Residual stress induced by metal deposition on cantilever

[guorenguoren]

hi,
everyone, now I am trying to deposite some metal layers on micro-scale cantilever surface on the purpose of bending it under the residual stress caused by metal deposition. I read some literatures which mentioned and even gave the exact value of residual stress happened in both the cantilever and metal layer. So I wonder how to get those values by calculation if the deposition is through sputtering system or by any experimental ways.
Thank you.

 

[Mapes]

Hi guorenguoren, welcome to PF. Not to discourage you, but it's notoriously difficult to predict the residual stress of sputter-deposited coatings. The process is just too sensitive to the chamber geometry, argon & residual contamination pressure, substrate bias, plasma power, and other details. It's probably most effective to just dive in, deposit the film in your own equipment, and see what you get.

 

[guorenguoren]

Thank you, Mapes.
It seems to be a really tough work. But is there any equation including the residual stress as a function of your mentioned parameters, i.e. chamber geometry, pressue. As I can't conduct the work without any theory support.

 

[PerennialII]

haven't seen any of those ... typically the results are such that "with this and this process for this sort of a coating/substrate system we ended up with this" (and even "this" is often somewhat unreliable). I'm actually a bit confused what you're after ... are you trying to find a method to compute those residual stresses when you bend your specimen after deposition (often beam theory with couple of stacked materials) or try to predict them beforehand or ... ? The former is fairly simple if it's a bend test or related, the latter at the very other end of the spectrum like Mapes stated (at that point might rely on what has been published for the system you've under works and try to go from there).

 

[guorenguoren]

thanks everyone
Perennial, your advice is helpful. I want to calculate the residual stress before deposition experiment, so is there any equations for that involving parameters, i.e. chamber geometry, pressue, without any experiment only pure theoretical calculation.

 

[PerennialII]

Ok, most analyses which have seen aiming at what you're after are molecular dynamics (MD) analyses. I.e. you create a model of your substrate, then start "shooting" the atoms you're depositing to the substrate on the basis of the parameters of your deposition process (this is the part I'm most in the dark about ... would think it involves figuring out the kinematics / initial conditions given to the depositing atoms on the basis of your "process parameters" and with what materials you're working with). And then repeat that until you've deposited a representable amount of material and you extract the atomic stress state (which has components arising from internal defect state & microstructure and the thermal mismatches within the system).

If you've no MD experience there can be quite a learning curve (the "quite" can mean easily months), however, there are plenty of publications out there which will describe the basic model building process and some MD codes have similar example problems (vaguely remembering something but pretty sure about this) which could be modified to yield some initial results and get a feel for the problem. Since it's an MD analysis it'll be directly limited in the material volume and range of time you can simulate (if do not couple it with something else, need some "real" computing hardware in any case), but it'll yield "something" .

Alternatively, you could try a different type of analysis, like a continuum type analysis utilizing the finite element method (FEM) where you add material simulating a deposition process. Here you could simulate the time history and material volume without that much of a problem, but you'd miss the intricacies an MD analysis can provide (but would provide information about residual stresses arising from thermal mismatch without that much of an issue).

Anyways, it's not an easy analysis, but nothing interesting rarely is .