Table of contents
Introduction to atomic force microscopy (AFM)
The field of scanning probe microscopy (SPM) began in the early 1980s with the invention of the scanning tunneling microscope (STM) by Gerd Binnig and Heinrich Rohrer, awarded with the Nobel Prize in Physics in 1986. In the same year, a major breakthrough was made with the invention of the atomic force microscope (AFM) by Gerd Binning, Calvin Quate and Christoph Gerber, which continues to revolutionize nanoscale characterization and measurements ever since. Today AFM is the most popular type of SPM, causing the terminology of AFM and SPM to be often used synonymously. In case of AFM, the probe is a cantilever, generally having a tip at its free end. The superfamily of SPM probes can also include simple metal wires (as used in STM) or glass fibers (as used for scanning nearfield optical microscopy/SNOM/NSOM).
Nowadays AFM includes a wide variety of methods in which the probe interacts with the sample in different ways in order to characterize various material properties. AFM can characterize a wide array of mechanical properties (e.g. adhesion, stiffness, friction, dissipation), electrical properties (e.g. capacitance, electrostatic forces, work function, electrical current), magnetic properties, and optical spectroscopic properties. In addition to imaging, the AFM probe can be used to manipulate, write, or even pull on substrates in lithography and molecular pulling experiments.
Due to its flexibility, the atomic force microscope has become a common tool for material characterization alongside optical and electron microscopy, achieving resolutions down to the nanometer scale and beyond. The AFM can operate in environments from ultra-high vacuum to fluids, and therefore cuts across all disciplines from physics and chemistry to biology and materials science.
This article describes the operating principle and most common measurement modes of atomic force microscopy, and some of the many properties that can be measured with AFM on the nanoscale.
Operating principle of AFM
The operating principle of atomic force microscopy is depicted in the following schematic:
The heart of the AFM lies with the cantilever/tip assembly that interacts with the sample; this assembly is also commonly referred to as the probe. The AFM probe interacts with the substrate through a raster scanning motion. The up/down and side to side motion of the tip as it scans along the surface is monitored through the “beam deflection method”. The beam deflection method consists of a laser that is reflected off the back end of the cantilever and directed towards a position sensitive detector that tracks the vertical and lateral motion of the probe. The deflection sensitivity of these detectors has to be calibrated in terms of how many nanometers of motion correspond to a unit of voltage measured on the detector. Nanosurf instruments provide a straightforward procedure for the calibration of this sensitivity and this procedure is described below in the calibration section.
The probe can also be mounted into a holder with a shaker piezo. The shaker piezo provides the ability to oscillate the probe at a wide range of frequencies (typically 100 Hz to 2 MHz) enabling dynamic modes of operation in the AFM. The dynamic modes of operation can be performed either in resonant modes (where operation is at or near the resonance frequency of the cantilever) or off-resonance modes (where operation is at a frequency usually far below the cantilever’s resonance frequency).
Electromagnetic scanners provide highly accurate and precise nanoscale motion in X, Y, and Z at low operation voltage in Nanosurf AFMs. These kinds of scanners provide significant advantages of highly linear motion and the absence of creep over other kinds of scanners such as piezoelectric scanners. The Nanosurf FlexAFM-based systems combine a piezoelectric scanner for Z motion with a flexure-based electromagnetic scanner in X and Y; this configuration provides fast motion in Z with maximum flatness in X and Y, which is optimal for the advanced capabilities offered by these systems.
Atomic force microscopes can be configured either to scan the tip over the sample (in which case the sample is stationary) or scan the sample under the tip (in which case the probe is stationary). All Nanosurf microscopes employ the tip scanning configuration. This configuration provides a significant advantage in terms of flexibility and size of the sample. Tip scanning instruments can accommodate large and unorthodox sample sizes; the only limitation on the sample is that it needs to fit into the instrument! Because the tip is moved and the sample remains stationary, the sample can be almost any size or weight and can still be scanned by the AFM. An example of sample flexibility is shown below with the NaniteAFM system (assembly in typical Nanosurf orange/black at the top) and a custom-built translation/rotation stage to perform roughness measurements on large concave and convex samples.
Cantilever/tip (probe) assembly
This assembly consists of a very sharp tip (typical radius of curvature at the end for commercial tips is 5-10 nm) that hangs off the bottom of a long and narrow cantilever. As mentioned previously, the cantilever/tip assembly is also referred to as the probe.
The two most common geometries for AFM cantilevers are rectangular ("diving-board") and triangular. An example of the diving board configuration of the levers is shown in the SEM image below; note the tip hanging off the end.
