[Spm] AFM imaging of 15 nm wide pits

[petercm at 295.ca]

Dear SPMers,

Recently, Joel Pikarsky and Don Chernoff responded to a question Rose
Neander had on the imaging of pits 15 nm wide, and I'd like to add another
angle to the analysis.

If we assume the AFM tip to be spherical and trapped at the opening to a
15 nm pit, we can establish the Pyth. equation
(RoC)2 = (15/2)2 + (B)2
where RoC is the tip's Radius of Curvature and B is perpendicular to the
sample surface from the sphere's centre to the elevation of the surface.
The tip's depth of penetration into the pits is then just D = (RoC - B).
If we further assume a "good" tip of 10 nm radius, the calculated depth
will be 3.4 nm, meaning that the scan will only show tiny dimples where
the pits are. Depending on the sample roughness, using "height"
cross-sections alone might not determine where these pits are, let alone
their width. Unless the pit edges show up in the "error" or "phase"
channels, this sample might be rather difficult to quantify. Using
specialty tips might be another option.

Depending on Rose Neander's deadline and interest, I might suggest she try
to image porous aluminum.  These are commercially available as AFM Tip
characterization Structures (e.g. Micromasch www.spmtips.com/pa) or in
bulk as membrane filters (e.g. SPI Supplies
www.2spi.com/catalog/spec_prep/filter2.shtml). The Anopore filters come in
three pore sizes (0.2 µm, 0.1 µm and 0.02 µm). Although the latter pore
size is slightly larger than the 15 nm wide pits that Rose Neander wants
to image, they would provide a good test sample. At 50% porosity, these
filters are nothing but holes, so if you can't image these with certainty
you'll have problems elsewhere.

My own experience with homemade porous aluminum was impossible with AFM
tips available at that time (15 to 25 nm radii) unless the pits were of
considerable width. To quote the reference given at one of the sites
above, "A reliable determination of the internal diameter and shape of the
pores is not well accomplished under the present experimental conditions."
(Yu Cheng Sui, Jose M. Saniger. "Characterization of anodic porous alumina
by AFM." Materials Letters 48 (2001) 127-136.)

Hope this information helps,

Peter Markiewicz.


Only he who has traveled the road knows where the holes are deep.
      - Chinese Proverb


>>On May 24 Joel Pikarsky wrote:

I've been thinking about this for a few days. Initially, I thought
there would be no effect due to the probe sharpness. Then I did a little
trig. Here's my first order result:

For a tip with (hemispherical) radius = 10 nm, the tip would have to
move ~1 nm across a perfect 90-deg edge to move vertically down 0.05
nm. I have seen the value of 0.05 nm used as the maximum acceptable
noise for a Dimension AFM at installation so I'm using this as the
minimum vertical deflection that can be observed.

So the "true hole diameter" may be ~2nm larger than what the AFM scan
indicates. This assumes a perfect 90-deg top edge.

You can try a "whisker" or "spike" type probe that has a radius ~2 nm.
Theoretically, this should give a measured diameter ~ 0.4 nm (or ~
diameter of one atom) larger than the "true diameter".

Another consideration: if your scan size is 500 nm and you are
collecting 512 points per line, the points are ~1 nm apart.this means
the uncertainty in the location of a feature is +/- 0.5 nm.

I don't know the "lateral" noise of a cantilever but it may also be on
the order of a nm.

Joel Pikarsky
"Scourge of the Cleanroom"