To obtain a reasonable measure of surface roughness on the nanometer scale, people most often use the atomic force microscope (AFM) or the scanning tunneling microscope (STM), not only because they offer the required resolution, but also, and more importantly, because AFM and STM images are height-encoded. This means we can measure the dimensions of the features in these images both in the plane (in x and y) and out of the plane of the sample surface (in z).

In fact, roughness my be the single most frequently made measurement in industrial applications of the AFM, and certainly an important measurement in academic research applications as well.¹

Typically, AFM users rely on root mean square (rms) roughness, S_q, as the measurement of choice. (A quick search on Google for “rms AND AFM” returned about 333,000 hits today.)²

   (Eq. 1)

where μ is the mean value of the height, z, across all in-plane coordinates (x,y):

   (Eq. 2)

This measurement, rms roughness, has some inherent limitations that are often neglected. Reporting the rms roughness is almost always useful, but frequently inadequate in accurately describing surface topography in a meaningful quantitative way. In some cases, the consequence of not knowing (or ignoring) the limitations of rms roughness is misperceptions and making poor decisions.

The limitations of rms (roughness) are well-known to those who work often and in some depth with statistics and probability theory, but not to most AFM users. The upshot of these limitations can be summarize by saying that rms roughness measurement can give nearly or identically the same numerical result for two surfaces whose roughness are qualitatively different, or very different; sometimes so different that even a simple visual inspection of the AFM images will reveal.

One important reason rms roughness is sometimes inadequate is that it is computed indiscriminately towards the polarity of the height value at a given pixel, relative to the mean height value across all the pixels in the image. In other words, as the formula (Eq. 1) shows, height values smaller than and larger than the mean value end up contributing to the rms roughness the same way, i.e., as positive numbers. The result is that the rms roughness may measure (very) nearly the same for two different surface, one for example a flat surface with many holes, the other a flat surface with many peaks.

It is clear that to distinguish at least between these two kinds of surfaces, a different kind of parameter from rms roughness is required. Such a parameter exists, and in fact it exists in most if not all commercial AFM image processing software. It is called skewness, and it is not nearly as popular with AFM users as the rms roughness is. (A quick Google search for “skewness AND AFM” returned about 15,000 hits today). The skewness, S_sk, is defined in a way that can quantitatively describe the asymmetry of a height distribution about the mean (and from there, it gets its name):³

  (Eq. 3)

The formula is similar to the one for rms, but unlike rms (roughness), the skewness can take on positive and negative values as well as zero (even if the surface is not perfectly smooth), because each term in the double summation is raised to an odd power.
Depending on the way z values are recorded in an AFM image, the mean value, μ, itself can do the same (see Eq.2), that is, take on positive or negative values. The difference is that the appearance of the third power in the double summation in Eq. 3 means that those features whose height is farther above or farther below the mean μ; make relatively heavier contributions to the computed value of the skewness, as compared to features closer to the mean.

For a symmetric surface, that is, a surface the height of whose features are statistically evenly distributed around the mean, the skewness will render a value near or equal to zero–the height distribution is not skewed.

For our example, the skewness will measure positive for the flat surface with peaks, and negative for the flat surface with holes, and yet the rms roughness may measure the same or nearly the same for both. In this example, if the sample is a piece of metal bearing whose friction performance is to be improved, then, it may make a big difference whether the surface is flat with many holes, or flat with many peaks. To settle for the rms roughness then may be to ignore the skewness risk.

I wrote earlier that the limitations of rms roughness measurement are well-known to those who work often and in some depth with probability and statistics, but not to most AFM users. In case I planted any doubt that rms roughness is overly subscribed outside AFM image analysis too, here goes: Millions of people make pretty important decisions about money using statistics and probability often, but not all of them in much depth (that‘s why I italicized the “and“). The celebrated French mathematician Benoit Mandelbrot, the inventor of fractals, has studied the implications of ignoring the skewness risk by analyzing financial markets using models (including perhaps the most famous one, the Black-Scholes model) that assume market “roughness“ has a symmetric distribution (zero skewness). Mandelbrot’s alternative ideas about this subject were published recently.⁴

Some AFM images are more pleasing to the eye than others. The beauty of every AFM image though is that it is height encoded. The availability, in the form of numerical values, of all three dimensions of every feature in an AFM image, opens up a myriad options for statistical analysis of surface topography on the nanometer scale. These options exist neither in scanning electron and transmission electron microscopy (despite their superior resolution) because the images are slope-encoded, not height encoded. Nor do they exist in other techniques that do offer height encoding, but that lack the required resolution, for example, optical and stylus profiling.