AFM cantilevers are typically madeof either silicon or silicon nitride, where silicon nitride is reserved for softer cantilevers with lower spring constants. The dimensions of the cantilever are very important as they dictate its spring constant or stiffness; this stiffness is fundamental to governing the interaction between the tip and the sample and can result in poor image quality if not chosen carefully. The relationship between the cantilever’s dimensions and spring constant, k, is defined by the equation:
k = Ewt 3 / 4L3,
where w = cantilever width; t = cantilever thickness; L = cantilever length and E = Young’s modulus of the cantilever material. Nominal spring constant values are typically provided by the vendor when buying the probes, but there can be significant variation in the actual values.
Nanosurf provides a straightforward manner of calibrating the spring constants of probes, which is described in the section below.
Deflection sensitivity calibration
This calibration is for the detector sensitivity in order to convert volts measured on the photodetector to nanometers of motion. The calibration is performed by measuring a force curve on an "infinitely stiff" surface such as sapphire. The "infinitely stiff" surface is chosen relative to the cantilever such that the cantilever does not indent into the sample during the force curve measurement. Once the force curve is collected of photodetector signal vs. piezo movement, as shown below, the slope of the repulsive portion of the wall is then calculated. This is the deflection sensitivity.
Note that on the Nanosurf Flex-ANA instrument and cantilever calibration options of other product lines this detector sensitivity calibration is automated, where multiple curves are collected and the average detector sensitivity value is calculated.
Spring constant calibration
Calibration of the spring constant of rectangular cantilevers is done via the Sader method on Nanosurf instrumentation and implemented for all current product lines. This method relies on inputting the length and width of the cantilever (these dimensions are provided by the vendor and read from a cantilever list in the AFM software). Generally, a thermal noise spectrum of the cantilever is recorded where the room temperature thermal motion is used to drive the cantilever. A sample thermal tuning spectrum is shown below. A single harmonic oscillator model is used to fit the peak in the thermal spectrum in order to extract the resonance frequency and quality factor. All these parameters are then input into the Sader model for hydrodynamic damping of the cantilever in a given environment, which then calculates the spring constant for the lever.
Alternatively, a frequency sweep can be used to calibrate the spring constant. Here the shaker piezo is used to drive the cantilever.
For spring constant calibration it is important that the cantilever is backed off the surface when these frequency sweeps (either by thermal method or piezo) occur. A lift of at least 100 µm off the surface is recommended.
The final concept that is important to understanding AFM operation is that of feedback. Feedback and feedback parameters are ubiquitous in our life. For example, temperature is the feedback parameter in a thermostat. The user will set the thermostat to the desired temperature, which is referred to as the "setpoint". As the temperature in the environment changes, there is feedback comparing it with the temperature setpoint so that the heater (or air conditioner) knows when to turn on and off in order to keep the temperature at the desired setpoint value.
Similarly in atomic force microscopes, depending on the different modes, there is a parameter that serves as the setpoint. For example, in static mode the feedback parameter is cantilever deflection, while in the most common form of dynamic mode, the cantilever oscillation amplitude is the feedback parameter. The instrument is trying to keep this feedback parameter constant at its setpoint value by adjusting the z piezo to move the cantilever probe up and down. The resulting z piezo movements provide the height information to create the surface topography.
Control of the feedback loop is done through the proportion-integral-derivative control, often referred to as the PID gains. These different gains refer to differences in how the feedback loop adjusts to deviations from the setpoint value, the error signal. For AFM operation, the integral gain is most important and can have a most dramatic effect on the image quality. The proportional gain might provide slight improvement after optimization of the integral gain. The derivative gain is mainly for samples with tall edges. If gains are set too low, the PID loop will not be able to keep the setpoint accurately. If the gains are chosen too high the result will be electrical noise in the image from interference from the feedback; the compensation for a deviation from the setpoint is larger than the error itself or noise gets amplified too strongly.
The other parameters that are important in feedback are the scan rate and the setpoint. If the scan rate is too fast, the PID loop will not have sufficient time to adjust the feedback parameter to its setpoint value and the height calculated from the z piezo movement will deviate from the true topography at slopes and near edges. Very slow scan rates are typically not an issue for the PID loop, but result in long acquisition times that can pose their own challenges such as thermal drift. Optimization of the PID gains and the scan rate are necessary in order to optimize feedback loops. The setpoint affects the interaction force or impuls between probe and sample. A setpoint close to the parameter value out of contact feedback is most gentle for the sample, but tends to slow down the feedback.
