Residual stress induced by metal deposition on cantilever

[guoren]

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.

 

[Demon3]

Try the PhD thesis Curing of Thermoset Films: Build-up of structure and residual stress in which a friend of mine gives the equations (KTH, Stockholm 1995, Dr. Jakob Lange).

As you cool the part the thermal contraction causes the stiffer material to bend the other material. Influencing factors are the amount of temperature change, modulus of each layer (flexural modulus) and the thickness of each layer. To calculate it properly I think you'd need to know the modulus of each material at every temperature experienced during cooling. That's what he measured in the above thesis by curing in a rheometer.

Rather than calculate it which requires a lot of time and measurement you would probably be better off experimenting until you get the degree of bend you need annd knowing that it's the above mentioned factors that affect the deformation.

There is not any memory with less satisfaction than the memory of some temptation we resisted.
- James Branch Cabell

 

[guoren]

Thanks, Demon3.
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.

 

[Demon3]

Think of the two materials as two springs, each one has a stiffness that depends on it's modulus and thickness. Each spring will try to stretch the other one as the temperature changes and they expand or contract.

There is no way to connect that with your chamber geometry or pressure without lots of experiments. The deformation depends on the properties of the layer you are depositing so you need to know the modulus, thickness and CTE of that. Only then you can correlate the deposition condictions with the properties of the metal layer.

There is not any memory with less satisfaction than the memory of some temptation we resisted.
- James Branch Cabell

 

[Compositepro]

The residual stress depends on how much the deposited material shrinks after the moment it is deposited and can resist stress (i.e., not yield or flow). Shrinkage can be due to cooling and CTE, freezing to a solid from liquid, crystalization, and numerous other factors. It basically can't be calculated unless you already know the answer.

What you want to accomplish requires a trial and error approach. One factor you can control is to flex the beam before you deposit anything. When you release the fixturing there will be stored stress in your deposited layer.

 

[davidmoul]

In fact it depends on temperature of deposition, and difference in CTE of both material, and of thickness deposited.

I don't have the exact formula here, but this is a quite simple formula that you must find on the net. If you can't find it, it must be easy to find...

 

[Demon3]

In theory perhaps, but metal deposited in that manner may well have a different morphology and modulus than bulk metal values found in the literature.

There is not any memory with less satisfaction than the memory of some temptation we resisted.
- James Branch Cabell