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Plastic deformation of freestanding thin films: Experiments and modeling

Joost Vlassak's picture

This is a paper we recently published in JMPS on a study of the mechanical properties on thin films comparing experimental results with discrete dislocation simulations. It provides insight in the strengthening that occurs in thin metal films when surface or interface effects become important.

The abstract is below; the full paper can be downloaded from here

Abstract - Experimental measurements and computational results for the evolution of plastic deformation in freestanding thin films are compared. In the experiments, the stress–strain response of two sets of Cu films is determined in the plane-strain bulge test. One set of samples consists of electroplated Cu films, while the other set is sputter-deposited. Unpassivated films, films passivated on one side and films passivated on both sides are considered. The calculations are carried out within a two-dimensional plane strain framework with the dislocations modeled as line singularities in an isotropic elastic solid. The film is modeled by a unit cell consisting of eight grains, each of which has three slip systems. The film is initially free of dislocations which then nucleate from a specified distribution of Frank–Read sources. The grain boundaries and any film-passivation layer interfaces are taken to be impenetrable to dislocations. Both the experiments and the computations show: (i) a flow strength for the passivated films that is greater than for the unpassivated films and (ii) hysteresis and a Bauschinger effect that increases with increasing pre-strain for passivated films, while for unpassivated films hysteresis and a Bauschinger effect are small or absent. Furthermore, the experimental measurements and computational results for the 0.2% offset yield strength stress, and the evolution of hysteresis and of the Bauschinger effect are in good quantitative agreement.


Hello Professor Vlassak,

Are the Cu grains in electroplated and sputter-deposited thin films typically random or is there an orientation relation to the deposit direction?




Bill Walsh

Joost Vlassak's picture

Dear Bill,

Very often there is a preferred orientation with respect to the substrate as a result of interfacial effects and strain energy. Fcc materials often have a <111> preferred orientation because the {111} planes have a relatively low surface energy. As the film grows thicker, the interfacial effects become less important. For elastically anisotropic materials like Cu, there may be effects of the strain energy effect in the film, which often promote a <100> type texture in fcc materials.

The effects of the deposition direction, e.g., when the sputter target or electric field is inclined with respect to the substrate, are more complex. Depending on the deposition conditions, geometric effects such as self-shadowing may become important, as well as sputtering by fast ions (e.g., when doing reactive sputtering). And those would certainly have an effect of grain morphology and on the orientation (both in-plane and out of plane).


Julia R. Greer's picture

This is a very good and useful paper for those of us working with dislocations near free surfaces. We also performed some experiments on passivated and unpassivated pillars, and our results on uniaxial compression of <111>-oriented gold nano-pillars with and without a surface layer (passivation) show a similar trend. We also see a 1/h scaling of the flow strength vs. pillar size, with the slope of the passivated samples being 2X greater than that for the uncoated samples. We observe similar stress-strain curves although in compression there does not seem to be a strong Bauschinger effect. Perhaps this is due to the instrumental factors.

Julia R. Greer

Julia Rosolovsky Greer

Joost Vlassak's picture

Hi Julia,

Thanks for your comments. I am glad to hear that your experiments confirm our observations. Given the many grain boundaries in our samples, I wouldn't expect dislocation starvation to play an important role in our experiments. Single-crystal pillars are of course an entirely different matter, even though the surface plays an important role in those also. How did you passivate your Au pillars?

It may be a bit difficult to model your pillars with the approach we used in our paper since that approach only applies to plane-strain conditions. Mort Gurtin and Lallit Anand have been working on a continuum version specifically for single crystal plasticity that may be applicable.

Joost J. Vlassak


Thanks for your reply.  I do not have experience in thin films, but, I've been curious on the effects of elastic anisotropy, especially in highly anisotropic materials such as copper, on mechanical surface response.  For instance, if an unpassivated thin copper film is relatively equiaxed and has a preffered orientation throughout its thickness, a tensile load applied to the film would behave much like a single crystal of that orientation.  All the grains composing the film deform in concert.  If the texture is random, however, the deformation in adjacent randomly oriented grains result in incompatibilities at the grain boundaries.  In the interior, the stresses resulting from the deformation incompatibilities are accomadted, but at the free surace, stress components normal the surface are zero.  The surface cannot accomadate the general stress components that interior is capable of, and therefore doesn't.  Less of the total tensile load is carried on the surface layer than in the interior.  This effect is probably insignificant in large bulk samples, but in thin films consisting of only a few grain layers, the effect might be noticible.  The plastic deformation following the elastic loading may result in a pattern of interior grains deform by slip first and surface grains follow.

