Plane Fitting & Bow Artifacts

While flattening subtracts an n-th order polynomial from every trace and retrace, plane fitting subtracts one polynomial uniformly in the X- and Y-directions. The polynomials can be of different orders in the two orthogonal directions.

Plane fitting is a necessary complement to flattening. While flattening tends to literally flatten out the large wavelength structure, the purpose of plane fitting it to preserve large scale morphology. It is very useful imaging patterned or lithographed structures where it is precisely the large scale structure that is of interest.

The images are 100 μm scans of a smooth PMMA coated surface. In the top image a 1st order polynomial-- an offset and a tilt-- were removed in both the X- and Y-directions. The surface which is very smooth over a large lateral length. The image looks like a bowl which is a scanner artifact called a bow artifact. It is due to the trajectory scanned by a scanned tip scanner over large distances. The sample really doesn't look like this. Regardless of where one scanned one would obtain a similar image.

The bottom image has a 3rd order polynomial removed in the X- and Y- directions. This has removed the bow artifact. One now has a realistic representation of the surface where surface defects and some large wavelength features on the order of several 10's μm are visible.

Flattening & Flattening Artifacts

AFM images generally require some post-processing. AFM images are generated by scaling the Z-piezo voltages to yield a height, and that voltage generally has an offset required to extend or retract the Z-piezo so that the probe can interact with the sample. There is often also a tilt to the sample due to mounting or the cleaving of the substrate which is irrelevant to the surface morphology but nevertheless reflected in the AFM image. The offset and tilt prevent a meaningful interpretation of the AFM image. Such an image is shown at top.


One method of post-processing is flattening. In this case a polynomial of order n is fit and subtracted from every trace and retrace. It is called "flattening" because this method of processing tends to flatten or unroll an AFM image. It is also a potential source of artifacts.

The second image shows a series of photo-lithographed Au pads for directed self-assembly. Flattening was applied in image post-processing. Note the dark regions extending in the fast scan direction on either side of the pads. In AFM any features that are consistently and uniformly aligned in the fast direction are suspect. According to the flattened image the substrate near the pads dips down-- but only on the right and left sides of the pads. This is physically implausible and suspect. Any sections, height, bearing or R_a measurements from this image would be erroneous.

To remedy these artifacts stop bands are placed on the pads allowing only the substrate pixels to be used in the flattening. In this final image stop bands are placed over the pads in the middle portion of the image showing a flattened image without baseline distortions.

In general, flattening works best post processing images that don't have high aspect ratio features: e.g. grains on a film surface. In these applications one is interested in the small scale structure, not the large scale morphology. Flattening long wavelength features away is in fact often desirable. In cases like these lithographed pads flattening can still be applied but beware of artifacts and use stop bands accordingly.

Image Artifact: Self-Similar Triangles

One common problem encountered in AFM imaging is image artifacts due to a damaged tip. The tip is at the end of a triangular pyramid, and if that pyramid is sheared it will be a small triangular area that is interacting with the surface, not a sharp tip. The result will be self-similar triangular artifacts in the image.

This is a tapping AFM image of the tip qualification standard. Even if one did not anticipate seeing sharp edges to the grains at the film surface, in AFM imaging it is always suspicious when all of the features are self-similar in shape. Many features look triangular. It is also a cause for concern in AFM imaging when all of the features are unnaturally oriented: every triangle is oriented in the same direction with one point towards the +X-direction. Every triangle is also a perfect equilateral triangle. It would be too coincidental to have such perfect alignment of surface structures.

Nanoindentation Probe

The top image is the image of a diamond nanoindentation probe. The triangular pyramid of the diamond itself is shown. A stainless steel cantilever extends to the top right of the image. The charging region towards the upper right quadrant is an epoxy used to glue the diamond to the cantilever. The bottom image shows the functional portion of the diamond indentation surface. It was inspected in SEM to ascertain whether the structures visible in optical microscopy near the probe tip were fractures or adhered material. It is clearly debris material from a previous scratch or indentation.