AFM (software) manufacturers are aware of the implications of this advantage beyond what the average AFM user seems to know. They implement numerous formulas in their software (and provide print and electronic support documentation) to give the users options for statistically quantifying surface topography beyond rms roughness (including with fractal dimensions, for example). Surface skewness, or the coefficient of surface skewness, to be more exact, belongs to a family of mathematical functions that work with statistical distributions. There are others like it included in AFM image analysis software. It is up to the users to simply apply them and see what happens beyond rms roughness.

Fadrad Michael Serry
http://www.michaelserry.com/
serry@michaelserry.com

---

¹STM is infrequently used in industrial applications, because it does not work with electrically non-conducting samples. This severely limits the kind of samples that are amenable to STM analysis.²The choice of symbols in the equations here is similar to those in the software package “Scanning Probe Image Processor“ from Image Metrology A/S, Lyngby, Denmark http://www.imagemet.com/.

³This is one definition of skewness; others exist. A list of some is available from Wolfram Research Corporation at http://mathworld.wolfram.com/skewness.html.

⁴Mandelbrot, Benoit B., and Hudson, Richard L., The (mis)behavior of markets: a fractal view of risk, ruin and reward, Profile Press, 2004, London, UK. ISBN 1861977654.

A colleague and I were discussing some ideas for this nanotechnology blog when we jokingly commented that if we wrote it about the Super Bowl we would probably get a lot more people tuning in to read it.  Out of sheer curiousity I ran a quick Google check on football and nanotechnology and found this interesting article about a contest being run by the American Physical Society.  http://blogs.zdnet.com/emergingtech/?p=807

One can win the smallest trophy ever made and a $1000 in cash by creating a video that demonstrates some aspect of physics in American football.  The winner will be announced on Super Bowl Sunday.  Sounds like fun!  Time to dig out your camcorder and go to work. 

The trophy will be built at the Cornell NanoScale Facility (CNF) on a silicon wafer in the shape of a football field.  In case you win the world’s smallest trophy - Agilent would be very happy to sell you an atomic force microscope so you can see it!  (How’s that for a shameless plug!)

Just about the time you think you know every instrument that exists - someone comes up with a new idea.  University of Maryland researchers have come up with something they refer to as a dielectric microwave microscope.  The combination of a microwave source and a AFM probe allows one to send microwave signals to dielectric material and look at the signals that are reflected back to the probe. 

Is this really a microscope?  According to the dictionary - a microscope is an optical instrument having a magnifying lens or a combination of lenses for inspecting objects too small to be seen or too small to be seen distinctly and in detail by the unaided eye.  So in the true sense, this isn’t a microscope because there are no optics and lenses.  However, it does allow one to “view” phenomena that is too small for the naked eye.  And I use the term “view” pretty loosely - a chance to better understand and/or characterize an object (or in this case, dielectric material). 

From my perspective I think we’re going to see a lot more combinations of traditional instruments to characterize / view new types of materials.  I applaud researchers who have found ways to combine different sources and sensors in order to better explain the properties and structures of nano materials.  If you would like to share your combination instruments or solicit ideas on combinational instruments - write back to this blog or send me an email (grant_drenkow@agilent.com). 

We would love to start a dialog on this subject that might lead to better measurements which in turn leads to breakthrough research and hopefully to products to improve our world.  Pretty lofty thoughts - but what you can’t measure … you can’t improve. 

To visit examples of unique measurements in the nano world - check out these application examples.   http://nano.tm.agilent.com/index.cgi?CONTENT_ID=1361&User:LANGUAGE=en-US

 

Today, Agilent begins an applications section of the nanotechnology website.  The new section is a reference of nanotechnology applications showing typical instruments being used in research projects.   Each example gives a brief description of the project, the instruments used, the measurements made, and the device or structure being studied.  It also cites the name of the article, the publication, and the authors if you want to read more about this specific application.  It is divided into chemical, electronics, life sciences, materials, and optical categories for easier reference. 

To see the applications section, go to www.agilent.com/find/nano and click on the Application Examples found on the left side navigation bar under Resources.

