident here.

What I find interesting is the falrly regular crack pattern, and the structure of the cracks. I sort of stumbled upon this accidentally while trying to deposit electrodes. I thougt this maybe the right forum to discuss these images.

Ni Thin Film Cracks

Ni Thin Film Cracks

Ni Thin Film Cracks

M.Y. El-Naggar

 

Teng Li's picture

Thanks for sharing these interesting SEM images.  The parallel crack pattern implies the swelling of the polymer in one preferred direction perpendicular to the cracks.  I'm wondering what the dimensions of your specimen are, e.g., film thickness, substrate thickness, aspect ratio, etc. How large about the swelling strain in the polymer?

-Teng 

>>>www.macroelectronics.org<<<

Teng,

I  think you're right about the unidirectional strain. It was unintentional. The substrate was fixed using adhesives on the back during deposition. It is quite possible that it was allowed to bend in one direction more than the other.

The film thickness is between 200 and 300 nm thick. The Nafion substrate is 180 microns thick and is  2 inches in diameter. The hydrolytic property is tricky, because not much (to my knowledge) has been measured between say vacuum and 50% relative humidity. Between 50% RH and being completely water soaked, the linear expansion is 10% !! So I think 10-20 % expansion between vacuum and room humidity is a usable figure.

 

M.Y. El-Naggar

Dear all, thanks for your answering the question by zaiwang. my questions as follows:

1.in professor Li's FEM simulation, the uniform deformation is greatly improved. and how about the elastic stage?

2.neckings occurred along both the thickness and width on the Cu films. in my SEM observations of deformed films, i

wonder if the graph in the attachment is the multiple necks?

Teng Li's picture

I'm on travel, with limited internet access. Just realized I missed the first round of this interesting discussion.
As for your questions:
1. The large uniform deformation of Cu films on PI largely results from its substantial "delocalized" plastic deformation, rather than from its elastic deformation, (which is negligible compared to the plastic strain). By contrast, a freestanding Cu film ruptures by strain localization, e.g., once a neck sets in, it leads to the failure of the film. Therefore the uniform deformation of a freestanding film is only comparable to it elastic limit, which is small.
2. In a real experiment, necking will occur at both thickness and width directions. If the thickness is much smaller than the width, the necking along the width may be negligible. In such case, the assumption of plane strain deformation becomes reasonable, which is adopted in our simulation. In other words, our "numerical" simulation only shows the necking in thickness
direction.
Your SEM image is amazing! They look like multiple necks, at least for my eyes. I'd be very interested if you can give more specs. Can you show an image with necking in both directions?
Again thanks for sharing with us your results.

-Teng 

>>>www.macroelectronics.org<<<

Dear professor Li, thanks for your reply and your recognize of my SEM image! i'am very excited!

The papers of both your and xiang have greatly enlightened me. I have done some experiments about the relationship of  microcracks evolution with thin films thickness, and the SEM image is part of my work. And i'm not sure it is the multiple necks. but at the same time, i'm sure it is! So i want some help from you.

As to what you said about more specific, i do'not know what your mean? why would you consider it similar to the multiple necks? What's your criteria? I am very sorry no images with necking along thickness, for the reason that the PI substrate is isolated, and the cross-section specimens are hard to make.

 

Teng Li's picture

Your SEM image shows multiple locations of local thinning in the Cu film. I'm wondering if you used any adhesion layer between Cu/PI or did any surface treatment of PI. Was the image taken in situ while the sample was still under tension? Have you tried even larger tensile strain to rupture the film? Thanks. 

-Teng 

>>>www.macroelectronics.org<<<

Zhigang Suo's picture

Perhaps I'm missing something.  Do you mean Niu's experiments actually showed local thinning, rather than just fracture?  What is the evidence?

Teng Li's picture

In this image, both local thinning and fracture seem evident.  Her another experimental image also showed both at even higher strain.

Dear Prof.Suo and Li,  thanks for your positive remarks on my work, which encourage me greatly!