To your knowledge, has this idea ever been looked at in thin films?


 Bill Walsh

Joost Vlassak's picture


You're making a point that is quite similar to an argument that Marc Geers at the University of Eindhoven made to me some time ago. The surface reduces the constraint on grains in the film and one would expect a weakening of the film as the film thickness approaches the grain size.

We haven't specifically looked for this effect in our experiments. Some time ago we did run a series of experiments in which we tried to keep the grain size of a film constant while changing the film thickness. This is the type of experiments one would have to run to measure this effect. As the film thickness went down, we noticed that the yield stress of films with grains that were slightly smaller than the film thickness was indeed a bit lower than expected, but it was hard to say if that decrease was significant or if it was due to the constraint effect.

Joost J. Vlassak

Hello Joost,

Thanks for sharing the results of film tests.

I agree that the reduced constraint at the surface has an effect of weakening a film and it is trying to understand why that intrests me.

In the elastic range, reduced constraint simply means that material adjacent to the surface is allowed to deform laterally due to an axial load where the material on the interior must deform respecting compatibility with adjacent material. For single crystals or poycrystals with strong orientation, there is no effect since all material moves in concert anyway.

For polycrystals with random orientation, lateral deformation at the surface from grain to grain will vary, some more than the average, some less, so overall elastic deformation at the surface will not differ greatly from the interior deformation.

The inablity to support normal and shear stress at the surface is the interesting effect. Again for single crystals and polycrystals with strong orienentation, all deformation acting in concert means no stress gradients within the material. For randomly oriented polycrystals, the incompatible deformations at grain boundaries result in local stress gradients which decay within the grain to the grains unique stress tensor, different form it's neighbors. The same occurs at the surface grain, however the surface facet cannot support stress so it does not. The surface layer of grains support less load, or are less stressed than interior grains.

At larger thicknesses, the effect would be imperceptible. As the grains become thinner, as in your experiments, in the elastic range, the film offers less resistance to an axial strain, resulting in a decreased apparent modulus.

If this reasoning is correct, randomly oreineted films would yield first in the interior. Even with dislocations escaping at the surface, it might be possible that the surface inelastic deformations are still less than the interior.

Again, the concept of interest is that there may exist a gradeint of inelastic strain with less plastic strain at the surface. This seems to be contrary to most of the thought regarding plasticity at surfaces and reduced constraint where it is assumed that the surface has greater plastic strain. Of course this is very difficult to measure.

Thanks for your correspondance. I've found the subject very interesting.

Bill Walsh

 dear all professor, i have a question about magnetron-sputtering copper films on PI substrate. the sputtering temperature is about below 100 degree, and deposition rate is about 8nm/min.The copper films have no evident texture, and the average grain size is about 50nm in 500-thick films. What i puzzled is the often observed twin or stacking fault in the larger grains. Does these twins result form strain during the deposition, just as the deformation twinning fromed in nano-Al or Ni?


Joost Vlassak's picture

Dear Mei Niu,

Copper doesn't usually form twins during deformation, except under very severe conditions. The twins you observe in these films are growth twins, i.e., a defect that occurs as atoms break the ABC stacking sequence of an fcc material as they are being deposited. This is a fairly common occurance in electroplated Cu, but also happens in sputtered Cu.

Joost J. Vlassak

dear prof. Joost, thanks for your reply.

Saurabh Puri's picture

Dear Prof. Vlassak, I have a question regarding Figure 10(b) in the paper. Can you please tell me what criterion do you use to decide the strain at which you stop the unloading and start reloading. In Figure 10(a) it seems like you go to zero stress in the unloading cycle before reloading but i am not able to sort this out for the case with film thickness of 0.6 micron (Figure 10b).




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