Hi, everybody, i had one problem. see the attached image.
Does anyone know how to get the strain function or strain energy of the perfect epitaxial film? Or could you recommend some textbooks or references about this topic?
Thank you
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Re: an epitaxial question
The strain in the film is the difference in the lallice constants of the film and the substrate divided by the latice constant of the substrate. A detailed discussion of thin film mechanical behavior is given by professor Nix, of Stanford University.
In reply to Re: an epitaxial question by Zhigang Suo
Dear Professor Suo, Thank
Dear Professor Suo,
Thank you for your reply. I may not make my question clear. Here I try to make this question more clear:
In detail, a cylinder-like simple cubic structure film (height: 500 nm; Diameter: 5nm) is epitaxial grown on a rigid simple cubic structure substrate without any defects except strain. I believe the strain along the radius direction is different: the core part should have a bigger strain than the shell part. Also, the strain along the axial direction is different: the part close the interface is larger than the outside part.
My question is: what is the strain field (strain function or strain distribution) along raidus and axial directions, respectively? An expotential function or others?
Thank you!
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In reply to Dear Professor Suo, Thank by Jian SHI
epitaxial film or needle
I'm puzzeled by the numbers: the height of the film is much larger than the diameter of the film. The object looks like a needle. In this case, the stress in the "film" is zero everywere except near the interface. I don't know who has solved this boundary value problem.
In reply to epitaxial film or needle by Zhigang Suo
You are right, the object
You are right, the object is more like a needle rather a perfect cylinder. People now have grown many single wires (called nanowires) vertically, heteroepitaxially and directly on substrates and attach is an image I got from a GaAs nanowire on Si (111) paper. See attach. Since people think islands combined film are the natural growth result. , this kinda phenomena is not expected before, right?
Instead of the top part, the lateral sides(surronding surfaces of the wire) could provide the relaxion. I am looking for a analytical solution for this strain or strain energy.
Attach: Here is one example: http://pubs.acs.org.ezproxy.library.wisc.edu/doi/full/10.1021/nl802062y
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i just got the solution,
i just got the solution, actually, i got a equation group with 9 partial differential equations for this problem. If anyone is interested, take a look Timshenko 198x Theory of Elasticity, Chapter 8.