 Let me highlight a few of the applications available this week.  If you are interested in carbon nanotubes, check out the chemical section to see how a gas chromatograph is used as a nanotube filter.  For those in electronics, this week’s applications include optical amplifiers tested with an oscilloscope and transistors tested with a semiconductor parameter analyzer.  In life science, genes are being identified with a bioanlyzer.  In in the optical section quantum dots being used as infared photodectors are tested using a semiconductor analyzer to accurately plot their current/voltage (I-V) characteristics.  In the nanomaterials section polymer micelles are characterized with a liquid chromatograph / mass spectrometer.  An LCR meter is used to plot the capacitance/voltage (C-V) curves. 

The applications section will have weekly additions, so visit it frequently.   My thanks to Jeff Harvey, a student at the University of Colorado-Boulder, who help us put together these research summaries.  If you have an application that you would like us to highlight- reply to this blog. 

AFM is a powerful characterization tool for polymer science, capable of revealing surface structures with unprecedented spatial resolution. It is extremely useful for studying the local surface molecular composition and mechanical properties of a broad range of polymer materials, including block copolymers, bulk polymers, thin-film polymers, polymer composites, and polymer blends. 

In addition to remarkably high spatial resolution, another key advantage of AFM is simultaneous multichannel data acquisition. In acoustic AC mode, tip-sample force interactions cause changes in the amplitude, phase, and resonance frequency of the oscillating cantilever. The spatial variation of the change can be presented in height (topography) or interaction (amplitude or phase) images. A feedback system monitors the oscillating amplitude of the cantilever at each sample location and tries to maintain a set value (set-point) by moving the scanner up or down based on the surface morphology. 

While the vertical motions of the scanner are used to generate a topographic image, the actual oscillation amplitudes and the phase lag between the AC drive input and the cantilever oscillation output can also be collected simultaneously to produce the corresponding amplitude and phase image, respectively. It has been demonstrated by many research groups that phase contrast is very sensitive to differences in material properties, such as variation of mechanical and adhesive properties. 

The visualization of different components of heterogeneous polymer materials via AFM phase imaging has been demonstrated in numerous studies of block copolymers, semicrystalline polymers, and mesomorphic polymers. For instance, compositional mapping with AFM is often used for observations of microphase separation of block copolymers, which occurs at the sub-100 nm scale. In addition to the compositional imaging of multicomponent polymer samples, visualization of amorphous and crystalline components is an important application of phase imaging. Besides amorphous and crystalline forms, many liquid crystalline polymers such as poly(diethylsiloxane) (PDES) usually exist in a partially ordered or mesomorphic form, which can also be characterized by phase imaging. 

Polymer or plastic materials can be divided into two major groups, thermoplastic or thermosetting, based on their response to heat. Therefore, knowledge of polymer behavior at different temperatures is essential for many practical applications. Although quite a few macroscopic techniques, such as differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and thermal mechanical analysis (TMA), are usually employed to probe the temperature changes of polymers, direct nanometer-scale visualization of polymers at different temperatures is still highly desired. With the development of both heating and cooling accessories, the use of AFM on polymer materials can be extended from ambient temperature to temperatures where polymer phase transitions occur. High-resolution AFM temperature studies can provide unique microscopic insight into polymer thermal behavior. 

We have documented many examples of the imaging of different polymer samples with the Agilent 5400 atomic force microscope that demonstrate its capabilities for visualizing important polymer nanostructures and monitoring structural changes caused by thermal transitions. The 5400’s outstanding thermal control is a rare feature for economically priced microscopes and the additional advantage of MAC Mode compatibility provides direct drive imaging in oscillatory mode in liquid and air. 

Please refer to the polymer-related application notes posted on our website. Detailed information about the 5400 atomic force microscope, thermal control, and MAC Mode can also be found on our website. 

In my continuing effort to show you the flexibility of an atomic force microscope (AFM) - let’s look at phase imaging.  

Phase Imaging is a powerful, dynamic force technique that can reveal many unique mechanical and chemical properties of a sample at the nanometer scale. In Phase Imaging, an AFM cantilever is oscillated vertically near its mechanical resonance frequency while it is in close proximity to a sample. As the AFM tip comes in very close proximity to the sample surface, the amplitude of the cantilever’s oscillation is reduced. The change in amplitude is measured and is used to track changes in the surface topography and roughness of the sample. Simultaneously, as the AFM tip encounters regions of different composition, a change in phase, relative to the phase of the drive signal, is measured and recorded. This change in phase is very sensitive to variations in material properties, including surface stiffness, elasticity and adhesion. The phase shifts are measured and displayed in a very straightforward manner that facilitates quantitative analysis and interpretation.

