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The effect of film thickness on the failure strain of polymersupported metal films

Nanshu Lu's picture

We perform uniaxial tensile tests on polyimide-supported copper films with a strong (111) fiber texture and with thicknesses varying from 50 nm to 1 μm. Films with thicknesses below 200 nm fail by intergranular fracture at elongations of only a few percent. Thicker films rupture by ductile transgranular fracture and local debonding from the substrate. The failure strain for transgranular fracture exhibits a maximum for film thicknesses around 500 nm. The transgranular failure mechanism is elucidated by performing finite element simulations that incorporate a cohesive zone along the film/substrate interface. As the film thickness increases from 200 nm to 500 nm, a decrease in the yield stress of the film makes it more difficult for the film to debond from the substrate, thus increasing the failure strain. As the thickness increases beyond 500 nm, however, the fraction of (100) grains in the (111)-textured films increases. On deformation, necking and debonding initiate at the (100) grains, leading to a reduction in the failure strain of the films.


Oleksandr Glushko's picture

Dear Nanshu,
thanks for the really nice paper with a lot of useful information!
A few months ago I've started to work in a project devoted to investigations of mechanical and electrical properties of thin metallic films and metallization lines for flexible electronics. This is a pretty new topic for me, so I'm trying to understand the basics of mechanical and electrical properties of thin cu films.
I've done a set of tensile tests with subsequent SEM characterization on 200 nm Cu films on PET substrate. Some of our samples strained to 30% look very similar to those shown in your paper (Fig. 2c, 200 nm film): transgranular cracking, lots of dislocation slip traces.
But actually I wanted to ask you about the resistance measurements, I would really appreciate if you help me to improve my understanding in it.
1. I do not understand why an assumption of constant volume during straining is applied so widely and why it works so well. Poisson's ratio of copper is 0.3-0.33, thus even in the elastic regime the volume is not constant.
2. From our stress-strain curves I've estimated the yield strain of Cu film+substrate bimaterial which appeared to be around 2 %. SEM pictures confirm that well showing the initiations of localized necks at 2% strain. Thus, after 2% strain it is pretty difficult to provide a theoretical formula for resistance change. But R/R_0=(L/L_0)^2 approximation still works very well! I just don't understand why.
3. What you think is the best way to measure the resistance during a tensile test? I am thinking to put all 4 wires under the grips (two on each side), so one can be sure that the contact is always good and that the distance between the sense wires is changing according to the elongation of the sample.

I would really appreciate if you can help me!

Thanks in advance

Oleksandr Glushko

Nanshu Lu's picture

Dear Oleksandr,

Thank you very much for your interest in our work. I am trying to answer your questions one by one.
1. Upon uniaxial tension, Cu thin films first elongate elastically and then start to yeild at strains of 1%. Within the elastic regime, the volume increase at small strain can be estimated by ΔV/V=(1-2ν)ΔL/L=(1-2*0.3)*1%=0.4%. During plastic deformation, volume conservation is widely accepted because this process involves dislocation mechanisms instead of changes in bond lengths.
2. R/R_0=(L/L_0)^2 relation is an ideal overall electrical resistance-elongation relation obtained assuming a) no volume and b) no resistivity change duing uniaxial tension. In real tests, volume conservation is just discussed in Question 1; scattered, isolated neckings do not change overall thin film resistivity too much either. Only interconneccted microcracks will change the overall film resistivity significantly and that's when the measured resistance starts to deviate from the ideal relation. I also want to point out that for a well-annealed 200nm-thick Cu film well bonded to a 12.7um-thick Kapton film through a 10nm-thick Cr adhesive layer, I could hardly find any necking after stretching by 10% but interconnected microcracks were found after stretching by 15%, at which strain the measured resistance also started to deviate from the ideal relation.
3. I used 4-wires resistance measurement as you described to minimize the contribution from lead wire or contact resistance. If the grips are metal, make sure that the leads are properly insulated from the grips.
Please let me know if you have more questions.



Oleksandr Glushko's picture

Dear Nanshu,
thanks a lot! So, the initial part (elastic deformation) of a resistance change vs. length change should be a straight line. But since the yield strain is normally small (0.5%-2%) the difference between linear and square dependence is negligible. In the figure below the stars show the R/R0=(L/L0)^2 dependence while circles are for the first-order (elastic) volumetric change. During plastic deformation no change in lattice constant is assumed but dislocation generation and slipping. I understand, thanks!
I've already done some resistance measurements which look pretty similar to your published results, see the figure below. All curves are for 200 nm Cu film on PET.
Regarding necking of the films, at 5% strain we already observe what I called "homogeneous necking", see the figure below. Our films are not annealed and have very heterogeneous grain structure.


Hopefully, our discussion is at least a bit interesting for you too.

Thanks for your help!

Best regards,


Nanshu Lu's picture

Hi, Oleksandr,

Thank you very much for the figures. They are great illustrations.

Regarding to the first figure, since metal thin films cannot deform elastically up to 20% so we don't need to compare the circles to the stars at such strains.

For the second figure, if you have corresponding micrographs to show the cracking actually initiates around the strain of deviation, that would be awsome.

I observed very similar neckings for unannealed 200nm Cu film on Kapton substrate as your Figure 3.






Oleksandr Glushko's picture

Hi Nanshu!

the 5% strain example shown in my previous post is a pretty typical one.

The surface after 10% looks like this:

 200 nm copper on PET after 10% strain

and after 15% like this:

200 nm copper on PET after 15% strain


By the way, there is something else that i don't understand. Why nobody is looking on stress-strain curves? Is it too trivial? I mean, even if the thickness of the substrate is ~ 100 times higher than the thickness of the metal film it is still interesting (at least for me) to compare bare substrate to film+substrate. For instance i can say that the yield strength of a film+substrate is higher than that of a bare substrate. Unloading is even more non-trivial: elastic substrate and ductile film, substrate "wants" to stretch back, film - doesn't. Did you observed any bending of your samples after a tensile test?


Best regards!

Nanshu Lu's picture

Hi, Oleksandr,

Thanks for the nice SEMs. The strain for crack initiation is around 10%, which actually matches well with the strain of resistance deviation. That's the point I tried to make in my paper.

You raised very good questions about the stress-strain and reloading behaviours of polymer-supported metal films. We didn't focus on the stress-strain because we wanted to mainly address the stretchability issues which is very pertinent to flexible electronics. I mentioned about the yield strengths of films with various thicknesses in the paper "The effect of film thickness on the failure strain of polymer-supported metal films " but not much about the overall stress-strain behaviour.

During unloading, as you pointed out, the substrate is elastic and recoverable but the elongation in the metal film is irreversible. So I suspect that the films have to deform plastically during the unloading. Although I haven't observed any buckling delamination of the film, I did see two cracked halves overlap onto each other.


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