I am looking for some extended information regarding the called "Theater Curtain" or "Waterfall" effect in FIB.

I checked in the book "Introduction to Focused Ion Beams: Instrumentation, Theory, Techniques and Practice" (by Lucille A. Gianuzzi and Fred A. Stevie), and in many articles ("Improvements in performance of focused ion beam cross-sectioning: aspects of ion–sample interaction", by Tohru Ishitani, Kaoru Umemura, Tsuyoshi Ohnishi, Toshie Yaguchi and Takeo Kamino was especially useful), but all the authors seem to describe it phenomenologically. I'm trying to get a deeper, more physical (basic) understanding of it, so I interpreted the descriptions and tried to figure out their meaning, but I'm not sure that my interpretation was fully correct.

If there is any expert in FIB milling or anyone who understands theater curtain effect well enough, just tell me what you think about it. Any help will be very appreciated.

For what I understood, the curtain effect is defined by the presence of striations in the milled cross-section, independently of their origin. Thus, if we classified it by the physical causes, there would be more than one kind of curtain effect, with different explanations for each one:

- A very typical case is when the topography of the samples is uneven due to an inefficient polishing or no polishing at all. We can take a rough surface as one with local "valleys" and regions with slope. In the valleys, the incidence angle will be ~90º and the sputtering yield will be maximum (the sputtering yield has a big dependence on the incidence angle), and in the regions with higher slope the sputtering yield will be very small.

If the beam is hitting a valley, the volume under the valley is milled. In this case, the beam tails won't have much importance since they will hit regions with a high slope and low sputtering rate (anything next to a valley has slope).

If the beam is hitting a region with a certain slope, the sputtered atoms will most likely go down that slope and cause a second order sputtering in the valley at the bottom of the slope, and the beam tails will do approximately the same. This way, the milled region will cover a larger area of the sample surface. I also think that it is quite possible that the ions themselves go down the slopes without the need of second order sputtering (something like ions not causing sputtering, but just rebounding with the slope surface) if the angle of incidence is small enough, but I am not really sure of that.

In any case, the combination of regions with valleys and varying slope will cause differences in the size of the milled regions of the sample, thus exhibiting the curtain effect.

- Another common case is when the composition of the milled material is not homogeneous, and consists in various components with different sputtering rates (due to different hardnesses, atomic numbers, etc.). As the sample moves (relatively to the beam) at a constant speed, the regions of its top surface (the one perpendicular to the beam) with lower sputtering rates get milled a smaller area than the regions with higher sputtering rates, which are more affected by the beam tails because milling is faster there.

If there wasn't anything else going on there, any changes in the composition under the top surface would also generate curtain effect (and kind of steps when the harder material is below), but to the extent I know, that doesn't happen. The explanation for that could be that because the tails affect mainly the parts closer to the top surface, instead of the cross-section being parallel to the beam, a slope is created in it (that actually is known to happen), so it covers a higher part of the top surface and more tails impact on it. The ions colliding against that inclined cross-section will generate sputtered atoms that will go down the slope, and cause second order sputtering if they hit an obstacle in their way, so that would sharpen the cross section in the direction (almost) parallel to the beam. That would explain why the changes in composition only have an effect in curtaining if they are in the top surface. Again, the possibility of ions going down the slope without causing sputtering in it would help that explanation a lot, since the sputtering yield against the cross-section is minimal due to the low angle of incidence. If ions from the tails rebounded against the cross section in a quite elastic way, they would go down it with almost the same kinetic energy than the others, and that would cause a higher concentration of ions than when the beam first impacts a region of the top surface. Due to this concentration of the beam, harder regions of the sample would be milled anyway.

- The third condition that can cause the theater curtain effect is the orientation of the sample, if it is crystalline, because ion channeling (ions penetrating greater distances across crystalline planes with lower Miller indices) results in preferential milling along low index directions. In this case I think that what simply happens is that, as planes with low Miller indices have greater distances among them, there is less linear density of atoms along their direction and more freedom for ions to travel across them (and the atoms of the sample are easier to move in those directions, too), so their impact on the material is greater.

I have seen other causes for curtain effect (the beam dose, bad aligning, the speed at which the sample is moved...), but I consider that they are circunstances that affect the three mentioned physical causes, but not causes by themselves.

That is what I was able to find out. Am I missing something? Is there something that I said that you don't agree with? Thank you very much in advance.

I'm sorry if it was messy to read. It was hard to explain it without any drawing.