But i am also wondering if my opinion in "Local thinning" is right?

Thanks!

Rongmei

Dear Prof. Li, i have made two figures about rupture strains of  films on elastomer according to the datas shown in your papers-- "Deformability of thin metal films on elastomer substrates" International Journal of Solids and Structures 43 (2006) 2351–2363. and "Stretchability of thin metal films on elastomer substrates" APL85(2004). According to the papers, where would be the curve with H/h =200 in the figures? Whether the rupture strain is even larger, according to your simulations?

In addition, how about the rupture strian of a relative thinner film on elastomer? Whether the thinner the films the higher rupture strains is, since "the stiffer or thicker the elastomer substrates, the larger rupture strains".

thanks a lot!

Rongmei

Zhigang Suo's picture

Rongmei:  Please make hyperlinks in your comments pointing to the figures you have posted in iMechanica.  Here is how to make a hyperlink.  It is really easy to do, and will help your readers to navigate and understand what you mean.  Thank you very much.

Teng Li's picture

Rongmei, the rupture strain of a metal film on an elastomer substrate depends on both their relative thickness and stiffness.  If the elastomer is assumed to keep hardening when strained (e.g., as a Neo-Hookean solid), the rupture strain of the metal film will continue increasing as the elastomer stiffness increases.  The increase of rupture strain due to the increase of substrate thickness, however, would become marginal when the thickness ratio is above some critical value.  In other words, further increase of substrate thickness helps little to improve the rupture strain of the film.  While further calculations are necessary to give a more accurate answer to your question, I speculate the rupture strain of the metal film with H(sub)/h(film)=200 will be comparable to that of the metal film with H(sub)/h(film)=50, as shown in Fig.5 in our IJSS paper.  Hope this is helpful.

>>>www.macroelectronics.org<<<

Dear prof.Li, thanks for your replies.

1. Cu films were fabricated by magnetron-sputtered onto PI substrate, and there is nothing between Cu and PI. The interface adhesion is very well, no peel off even after a big deformation as indicated in "High ductility of a metal film adherent on a polymer substrate", (Applied Physics Letters, 87, 161910 (2005)).

2. The image was ex-situ taken. With further deformation, these local thinning would become microcracks and connect with each other zigzagly. Please see the image sent to your email.

3. In addition, i have a different view as the the fracture mode as referred in Xiang ---"the mixture of loacal thinning and intergranular fracture". In this paper, the grains size are not given, which has a important role on the fracture mode. If the grains size are nano-scale, cracks may  be along grain boundaries, while if the grains size in micro-scale or larger, then a intragranular fracture would occur.

4. As to the ductility of Cu films on PI, no matter the thickness or stiffness of metal thin films or substrate, and the interface adhesion, i suppose that constraint between films and substrate are crucial .

Weak constraint would lead to a poor ductility in the form of single necks as the free-standing film: when the film is thick enough to suppress the deformation of PI sub. ,then it would perform as the corresponding bulk; when the film is too thin too effect the PI sub. , it would be enlongated with a higher rate, due to the soft sub., and then fracture at a low strain in a brittle mode, though by the means of multiple cracks on film surfaces.

While strong constraint  is helpful to a larger uniform defromation due to the multiple necks on films surfaces. In such a case, the film and sub. could deform simultaneously, and the interface decohesion could be delayed to a larger strain.

How about you? Do you think so? Please share with me your opinion!

Thanks

Rongmei Niu

Zhigang Suo's picture

Dear Rongmei:

Thank you very much for sending me images of fracture and local thinning of Cu films by email.  They look great and very persuasive!  You and your coauthors have to decide if you wish to post them online. Elsewhere I wrote points concerning copyright.

I agree with all your points above.  Would you please clarify your point 3, a remark on our paper?  I'm not sure what is the difference of views between yours and what were in our paper. 

Best wishes for the new year and say Hi to Prof. Sun.