See below for an image that was collected with various PID gain settings at the same scan rate. In the red area the image is all electrical noise, because the gains are set too high. The area framed in orange also has some streaks of electrical noise illustrating the same problem. On the bottom, in the blue section, there is poor tracking due to gains being too low. A selected too high scan rate would have a similar appearance. The optimal image and parameter settings are in the green area.
AFM imaging modes
Static mode (contact mode)
Static mode, or contact mode, is the original and simplest mode to operate an AFM. In this mode, the probe is in continuous contact with the sample while the probe raster scans the surface. In other words, the probe "drags" across the sample. The most common configuration of static mode is to operate it in constant force or deflection feedback mode. In this mode, the cantilever deflection is the feedback parameter. The cantilever deflection is set by the user and is related to how hard the tip pushes against the surface so that the user controls how gentle or aggressive the interaction between the probe and the sample is.
Static mode can also be operated in constant height mode where the probe maintains a fixed height above the sample. There is no force feedback in this mode. Constant height mode is typically used in atomic resolution AFM, though it is uncommon for other AFM applications.
Finally there is a configuration known as error mode. This mode is operated in constant force mode). However, the topography image is then further enhanced by the addition of the deflection signal to the surface structure. In this mode the deflection signal is also referred to as the error signal because the deflection is the feedback parameter; any features or morphology that appear in this channel are due to the "error" in the feedback loop, or rather due to the feedback loop needing to kick in to keep the deflection setpoint constant.
In static mode with constant force, the output consists of two images: height (z topography) and deflection or error signal. Static mode can be a useful, simple imaging mode, especially for robust samples in air that can handle the high loads and torsional forces exerted by static mode, but also, surprisingly, for more delicate samples in liquid, as long as the force can be controlled below 100 pN.
Imaging of membrane proteins like bacteriorhodopsin (BR) is an example for the latter. The topography image below shows contact mode imaging on membrane patches containing BR adsorbed on mica, recorded with a FlexAFM and a soft, 0.1 N/m probe. The overview image shows two membrane patches facing the cantilever with different sides: left the extracellular side and right the cytoplasmic side. The difference in height is explained by different electrostatic interactions between membrane and mica and cantilever. In the right hand image there is a smaller scan area, in which individual trimers can be discerned in their native, crystalline matrix, with a distance of 6.2 nm between trimers.
Static mode is available on all Nanosurf AFM product lines.
Lateral force mode
Lateral force mode or frictional force mode is a form of static mode (contact mode). In lateral force mode, the imaging is exactly as it is in static mode except the cantilever scanning motion is generally performed perpendicular to the axis of the cantilever, as opposed to a freedom of scan rotation for conventional static mode. A schematic of the lateral force mode scan configuration is shown below.
This mode is particularly effective for measuring the friction of a surface as the side to side twisting of the cantilever by torque, measured as the probe raster scans along the surface. Lateral force measurements can be converted to frictional force through calibration of the torsional spring constant of the cantilever.
When operating in lateral force mode, it is important to be aware of topography that can convolute the lateral force signal. This is because changes in topography will incur a torsion onto the cantilever as well. In order to account for this topographic convolution, frequently lateral force images are collected both in the forward (retrace) and reverse (trace) scan direction and then subtracted from one another.
This concept is illustrated in the schematic below. The left image shows the effect of a feature in the surface (black semicircle) with friction contrast from the rest of the sample. The forward and reverse scan directions both show a change in friction over this feature; but the change is in opposite directions (blue trace and red trace). Subtracting the forward and reverse scans will enhance the difference in the frictional response. On the right hand side, the results of a topographic feature inducing a response in the lateral force (friction) response are shown. Now both forward and reverse traces show a signal in the lateral force channel in the same direction that is due to topography in this case, not actual frictional change. By taking the difference of the two images, the measured lateral force response is now reduced.
Lateral force images can be very effective at picking up material differences in the sample. Below are AFM images of a polymer blend of polystyrene and polybutadiene. The left shows topography where the two components in the blend are hard to discern. In the middle and the right are the two lateral force images in the forward and reverse direction where differentiation between the two components is easily observed.
The friction is further illustrated in the profile line graph through the image (left graph below), in which the black profile belongs to the forward and the gray to the backward scan direction. Note to display data as "raw data" to correctly display the torsion working on the cantilever. Taking the difference, Δ/2, of the forward and backward movements results in the friction with less cross-talk from topography (black solid profile in right graph below). Taking the average, Σ/2, of the forward and backward lateral deflection gives a signal dominated by the height variations and almost without friction information (gray dotted line in right graph below).
The image below shows the friction calculated from the difference data overlayed on the 3D topography. The image is rotated by about 180° compared to the images above.