Both inorganic and organic materials have been examined with phase imaging. Phase imaging has been found to be particularly useful to map the various components of composite materials, to study variations in composition and contamination in materials, and to measure adhesion, surface hardness and elasticity. It has been applied to thin film studies, the materials sciences, and composite characterization.

Phase Imaging is included with Acoustic AC Mode and MAC Mode. It can be conducted with or without temperature control, in air, in liquid, and even under controlled atmospheres.

Phase Imaging can reveal material properties that can not be observed in surface topography and it can identify properties that might otherwise be obscured by topography. It is a sensitive, quantitative, high lateral resolution AFM method that is often more convenient and gentler than other surface property methods that are based on contact mode operation.

SPM is the acronym of scanning probe microscopy.  An AFM (atomic force microscope) is a subset of SPM. 

STM is the acronym of scanning tunneling microscopy.  STM is a mode of AFM.  So what is it, you ask? 

STM (Scanning Tunneling Microscopy) was invented in 1981 by G. Binnig and H Rohrer who shared the 1986 Nobel Price in Physics for their invention. STM uses a sharp conducting tip and it applies a bias voltage between the tip and the sample. When the tip is brought close to the sample electrons can “tunnel” through the narrow gap either from the sample to the tip or from the tip to the sample, depending on the sign of the bias voltage. This tunneling current changes with tip-to-sample distance, it decays exponentially with the distance, which gives STM its remarkably high precision in positioning the tip (sub-angstrom vertically and atomic resolution laterally). For the electron tunneling to take place, both the sample and the tip must be conductive. Therefore STM cannot be used on insulating materials.

 

STM can image a sample surface in either constant-current mode or constant-height mode, as shown in the image above. In constant-current mode, in order to keep the tunneling current constant STM uses feedback to adjust the height of the scanner at each measurement point, e.g. when the system senses a tunneling current increase, it adjusts the voltage applied to the piezoelectric scanner so that the scanner lifts the tip and give an increase in the tip-sample distance. The scanner height measured at each location on the sample surface constitutes the topographic image. The constant-current mode is thus generally used to acquire surface height data, its scan speed is limited by the feedback response and thus it takes longer to image an irregular surface at a larger scan size. In constant-height mode, the tip scans at a constant height above the sample and the tunneling current changes due to the topography and the local surface electronic properties of the sample. The current image is a result of measured tunneling current at each location on the sample surface. The constant-height mode can acquire data faster because the system doesn’t have to move the scanner in the vertical direction, so it is most often used for imaging relatively smooth surfaces.

Strictly speaking STM tunneling current is correlated to the surface electronic density of states, i.e., the number of filled or unfilled electron states near the Fermi level, within an energy range determined by the bias voltage. So STM measures constant tunneling probability instead of the physical topography at the surface. STM tunneling spectroscopy, looking at the current-voltage relationship at a constant tip-sample distance or the current-distance relationship at a constant bias voltage, is a useful tool to study the electronic structure and property of a sample surface at the atomic level.

In our continuing series on ways to use an AFM - let’s look at force measurements.  These measurements are important in life science, polymer structures, semiconductors, and composite materials.  Force measurements can be made in air or liquid and under controlled conditions like temperature and humidity. 

Force Modulation mode is a fast, very sensitive imaging method that is especially useful to measure and detect variations in a surface’s mechanical properties, including stiffness and elasticity. In this technique, a modulated driving signal at a constant frequency is applied to the AFM cantilever while the AFM tip is in contact with the sample, and the amplitude variation and phase lag during the scan are measured. Force modulation provides the user with simultaneous surface topography measurements, material elasticity or stiffness (the amplitude of the modulated signal), and energy dissipation characteristics of the sample (from the phase of the cantilever response). When an AFM cantilever is modulated with the driving signal, elastic materials will result in relatively larger modulated amplitude compared to stiffer materials because the AFM tip can indent an elastic material.