Phase Contrast Imaging

In tapping AFM, the phase of the cantilever is often a good probe of composite systems. Because of the high spatial resolution of the AFM, inhomogeneity can be probed at a very small length scale.

This AFM image shows a rare-earth complex dispersed on V4 mica. The complex had evaded crystallization so the hope was to directly image the complex itself on the very smooth mica substrate. This had been reported previously for these complexes evaporated onto smooth substrates in vacuuo. What was observed were chains of aggregated material. They did not appear to be small crystal habits which was not surprising as XRD data did not suggest crystallization of the complex.

To understand the nature of these aggregated structures, higher resolution images of the individual globules were examined using phase contrast AFM in tapping mode. Even below a length scale of 1 μm, these aggregated globules demonstrated considerable internal structure as evidenced by phase contrast AFM. Phase contrast AFM probes local changes in the phase of the tapping probe due to local differences in the impulse experienced by the tip due to variations in density, elasticity, etc. The phase contrast AFM showed uncorrelated domains at a length scale of a few 10's nm. Thanks to Dr. Michael Shatruk of FSU Department of Chemistry.

Fast MFM in Contact Mode

In tapping AFM one generally lowers the scan rate drastically to scan large areas without scanning image artifacts. At 0.1 Hz 85 minutes are required to take a 512x512 pixel image. Since an MFM image requires the additional interleave scan at the lift height, such an MFM image would take 170 minutes.

Contact AFM scan rates can be quite large even over large scan areas. This MFM image was taken over a 60 μm field of view at 1 Hz using a magnetically coated contact tip- the Veeco MSNC-MFM. Including the interleave MFM scan, this image took 17 minutes, a 10X improvement in acquisition time. The image shows a magnetic tape with several tracks of recorded domains.

Tapping AFM of Buckypaper

This image is a tapping AFM image performed on a Buckypaper sample made of carbon nanotube bundles precipitated into a fibrous paper. Even though the system consists of free-standing fibers with very deep pores, it could be easily imaged.

Nanoscratching & Nanotribology: Scratches

In some applications it is more interesting to look at the behavior of materials under shear force rather than normal force. In this case the nanoindentation probe can be used to form nanoscratches.

This image shows a series of nanoscratches across a region of a polished tooth section of composite structure. The scratches are more deep in the darker regions which were assumed to be softer as more material was removed from these regions upon polishing. It is thought that these harder regions might prevent fractures from propagating through the tooth region, allowing the tooth to remain functional after a crack. The lack of material piled up on the sides of the scratch indicates that the deformation if primarily fracture and not plastic in nature.

This is a very striking demonstration of nanoscratching. A single scratch was made on a polished tooth section in the region at the interface of the enamel and dentin. A very deep trough with pile-up due to plastic deformation is seen in the dentin, while there is a very shallow scratch with very little sign of plastic deformation in the enamel, consistent with fracture deformation.

Thanks to Dr. Greg Erickson, FSU Biology.

Feature Depths

Feature depths can be determined from image sections. In such cases a feature depth is then determined by the placement of a single cursor on the top and bottom of the feature. A more statistically robust method of determining feature depths is the use of the "depth" feature which exploits image bearings or pixel histograms.

This image shows a 10 nm thick film of AuPd for SEM coating on V4 mica. An area has been scratched to allow for a film thickness measurement. A box has been place over a region of the scratch. The right shows a histogram of the pixel heights in that box. The broader portion of the bilobed distribution represents the film-- the narrower portion the substrate. For an ideally plane-fit image, the broadness of these histograms would reflect the R_a. The separation of the two distributions represents the feature depth which is found to be 10.12 nm. For this application that is ideal as a 10-12 nm film of AuPd is ideal for coating for SEM.

Lateral Force Microscopy

This image shows a typical polished metal surface in contact mode. Polish marks and various forms of particulate material are visible on the surface. In contact AFM one is measuring the surface morphology by keeping the tip deflection constant and thus this image reflects an image taken at nearly constant normal force. As the tip encounters changes in morphology there will be momentary changes in normal force until the scanner feedback mechanism is able to adjust the Z-piezo to maintain the deflection set-point. This is accomplished through the integral and proportional gains.