Dear prof.Suo, Thanks for your replies. What i mean is that when the grain size or film thickness is lower than some critical value, intergranular fracture would be more likely. Grain boundaries deformation (by GBs slinding or emitting partial dislocation)would be dominant in such a small grain size. And Loacal thinning might become less visible with decreasing thickness.I suppose that Xiang's image is more a intergranular fracture than local thinning. 

 

Rongmei

Zhigang Suo's picture

Dear Rongmei:

Thank you very much for this clarification. Xiang's image did show that fracture goes along grain boundaries. However, even in his case, fracture occurred after about 10% strain. You are quite correct that our APL did not produce good evidence for local thinning. Your image of local thinning looks convincing to me, but I'm a theoretician, and would listen to experimentalists like you and Xiang as to whether the image indeed shows local thinning.

Our APL and your work now clearly show that the polyimide substrate allows copper film to go to higher strain than a freestanding film. Our theoretical model suggested this trend. However, the model also suggested that the Cu film can go much higher strain than Xiang and you have observed. So why is this discrepancy?

Here are two possibilities. First, the copper film is not as ductile as we assumed in our calculation. For example, it undergoes intergranular fracture, as shown in Xiang's image. Second, the interface is not as well bonded as we assumed in calculation. Or more likely, the interface has degraded as strain increases. As far as I know, we don't have clear evidence if this interfacial degradation is happening.

Hope further experiments will soon succeed in clarifying this discrepancy between experiment and theory.

Dear Rongmei,

Although not stated explicitly in the paper, the grain size of our Cu films is indeed on the order of tens of nanometers, as shown in Fig. 4(c). This high maganification SEM image of the crack tip clearly indicates a mixture of local thinning and intergranular fracture in the 170-nm-thick Cu film that was stretched to 30%. I agree with you that at larger grain size, interganular fracture would be more difficult. What is the grain size of your Cu films?

Thanks,

Yong

the grain size of my Cu films is about 25nm.

Joost Vlassak's picture

Dear Rongmei,

Could you please explain your comment number 3 regarding the fracture mode? It seems to me that the presence of the substrate suppresses local necking. That does not mean the film cannot fail by another mechanisms such as intergranular fracture. We are currently exploring the failure mechanism in more detail, and in particular we are evaluating the effect of grain size.

 Joost J. Vlassak

Dear Prof. Vlassak, i am very glad to answer your questions! I have read some papers of your group, especially the constraint between films and substrate, which give me a great help, thanks! 

1. it seem to me that the presence of the PI substrate help to form multiple thinning on films surfaces. Beside grains size, local thinning still depends on films thickness with the same flexible substrate, and the degree of thinning and number of necks change with films thickness. The thinner the Cu films, the more invisible the local thinning, and on my 60nm-thick Cu films surfaces, the straight channeling cracks are often, and no evident local thinning;  On my 340nm-thick Cu films surfaces, local thining or pre-necks (verified by Prof. Suo and Li)increase, cracks are zigzag.  And the rupture striain of 60nm-thick films is lower than that of the thicker films(340nm-thick).

2. I suppose that, the films deform and fracture  by intergranular or intragranular depends  greatly on grains size in films. When grain size in the range of about 30nm, the fractrue would be intergranular, and grains boundaries(GBs) distribute large number of atoms and deform by GBs sliding or GB emitting partial dislocation; for sub-micro scale grain size , fractrue by intragranular would be more likely.  

Whether is my view is correct? If wrong, please correct and  help me and share me with yours! Thanks!

Joost Vlassak's picture

Dear Rongmei,

I have no doubt that the failure mechanism changes as you decrease the film thickness. Plastic deformation through dislocation motion becomes increasingly difficult and the importance of grain boundary mechanisms increases. Keep in mind that the substrate postpones the onset of necking, but doesn't necessarily prevent other failure mechanisms. One of my students, Jennifer Furstenau is working on exactly this aspect of the fracture of metal films on polymeric substrates. You may want to contact her at jfursten@fas.harvard.edu.

Joost J. Vlassak

Dear Prof. Suo, i have sent to your an email, and it may be useful.   

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