If you want more information on Agilent AFM’s go to our website at www.agilent.com/find/afm

Atomic Force Microscopes (AFM) do more than just provide a topographical image of the surface.  So for the next few blogs I’m going to describe some of the “modes” of the AFM.  Let’s start with contact mode.

In contact mode AFM, interatomic van der Waals forces become repulsive as the AFM tip comes in close contact with the sample surface. The force exerted between the tip and the sample in contact mode is on the order of about 0.1-1000nN. Under ambient conditions two other forces besides van der Waals interactions, are also generally present. These forces include the capillary force from a thin layer of water in the atmosphere, and the mechanical force from the cantilever itself. The capillary force is due to the fact that water can wick its way around the tip, causing the AFM tip to stick to the sample surface. The magnitude of the capillary force should vary with the tip-sample distance. The mechanical force resulting from the cantilever is similar to the force of a compressed spring and its magnitude and sign (repulsive or attractive) is dependent on the cantilever deflection and the cantilever’s spring constant. Consequently, in contact mode AFM, the repulsive van der Waals forces arising for the AFM tip to sample interaction must balance the sum of the forces arising from the capillary force plus the mechanical force from the cantilever.

The thin layer of water present on many surfaces in air exerts an attractive capillary force and holds the tip in contact with the surface. Thus, when scanner pulls the tip away from the surface, the cantilever bends strongly towards the surface and the scanner has to retract further so that the tip can snap off of the surface. The cantilever returns to its original unbent status as the scanner moves the tip away from the surface beyond the snap-out point. In liquid, since the large capillary force is isotropic and the total force that the tip exerts on the sample can be reduced to some extent.

In order to improve imaging in air and liquid environments, Agilent offers Magnetic AC mode (MAC Mode). In MAC Mode, a cantilever that is coated with a magnetic material is driven into oscillation by an AC magnetic field that is generated by a solenoid positioned close by the cantilever. The result is a clean cantilever response that has no artifacts or background signals when the cantilever is vibrated in air or in liquid.

For more information on Agilent AFM’s - visit the www.agilent.com/find/afm

Agilent has a long history of electronic measurements but I often get questions about our newest product line - the atomic force microscope or AFM.  So what is an atomic force microscope and how does it work?

AFM stands for Atomic Force Microscopy or Atomic Force Microscope and is often called the “Eye of Nanotechnology”. AFM, also referred to as SPM or Scanning Probe Microscopy, is a high-resolution imaging technique that can resolve features as small as an atomic lattice in the real space. It allows researchers to observe and manipulate molecular and atomic level features.

How AFM works is illustrated in the figure below. An AFM works by bringing a cantilever tip in contact with the surface to be imaged. An ionic repulsive force from the surface applied to the tip bends the cantilever upwards. The amount of bending, measured by a laser spot reflected on to a split photo detector, can be used to calculate the force. By keeping the force constant while scanning the tip across the surface, the vertical movement of the tip follows the surface profile and is recorded as the surface topography by the AFM.

The predecessor of AFM is STM, Scanning Tunneling Microscopy or the Scanning Tunneling Microscope, was invented in 1981 by G. Binnig and H. Rohrer who shared the 1986 Nobel Price in Physics for their invention. An excellent technique, STM is limited to imaging conducting surfaces.

AFM has much broader potential and application because it can be used for imaging any conducting or non-conducting surface. The number of applications for AFM has exploded since it was invented in 1986 and now encompass many fields of nanoscience and nanotechnology. It provides the ability to view and understand events as they occur at the molecular level which will increase our understanding of how systems work and lead to new discoveries in many fields. These include life science, materials science, electrochemistry, polymer science, biophysics, nanotechnology, and biotechnology.

 AFM has a number of advantages over other techniques making it a favorite among leading researchers. It provides easily achievable high-resolution and three-dimensional information in real space with little sample preparation for low-cost. In-situ observations, imaging in fluids, temperature and environmental controls are all available.  The Agilent AFM’s have a number of modes that let one measure hardness, elasticity, friction, and adhesion in addition to the 3D topology.  Over time we plan to add more modes to our AFM’s - stay tuned. 

If you want more complete information on the Agilent atomic force microscopes - go to the Agilent AFM website at www.agilent.com/find/AFM.

Click on the AFM Image Library on the nanotechnology home page (www.agilent.com/find/nano) to see examples of images and applications that are possible with the Agilent atomic force microscopes.