Lateral force mode is available on the CoreAFM and FlexAFM product lines. For more information there is an application note on lateral force microscopy of PS-PB.
Dynamic mode (amplitude modulation)
Dynamic mode refers to a collection of AFM modes in which the cantilever oscillates at a high frequency at or close to resonance. A specific kind of dynamic mode, referred to as amplitude modulation mode (AM-AFM) is the most common AFM imaging mode. In AM-AFM, the amplitude of oscillation is the feedback parameter; other dynamic modes have different parameters for feedback such as frequency (frequency modulation) or phase (phase modulation). AM-AFM is also referred to as tapping mode or intermittent contact mode by other vendors.
As an imaging mode, amplitude modulation mode offers several key advantages. Because the cantilever operates at resonance and interacts with the sample as the probe "taps" along the surface, it is a gentle interaction with the surface relative to static imaging modes that can preserve the sharpness of the tip. This kind of interaction also minimizes torsional forces between the probe and the sample, which are especially exacerbated in static imaging mode. These two advantages are particularly important for soft materials such as polymers or nanoparticles or fibrillar samples where dynamic modes are less destructive to the sample. Finally, by using the cantilever’s oscillation amplitude as the feedback parameter, the user is able to fine-tune the interaction between probe and sample between different regimes such as attractive and repulsive regimes.
In dynamic mode, the cantilever is generally driven with a shaker piezo and starts vibrating at the excitation frequency. By sweeping the frequency across a suitable range, the peak in the frequency spectrum that corresponds to the resonance frequency of the cantilever can be found. The Nanosurf software has a table with cantilever properties, allowing it to set the suitable search range automatically. Note that due to the small size of these cantilevers, typical resonance frequencies are in the kilohertz and even Megahertz regime. A sample frequency tune is shown below.
The cantilever is then driven with a sinusoidal motion at a fixed excitation energy, and it behaves as a damped spring or a single harmonic oscillator. As the oscillating cantilever is brought closer to the surface, the cantilever cannot oscillate at its full amplitude anymore and the amplitude of oscillation is reduced, as shown in the schematic below:
This amplitude reduction is the source of the feedback; the user sets an amplitude based on the type of interaction that is desired. The changes in amplitude are caused by changes in the resonance frequency of the cantilever during interaction. A more elaborate explanation how repulsive and attractive tip-sample interactions affect the cantilever can be found in the force spectroscopy section.
Parameters to optimize
The user should tweak 3 parameters during operation of dynamic mode:
- Cantilever spring constant:
The stiffness of the lever must be appropriately suited to image the material. Often some empirical trial and error is required to find a suitable cantilever. If the cantilever is too stiff, the result may be destructive to the sample or cause tip wear. If the cantilever is too soft, it may not be able to interact with the sample to generate any contrast or it stays in contact with the surface.
- Free vibration amplitude:
This is the amplitude of the oscillation by the cantilever when the cantilever is vibrating in free space away from the sample. This parameter is set in units of voltage. Rougher samples need a larger free vibration amplitude.
This is the reduced target amplitude, which results after the tip is in intermittent contact with the sample (see schematic above). The setpoint is expressed as a percentage of the free vibration amplitude. Lower amplitude setpoints will favor a more aggressive tip-sample interaction or a more repulsive tip-sample interaction.
Dynamic mode is available for all Nanosurf AFM product lines. Note, however, that amplitude and phase are measured differently by the various product lines. On the NaioAFM and on systems with the Easyscan 2 controller, a single channel lock-in amplifier is used to measure the phase, while the amplitude is measured by an RMS-DC converted. On all other systems, both amplitude and phase are measured by a two-channel lock-in amplifier, enabling a more sensitive measurement of both amplitude and phase, and a true 360-degree phase shift even at low oscillation amplitudes.
Phase imaging is one of the most common (if not the most common) AFM imaging methods to obtain contrast based on material properties. Phase imaging is a form of amplitude modulation mode imaging, and refers to the phase channel that is collected during this mode. An excited cantilever oscillation will exhibit a phase shift (φ) between the drive and the response, as defined by the equation:
d = A sin (2πft + φ),
where d = deflection; A = amplitude; f = frequency; t = time; and φ = phase shift.
