1. Delamination of stiff islands on stretchable substrates
Zhigang Suo
Harvard University
Lu, Yoon, Suo
Int. J. Mater. Res. 98, 717 (2007)

2. The future of knowledge?
Information
Display

3. Flexible electronics Mechanical Challenges Metal fatigue Coating
Polymer substrate
Hermetic coating
Mechanical
Challenges
Usually devices such as organic light-emitting diodes are easy to degrade when exposed to air. So hermetic coatings are needed to prevent air and moisture. As we can expect, there are lots of mechanical challenges regarding to such a structure.
The first challenge is the critical size of stiff islands, which limits the number of electronics can be fabricated on it. Islands may fail from self-cracking or delamination from the polymer substrate. My main topic in this presentation will be island debonding.
The second challenge is the stretchability and functionality of metal thin film on polymer substrate. My senior group member Teng Li mainly did research on this. I am going to do some experiments to try to improve the strechability of Cu thin film on Kapton substrate in Joost’s lab.
Failure is also easy to occur at island-interconnect crossovers and multilayer hermetic coatings. These challenges will remain to be potential future research topics.
Island
debond
Metal fatigue
Coating
crack
Island
crack

4. Island debond No debond at 25% strain Debond at 5.6% strain
The motivation of studying critical island size comes from two seemingly inconsistent experimental results. Regarding to island/substrate systems, there are two candidates for flexible electronics. One is SiN thin film on Kapton substrate, with modulus ratio of The other is DLC thin film deposited on PDMS substrate, with modulus ratio less than 10-5.
People found delamination and slip occurred at 5.6% strain for 40X40um2 SiN islands on Kapton substrate; while on the other hand Lacour found 200x200um2 DLC islands on PDMS substrate remained intact even under 25% strain. The apparent key difference of these two structures is the substrate to island modulus ratio. When elastic mismatch is smaller, the island is more susceptible to debonding. We would like to find out why is this and consequently how to determine the critical island size.
Debond at 5.6% strain
No debond at 25% strain
Bhattacharya, Salomon & Wagner, 2006
Lacour, Wagner, Narayan, Li, Suo, 2006

5. Energy release rate depends on flaw size
This is a typical energy release rate curve for 2D island debonding. In the x axis we use a to denote the crack length. When a is small or comparable to the island thickness, we call it initial stage. When a is bigger, sometimes steady state is reached, in which case we should have a plateau here; most times we do not have steady state, so we call it transitional stage in general. When a is extremely large so that the bonded portion is small compared to the island thickness we call it convergent debonding. Finally the whole structure is failed. In the following presentation I will talk these three stages one by one.
Design criterion

6. Initiation
Here we plot the two singular exponents as functions of island/substrate modulus ratio. From the plot we can see while lambda1 is always close to 0.5, lambda2 approaches zero as the island is much softer than the substrate. When the island is rigid, namely Ei/Es goes to infinity, there’s no difference between the 90 wedge and the interface cracking, hence those two exponents degrade into the same number, 0.5.

7. Steady state h G a
Gss
Split singularity method breaks down when a/h becomes large. The interface crack then enters our so-called transitional stage. A special case of transitional stage is the steady state. Steady state requires the crack tip is far away from both film edges and another crack tip, so that the situations are undistinguishable no matter the crack tip is here or here. Energy only released from the debonding portion of the film and it reaches a plateau called Gss in the G~a plot.
Suo and Hutchinson, IJF (1990)

8. Converging debond Ligament length 2c
We immediately recall an analogous problem: collinear periodic cracks. The stress field is solved by Westergaard in And the energy release rate can be easily obtained. For our collinear periodic islands, why not just make a guess? The guessed form is provided here with the prefatory 1/8 comes from the convergent debonding result, namely when ligament length c is much smaller than the period, G is able to recover this result. Then how to prove our hypothesis?
He, Evans & Hutchinson, 1996

9. Effect of substrate compliance on G(a)
When the crack is extremely long and the ligament length L-2a is much smaller than the island thickness, so that it can be viewed as two semi-infinite plane bonded at a ligament length 2c=L-2a, the situation is called convergent debonding. He, Evans and Hutchinson analyzed this case and provided a neat formula. When the substrate is much more compliant than the film, G is reduced to this form. We plot the convergent debonding formula in dashed line here to compare with numerical results. It work quite well when crack length a approaches half island size and the slope reduces as substrate modulus decreases.

10. Gmax overshoots Gss Overshooting Gss
Another phenomenon calls for people’s attention. Take this structure for example, the modulus ratio is 40, dimensions are fixed, the G~a curve is given by ABAQUS calculation. However, what is the Gss for this case? We can see it is well below the maximum energy release rate. We call this overshooting. How to understand this? We should be careful about the source of elastic energy be released. Generally speaking, the energy release rate should be referred to the whole system. But because the substrate is held by prescribed displacements and its modulus is very small, we neglect the energy released from the substrate. But remember, for the film we still have two parts, the debonding portion and the bonded portion. Elastic energy actually release from both of them. For steady state, we only account the energy released from the debonding portion because the bonded portion is infinitely long and cannot deform. However, when the bonded portion is of finite length, when the substrate is compliant, the bonded portion of the stretched film can horizontally shrink a little away from the crack tip and release part of its elastic energy. However, as a grows, the relative contribution from the bonded portion to the detached portion decreases. So that’s why G eventually goes down beneath Gss.
Gss

11. Critical island size
With above results, we are able to determine critical island size. Find out the Gmax for each G~a curve under a fixed modulus ratio and plot each point into the corresponding G~L graph, we can construct a Gmax~L curve for such modulus ratio. We did it for several modulus ratios and have several curves here. If the interface toughness Gamma_i is given, the condition Gmax=Gamma_i represents a horizontal line here. The intersections of this line with various curves predict the critical island size. For islands smaller than this size, it will be safe from interface debonding. With the same interface toughness, more compliant substrate can support larger island.
With the same interface toughness and the same applied strain, more compliant substrate allows larger critical island size

12. Summary Islands debond when exceeding critical size.
Gmax overshoots Gss.
Critical island size is large when the substrate is compliant.
Lu, Yoon, Suo, Int. J. Mater. Res. 98, 717 (2007)