A constant normal force allows one to measure frictional forces if one is able to measure the torsion of the contact cantilever. This is possible if one sets the scan angle to 90 degrees and the data channel to "friction". While cantilever deflections are measured by the laser beam reflecting from the cantilever moving up and down between the top and bottom halves of the four quadrant photodetector, frictional forces manifest as a lateral motion of the laser beam between the left and right halves. This SPM imaging mode is lateral force microscopy or LFM.

This image shows an LFM image of the same region. Some torsion of the contact probe is seen around morphological features such as the longitudinal polishing scratches, but what is more interesting is a circular region of modified friction in the center of the image that does not seem to correlate with any morphological features. This is due to a modification of the surface that does not alter the morphology of the region-- the presence of an adlayer that modifies surface electrostatic forces.

The contact probe can also be chemically modified itself to allow for chemical force microscopy or CFM. In this case the probe is chemically functionalized to optimize the electrostatic interaction with species on the surface. In this case the torsion friction signal can be used to map those species on the surface. In the case of dip-pen nanolithography or DPN, CFM is a very natural method of imaging the regions functionalized because of the presence of those species on the dip-pen probe.

Nanoindentation & Nanotribology: Indents

The mechanial properties of surfaces are often different than those of bulk materials. A diamond probe can be used to perform nano-indentations of materials at known normal force in the range of 1 to 100 μN. Knowing the contact area of the nano-indenter and the normal indentation force one can determine a nano-hardness number.

In addition one can study the mode of deformation. This image shows a nano-indentation of glass with a normal force of roughly 10 μN. The pile-up on the side of the indentation is indicative of plastic deformation. These nano-indentations are generally performed in arrays of increasing normal force, or, as in this case, they can be placed at a region of interest. The nano-indentation probe itself is used to image after the indentation so the image quality is slightly reduced.

Noise Floor & Near Atomic Resolution

The Dimension 3000 is a scanned tip SPM which allows for great flexibility: imaging in liquids as well as imaging with magnetic and non-ambient temperature stages. What is lost is lateral stability of the scanner due to the large lateral scan range of 100 μm. The vertical noise floor is still quite good at ~ 0.75 Å.

To test the noise floor one images freshly cleaved mica. The image is a 25 nm scan of V4 mica in contact mode with nearly zero normal force-- i.e. no deflection. Image drift has been minimized by scanning for an extended period to eliminate any piezo hysteresis and to allow the sample mounting to fully relax. The Z-limit has been set to its minimum value for maximum Z-piezo digital resolution. A sharpened Veeco SiN DNP-S probe with 0.12 N/m spring constant was used.

Note that some period structure is visible through the noise. 2D Fourier transform of the image shows significant noise bands in the vertical direction-- i.e. the slow scan direction-- which prevents spectral filtering and recovering of a high resolution atomic level image. The roughness, Ra, is 0.95 Å which is a bit above the spec'd noise floor of 0.75 Å.

This image is a 500 nm AFM image taken with an Veeco OTESP Si tapping tip. Again the X-Y hysteresis and sample drift were minimized by scanning for some time. The Z-limit was minimized for maximum Z-piezo digital resolution. Note the R_a of 0.45 Å which is a typical noise floor measurement for this system.

Tip Qualification

Tip quality is essential to quality AFM images. In a very general sense, an AFM image is the convolution of the tip morphology with that of the surface being imaged. Ideally an AFM probe has a radius of curvature (ROC) < 10 nm which allows for high resolution imaging of small features. When the ROC is increased due to wearing of the tip or the adhesion of a foreign object to the tip, the imaging resolution is degraded. In some cases, image artifacts may arise. The most common artifacts are self similar features. In some cases all the image structures are triangular in shape due to the fracturing of the AFM tip pyramid or ovoid in shape due to the wearing of the tip or the attachment of a foreign object to the tip. While a radical change in tip performance is readily visible, small changes often go unnoticed and these changes of more difficult to identify on certain types of samples. As such a standard surface morphology is desirable. An ideal standard should be capable of providing quantitative information about the tip quality.