At resonance, the phase shift is 90 degrees compared to the phase well below resonance, as reflected in the amplitude vs. frequency and phase vs. frequency plots below (note that in the Nanosurf control software, the phase is set to zero at the selected oscillation frequency):
When the interaction between an oscillating cantilever and a sample changes, the resonance frequency of the cantilever will shift: to lower frequencies for attractive forces, to higher frequencies for repulsive forces. Consequently, the phase at a fixed frequency shifts when the cantilever-sample interaction changes, for example when the material properties change; this is the reason that phase is a common imaging mode when contrast based on material properties is desired. However, the challenge with phase is that it will shift due to a convolution of multiple material properties, such as: adhesion, stiffness (modulus), dissipation, and viscoelasticity. Thus, while phase is a very useful imaging channel, it can be difficult to interpret the contrast with respect to individual material properties. For example, a sample might have 2 components in it where one is very soft (but not sticky) and the second is sticky (but hard). Even though these are fundamentally different material properties, they could induce similar or even identical phase shifts so that the two components look the same in the phase image.
Below is an experiment on a blend of poly(styrene-butadiene-styrene) (SBS) and polystyrene (PS), showing the power of phase imaging. On the left is a topography image where the two components show some height differences, though the absolute height cannot be correlated with a polymer. In the right phase image, the two components are easily differentiated. These images have a scan size of 10 µm × 10 µm and were measured with a CoreAFM. More data on SBS-PS can be found here. An example of another polymer blend (polystyrene and polybutadiene) measured with NaioAFM can be found here.
An additional challenge of phase imaging is a propensity towards imaging artifacts such as reversal of contrast or loss of contrast. These artifacts are primarily due to the problem of attractive-repulsive bistability where the tip-sample interaction toggles between net-repulsive and net-attractive regimes. This bistability can be controlled with a proper understanding of the cantilever physics and appropriate adjustment of operating parameters. An example of this challenge is illustrated in the polymer mixture image below. Two phase images were collected under different conditions. Note that in the image on the left there is little contrast between the two materials, whereas in the image on the right the contrast between the materials is distinct.
Phase imaging is available on all Nanosurf AFM product lines.
Advanced AFM imaging modes
Additional measurement modes often in combination with special cantilevers enable the measurement of sample properties beyond the topography. Examples are Magnetic Force Microscopy (MFM) and several electrical AFM modes. Some of the modes depend on the detection of magnetic or electrical fields. Key in such measurements is to separate the short-range van der Waals forces from the longer range electrical or magnetic forces. A lifting mechanism enables the probing of longer range electrical and magnetic forces, and deconvoluting them from the short-range van der Waals forces that are present during topographic imaging. The height that the tip is lifted over the sample is often a parameter that needs to be optimized by the user in order to have successful imaging of the magnetic or electrical properties and is typically in the few to hundreds of nanometer range.
The lifting can be done in so called single, interlaced and dual scan line modes. In a single-pass or constant height setup, the slope of the surface is measured from a completed topography image or line before the imaging of the long range interaction is started, and then the tip is scanned at a fixed height above the sample, compensating for the average slope.
Alternative to the single pass are the interlaced and dual pass imaging modes (left and right in schematic below, resp.), providing the topographical information of the surface along with the functional signal. In interlaced mode the forward pass records the topography of a scan line and then the tip is lifted above the sample during the backward pass. In dual pass topography is measured forward and backward in the first pass and the long range signal in the forward and backward movement of the second pass. Dual scan provides the more accurate correlation between topography and long range signal, wheras the interlaced mode is faster.
Since the long range interactions depend on the distance between tip and sample, additional phase contrast is generated when moving at constant slope over a sample with considerable height variation. Contour following, which is an option available for interlaced and dual scanning imaging mode on C3000 and CoreAFM product lines, scans the cantilever above the sample, keeping the separation constant, as depicted schematically below. For very flat samples like hard discs or polished steel contour following is not critical, whereas it may become essential if surface protrusions exceed some tens of nanometers, as shown for an Electrostatic Force Microscopy (EFM) example with 100nm high pedestals.
Magnetic force microscopy (MFM)
MFM is a phase imaging mode that uses atomic force microscope cantilevers with a thin magnetic coating in order to probe the magnetic field between a sample and a magnetized tip. This method is commonly used to image any materials with heterogeneous magnetic properties such as magnetic-based hard drives. It can be operated in single, interlaced and dual scan line modes. Any of these modes require optimization of the height above the sample at which the MFM image is collected.
The measurements below show 80 µm topographic (left) and MFM (center) images of steel plus a zoomed in image of the MFM signal (right). The topography shows minor topographical features, whereas the corresponding MFM image reveals 3 distinct areas: the areas showing meandering being the magnetic ferrite phase, in which contrast and frequency depend on the domain orientations.
Electrical measurement modes
AFM can probe a wide variety of electrical properties of materials and surfaces. These methods operate either in static mode or dynamic mode, depending on the information being sought. Probing properties such as current, conductance, surface potential, and capacitance are increasingly important in a number of applications including research on semiconductors, solar and battery cells, conductive polymers, and nanoelectronics. These applications have in common that the electrical properties of increasingly miniaturized devices and features need to be measured. Note that all these methods require specialized tips, usually in the form of a conventional silicon AFM cantilever coated with an electrically conductive coating. Probes made of conducting diamond are also suitable for some of these methods. All these modes provide simultaneous topography and electrical property data. A review of some of the main electrical modes and properties are given here.
These electrical modes also often take advantage of interlaced and dual pass scan methods, in which the probe measures topography on the forward or first pass and then the probe is lifted a prescribed distance away from the surface on the backward or second pass, optionally following the topography (contour) of the sample, as shown in the advanced imaging modes section.
Conductive AFM (C-AFM)
This is a static mode method where both the current distribution and topography of a surface are mapped simultaneously. It is similar to scanning tunneling microscopy as in both modes a bias voltage is applied between tip and sample, and the tunneling current is measured between the two. However, the advantage of C-AFM, which uses a conductive cantilever as opposed to a sharp metallic wire, is that it provides topography information and current information independently. Single point measurements that measure the current vs. voltage curves (commonly referred to as IV curves) can also be collected in this mode to probe the detailed electrical properties at a position.
Current measurements in air may prove challenging. The contact area between tip and sample is very small (diameter in the 10nm range). Therefore the current density (current per surface area unit) can become very high, rapidly hampering the conductive properties of the cantilever coating. Here a resistor inline with the sample reduces this risk of highly conductive samples.
Surface contamination and a water film between tip and sample commonly present at ambient conditions additionally reduce reliability and repeatability of C-AFM: Only a few nanometers of debris on the tip can block the flow of electrical current. Therefore higher forces are sometimes needed, which require harder tip materials or coatings like conductive diamond-like coatings or platinum silicide.
Such problems are reduced in vacuum systems, like in the example below, recorded in the vacuum of an SEM. The gradual effect of electron beam irradiation on topography and conductivity of a Pt(C) film was measured in situ with AFSEM™. The reduction of height shows the compacting of the film with irradiation dose. At the same time, an increase in local conductivity was observed at higher doses.
3D topography of Pt(C) film irradiated with different electron beam doses
Current through the film of the area inside the blue rectangle in the topography
C-AFM is available for all Nanosurf AFM product lines.
Piezoelectric force microscopy (PFM)
This static mode based method is geared towards the study of ferroelectric or piezoelectric materials, which are materials that respond mechanically to the application of an electric field. This mode measures topography simultaneously with mechanical response of the material when an electric voltage is applied with a conductive AFM tip. A sharp conductive AFM tip is brought into contact with the sample and an AC voltage is applied between the tip and sample. The sample will either expand or contract oscillatory due to this applied voltage. The sample motion is then tracked by the cantilever deflection, which is detected with a lock-in amplifier. The amplitude gives information on the piezoelectric tensor of the material and the phase provides information on the polarization direction.
Shown below is a PFM image of a common piezoelectric material, lead zirconate titanate (PZT). The topograph is shown on the left and a 3D view on the right where the coloring represents the piezo response. The phase clearly reveals striped domains inside the grain that were not visible in the topography.
Electrostatic force microscopy (EFM)
This mode is the electrical equivalent to MFM and operates in phase imaging mode, but now used for imaging variations in the electric field of the substrate. When scanning the tip lifted above the surface (typically only a few tens of nanometers), a voltage is applied between tip and sample to create a long-range electrostatic force.
EFM images reveal information about surface potential and charge distribution from the phase image: with increasing magnitude of the potential difference between tip and sample, the resonance frequency drops, causing reduction in phase. Thus, a lower phase indicates a larger (absolute) potential difference. This also means that the contrast can be varied with the applied voltage. The example below demonstrates that the phase contrast can be inverted by changing the potential. In this measurement aluminum pedestals on top of a gold substrate were imaged with 3V (top) and -3V (bottom) tip voltage in contour following EFM mode.
Kelvin probe force microscopy (KPFM)
This mode images the surface potential distribution of a sample without direct electrical tip-sample contact. It operates in dynamic mode with either a single or dual-pass setup. In the single-pass setup the tip is closer to the sample so there is higher sensitivity and resolution in the Kelvin force measurement, but the topography resolution may suffer somewhat. In the dual pass setup, the tip is further away from the sample, resulting in lower sensitivity and resolution, but the topography can be sharper.