The image above is a titanium surface that has very sharp crystallites emerging from the surface. This is an ideal tip qualification standard as these sharp edges can be used to deconvolute the shape of the AFM tip. By imaging such a sample the sharp edges of the crystal habits can be identified and their shape profile then used to estimate the rip ROC. This process is known as tip qualification, and can be performed just before and after a series of images to certify they are of the highest quality.

This image shows the actual tip qualification. The top left image shows a green "+" at each tip qualification point-- a sharp edge on the titanium crystallites. The bottom left image shows an estimate of the tip shape. The top right image shows the cross section of the tip 10 nm from the tip apex while the bottom right image shows it 20 nm from the tip apex. The diameters of these cross sections are estimated, and user defined upper limits are used to determine if the tip is "good", "suspect" or "bad". This tip is considered "suspect" because the diameter 20 nm from the tip apex is greater than the threshold value of 60 nm.

Magnetic Force Microscopy

One of the advantages of SPM is the ability to exploit specialty probes. Standard silicon tapping cantilevers can be coated with a magnetic alloy, typically 10-150 nm of CoCr alloy on 1-10 nm of Cr, to allow for magnetic contrast. The SPM probe tip which is in the form of a 3-sided pyramid, is magnetized using an external hard magnet. This external magnetic field aligns the domains formed on each of the sides of the pyramid, allowing the tip to act like a magnetic dipole.

The force exerted on a dipole is the dot product of the dipole moment and the gradient of the field at the surface. In magnetic force microscopy-- MFM-- these dipole magnetic forces are detected as a change in cantilever phase and amplitude a finite distance above the surface. In an MFM image, the tip is tapped on the surface to measure the surface morphology, and then re-scanned across the surface 50-150 nm above the surface to measure magnetic contrast. This re-scan above the surface is done in what is called lift mode. MFM in lift mode is just one of many interleave scans that can be performed-- a scan across the surface between morphology scans.

The left image shows the morphology of a computer hard-drive. Visible are highly oriented surface scratches. The right image shows MFM magnetic contrast in the tapping amplitude using a 100 nm lift distance with a magnetized Veeco MESP MFM probe.

Digital Instruments Dimension 3000 SPM

The CMMP group at the Florida State University Department of Physics has a Digital Instruments Dimension 3000 scanning probe microscope (SPM) that is available to the local research community. A small fee of $25/hour is assessed for usage of this instrument. The cost of probes is extra.

Scanning probe microscopy, or SPM, refers to a collection of microscopies that exploit a physical probe to image a surface. By using a vertical piezoelectric device (Z) the probe is maintained constant as it is scanned across the surface using two orthogonal horizontal piezo's (X & Y). In the case of scanning tunneling microscopy (STM) that probe is a tunneling current, while in the case of atomic force microscopy (AFM) that probe is the amplitude (tapping AFM) or deflection (contact AFM) of a mechanical cantilever. The Dimension 3000 SPM can perform all these imaging techniques-- STM and both contact and tapping AFM-- in air as well as in liquids. Since the surface morphology is imaged directly, such measures of surface character as average roughness (R_a), bearing, feature depth, surface area and surface fractal dimension can be directly obtained. Digital filtering and editing of images is possible to produce high quality 2D and 3D images as well as 1D sections.

Advantages: direct imaging of surface topography; ability to exploit specialty tips for special imaging techniques (e.g. MFM, LFM, CFM); accuracy and precision of feature measurement; 2D and 3D images as well as 1D sections; ability to image in air as well as liquids; specialty magnetic and non-ambient temperature stages; nano-identation and nano-scratching for nano-hardness and wear measurements; direct surface measures of Ra, surface area, feature dimensions, etc.

Disadvantages: slow compared to SEM and profilometry; cost associated with probes.