In KPFM an AC plus DC voltage is applied to the cantilever causing an oscillating electrostatic force between tip and sample. The resulting deflection oscillation is detected with a lock-in amplifier and minimized by the DC voltage. The DC voltage used is the local contact potential difference (CPD) between tip and sample. Applications include imaging the Kelvin potential or work function of a surface and measuring applied voltage differences between conductors.
Below is an image illustrating the utility of KPFM. Graphene was deposited onto copper, which was subsequently oxidized. The topography image is shown in the inset revealing the two striated graphene domains and the copper domain in between. The Kelvin probe image shows new features in the surface such as crystal defects within the graphene (circled in white) and differences in coupling to the substrate (circled in grey).
In another example, local charges were placed on an insulating oxide surface layer in a Swiss cross pattern. Imaging the sample with topography (left) did not reveal the pattern, but imaging it in KPFM mode (right) that records the surface potential clearly showed the pattern.
Force spectroscopy refers to single point measurements in which the cantilever approaches and “pokes into” the sample, and then withdraws. During this measurement the cantilever deflection vs. piezo movement is measured, and this can ultimately be converted to a force vs. tip sample separation measurement that provides mechanical information about the sample. This conversion requires the calibration of the spring constant and deflection sensitivity. A model force curve of cantilever deflection vs. z piezo looks as follows:
The force curve can be divided in different segments where A-C (black line) refers to motion where the tip is approaching the surface and D-F (gray line) is when the tip is retracting from the surface. The gray line has been given an artifical offset for illustrative purposes:
- Cantilever is approaching the surface. If there are attractive or repulsive forces between the tip and the sample, those could be measured in this segment by the resp. down or up bending of the cantilever.
- “Snap-in”: the cantilever snaps into contact with the sample. This snap-in is due to tip-surface interactions, like capillary forces.
- Repulsive portion: the tip and sample are in contact and bends up upon further movement of the z-piezo. This section is referred to as the net-repulsive portion.
- Repulsive portion on withdrawal: the tip is now unbending while being withdrawn from the surface.
- Pull-out: the tip gets “stuck” in an adhesive dip before it is able to emerge from the adhesion at the interface.
- The cantilever has returned to its unperturbed state while the z-piezo further increases the tip sample distance.
Force curves can be mined for various mechanical properties of the sample including adhesion, stiffness (modulus), and indentation depth (how much the tip penetrates into the sample at a given load).
Shown below are example force curves from different polymer samples collected on a Flex-ANA. Clearly the sample on the left is very soft and has high adhesion compared to sample on the right, which is stiffer (higher slope on repulsive wall) and less sticky.
Contact mechanics models that model the tip-sample interaction are needed in order to extract the pertinent mechanical information from the force curve. There are a variety of contact mechanics models such as Hertz, Sneddon, DMT, and JKR that can be used depending on the sample and the specifics of the tip-sample interaction. The force curve data are fit with the appropriate model in order to extract the mechanical property information.
Measuring the stickiness or adhesion of a sample can be done by measuring the adhesive dip in a force curve collected through force spectroscopy. The adhesion was measured on the blend of polybutadiene and polystyrene revealing quantitatively different adhesive dips on the 2 materials, as shown in the force curves below on the two materials.
Adhesion measurements can also be extended to single cells and bacteria with Flex-FPM — which uses FluidFM™ technology with hollow cantilevers and a microfluidics control system. In such experiments cells are aspired to a hollow probe like a sock to a vacuum cleaner and subsequently pulled away from the surface, while measuring the cantilever deflection.
Unfolding and stretching measurements
Another application of force spectroscopy is the stretching of molecules tethered between the cantilever tip and a sample. In biological research it has gained a lot of popularity to study phenomena such as protein unfolding, which is challenging or impossible with other techniques. An intensively studied example is the sequential unfolding of bacteriorhodopsin (BR), a light-driven proton pump. The cantilever/tip is able to grab onto the bacteriorhodopsin and pull it out of the membrane. During this process discrete unfolding steps are captured in the force curve measurement as shown in the data below. The protein unfolding events can thus be quantified by yielding the force needed for the individual unfolding steps as well as the (increase of) length of the unfolded stretch of molecule tethered between tip and membrane from one unfolding event to the next.
Because force curves are single point measurements, often many measurements are needed in order to obtain accurate and meaningful data in what is termed force mapping. All Nanosurf product lines are capable of force mapping with grid automation, in addition to automated analysis to calculate slopes, snap-in, and adhesive forces. On the PS-PB polymer blend below, for example, a grid of force curves was collected and the adhesion measured. The 3D map where the adhesion is colored onto the 3D topography clearly shows the different adhesive properties of the two components, where the polystyrene (round domain in the right bottom) has higher adhesion than the surrounding polybutadiene. The data were subsequently compiled into a histogram for further quantification.
With histograms, parameters obtained from force curves, like the adhesion above, are easier to quantify, obtain the average values of the different peaks as well as their separation, and their distribution via the standard deviation or full width at half maximum for a peak.
The elastic modulus can be analyzed similarly. Using force curve mapping where force curves are collected over an area, the mechanical properties of medical tubing was investigated and shown in the data below. The three tube samples were uncoated, and then coated with different polymeric coatings. In a single run, the automated Flex-ANA was able to measure the elastic modulus on all 3 samples, which were equilibrated and immersed in PBS buffer, revealing that the coated tubing was much softer than the uncoated tubing. The softness in this case was a desirable feature, as it is comparable to that found in soft biological tissue, thus making it appropriate for medical applications.
Sophisticated force mapping that can accommodate a wide variety of sample configurations and automated collection and software analysis, with a choice of contact mechanics models, is offered in the Flex-ANA. With this instrument, a series of samples can be programmed for force mapping, followed by a streamlined quantitative analysis and integration of multiple data sets. Individual force curves are displayed during collection, and a histogram of the various properties builds up in real time, as shown in the software screenshot below.
This platform was used to analyze a blend of polymers as shown below. The force mapping showed a clear bimodal distribution in the analyzed modulus data, revealing two distinct moduli for the two different components in the sample.
Lithography and nanomanipulation
In addition to imaging and single point measurements, the AFM cantilever/probe can be used to actually write or manipulate features on the nanoscale. Typically operated in static mode, the cantilever/probe can carve out patterns or structures on surfaces through an aggressive interaction between the tip and sample configured with a high deflection setpoint. In this way a stiff cantilever was used to scratch an "X" into the sample below.
The probe can also write structures and patterns through local oxidation at the point between the probe and the sample. In the example below, a Nanosurf logo was etched using local oxidation of titanium by applying 3 V between the sample and a conductive diamond tip.
In terms of manipulation, the probe can be used to cut or move around structures. In the example below, the probe performed a "surgery" on a bacteria (the elongated white structure in both images below) and divided it into two parts. The cut through the bacteria is evident.
More advanced setups such as the Flex-FPM — which uses FluidFM™ with hollow cantilevers connected to a microfluidics control system — can also be used in lithographic mode to write or deposit molecules from a liquid that can be delivered to the surface through the hollow cantilever. The volumes involved are tiny (femtoliters) and are combined with micrometer accuracy to write fluidic patterns such as the ones shown below. On the left is a grid written in biomolecules as a function of application time and pressure steps, resulting in well-controlled spots of different sizes. On the right is the Nanosurf logo written in air with a solution of 50% glycerol and a back pressure of 200mbar.
In this way DNA and RNA has been spotted on a surface for single cell content analysis. With its hollow probes, FluidFM is a more versatile technology than just a tool for spotting and nanolithography. A FluidFM probe exhibiting an opening next to apex of the tip can be used as a syringe for single cell injection or extraction.
Electrochemical AFM (EC-AFM)
Electrochemical AFM mode enables measurements while electrochemical reactions are taking place in electrolyte solutions on an electrode surface. Electrochemical reactions are processes in which electrons flow between solid electrodes and substances in solution, involving a reduction reaction (at the cathode) and an oxidation reaction (at the anode). These reactions are widely studied in applications such as corrosion and photovoltaics. EC-AFM measurements enable monitoring of the electrode structure during such reactions and establishing the relationship between the electrode structure/morphology and its electrochemical activity.
Because these studies typically occur in aggressive liquid environments, excellent environmental control and protection of AFM electronics is necessary for effective imaging. The Nanosurf Flex-Axiom series, combined with the electrochemistry stage ECS204, is ideally suited for these measurements, as all the AFM electronics are protected and positioned above the liquid, and the cantilever holders are made of a special corrosion-resistant material.
Shown below is a study of nucleation and growth of copper clusters under electrochemical control. Cyclic voltammograms were used to charactize the electrochemical reactions and establish suitable potentials to observe topographical changes under stable electrochemical conditions.
Nucleation was observed by AFM at E = -50mV in sulphoric acid vs a platinum quasi reference electrode. Increasing the potential E = -10mV reduced the growth rate and a single copper cluster could be followed by time-lapse AFM. This reaction is reversible and at positive potentials the cluster was dissolved again.
The height of the ECS204 electrochemical stage is constructed so that it can also accommodate standard, rod-like electrodes. In the example below, dissolution of deposited copper clusters on a polished rod-like platinum electrode at oxidizing conditions was observed by AFM.