Atomic Force Microscopy: Vibration mode (Dynamic mode)

In dynamic mode, the cantilever is oscillated close to its resonance frequency. This vibration mode operates at a frequency-modulation (FM) mode or the more common amplitude-modulation (AM) mode, which are basically the same as the frequencies used in radio communication. In the FM mode, a z-feedback loop keeps a constant force between the tip and the sample while the tip follows the contours of the surface by maintaining the resonance frequency. In the AM mode, the z-feedback loop keeps the constant tip-sample interaction by maintaining the amplitude of oscillation.

1. Intermittent contact mode

The cantilever in dynamic mode can easily be vibrated by a piezoelectric ceramic called a bimorph actuator. In air, the cantilever is oscillated close to its resonance frequency and positioned above a sample surface. When the vibrating cantilever comes close to the surface, its oscillation amplitude may change and can be used as the control signal. In this AM mode, the tip is still in contact with the surface, but it just contacts or "taps" on the surface for a very small fraction of its oscillation period. This operation mode is best known as tapping mode in commercial AFMs and more generally as intermittent contact mode.

As a raster scan moves the tip on the sample, the four-segment photodiode measures the vibration signal of the cantilever. The detected signal can be changed to root mean square values by an analog-to-digital converter. In constant force mode, the z-feedback loop adjusts so that the averaged amplitude of the cantilever remains nearly constant. Each contour of the surface causes a movement of the tip in the xyz-direction, resulting in a change of the oscillation amplitude of the cantilever. This change is measured through a photodiode and finally translated to an image. In air, friction forces due to the surface water layer are dramatically reduced as the tip scans over the surface. Tapping mode may be a far better choice than contact mode for imaging of biological structures due to their inherent softness. In tapping mode, the cantilever can be vibrated at an amplitude of less than 100 nm. Additionally, changes in the phase of oscillation under tapping mode can be used to discriminate between different types of materials on the surface.

1.1 Tip-sample interaction

The mechanical resonance of the cantilever plays a major role in the response of the system for an interaction between a tip mounted on a vibrating cantilever and a non-homogeneous external force [23]. Even though basic equations governing the operation of a bimorph actuator used to vibrate the cantilever are not introduced here, the position of the bimorph is given by:

u = u o + A ex cos( w t + j )

 Where u ois the equilibrium position and the excitation is done with amplitude A ex, a frequency w, and a phase shift j . The fundamental resonance frequency of the cantilever can be approximately calculated from equating its strain energy at the maximum deflection to the kinetic energy at the point of zero deformation. A more accurate method, which takes into consideration all the resonance frequencies of the cantilever together with the modes of vibration, can be obtained by solving the equation of motion subject to the boundary conditions [23]. We briefly introduce a basic equation to describe the motion of the cantilever. If the tip-sample interaction is uniform and includes dissipative force in Newton's second law, the vibration system including the cantilever can be described as follows:

F(z) = k (z – u) + g (dz/dt) + m (d 2z/dt 2)

 Where F(z)is the tip-sample interaction force, kis a spring constant of the cantilever, zis the vertical position of the cantilever, u is the motion of the bimorph, g is the dissipation term i.e. the friction coefficient of the material and/or the environment, and mis the effective mass of the cantilever. For the constant amplitude mode, we assume that the frictional force g (dz/dt)is compensated for by the driving force F ex = kA excos( w t + j ). Then, the equation of motion is reduced to F(z) = k z + m (d 2z/dt 2). If a strong tip-sample interaction occurs only at the point of contact, the motion of the cantilever tip can be almost perfect harmonic oscillation, z = zo + A sin w t.

1.2 Resolution and Tip effects

The resolution obtained by an AFM depends greatly on the sharpness of the cantilever tip. Broadening effects usually arise when imaging biological structures having extremely small surface features like a DNA strand [4]. If a tip with a radius of curvature of about 20 nm is used to image DNA on a substrate surface the observed width is about 20 nm. This is considerably greater than the expected value of 2.4 nm deduced from the van der Waals radii of DNA. When the tip radius is comparable with the size of the feature being imaged, it is important to evaluate the radius of the tip end. As such, the development of sharper tips is currently a major concern for commercial vendors. This is also of interest for biologists whose work would greatly benefit from much faster scanning. Recently, improvement of the scanning speed in AFM is one of the most important topics. The tip-sample interaction also tends to distort biological structures because they are relatively soft [31].

1.3 Phase imaging

Phase imaging is an extension of tapping mode based on the measurement of the cantilever phase lag [32]. The dependence of phase angles in tapping mode AFM on the magnitude of tip-sample interactions has been demonstrated. The phase images of several hard and soft samples have been recorded as a function of the free amplitude and the reference of the tapping amplitude. It is thought that the elastic deformation associated with the tip-sample repulsive force can be estimated by the repulsive contact interaction. In many cases, phase imaging complements the LFM and force modulation techniques often providing additional information along with a topographic image. Phase imaging like LFM can also be applied to CFM by using a modified tip with chemical functionality.

1.4 Pulsed force mode

Pulsed force mode (PFM) is a non-resonant and intermittent contact mode used in AFM imaging [33] . It is similar to tapping mode in that the lateral shear forces between the tip and the sample are also reduced. In contrast to tapping mode, the maximum force applied to the sample surface can be controlled, and it is possible to measure more defined surface properties together with topography. This mode is similar to the force modulation techniques of CFM in that a chemically modified tip is used. A series of pseudo force-distance curves can be achieved at a normal scanning speed and with much lower expenditure in data storage. A differential signal can be amplified for imaging of charged surfaces in terms of an electrical double layer force.

2. Non-contact mode

A reconstructed silicon surface has been imaged in a non-contact mode by AFM with true atomic resolution [34]. The operation of the AFM is based on bringing the tip in close proximity to the surface and scanning while controlling the tip-sample distance for the constant interaction force. The tip-sample interaction forces in non-contact mode are much weaker than those in contact mode as shown in figure 5. The cantilever must be oscillated above the sample surface at such a distance as is included in the attractive regime of the intermolecular force. Most surfaces are covered with a layer of water, hydrocarbons, or other contaminants when exposed to air. This makes it very difficult to operate in ambient conditions with non-contact mode. Under ultrahigh vacuum, clean surfaces tend to stick together, especially when the materials are identical. The FM mode used in non-contact mode can keep the constant tip-sample interaction by maintaining the resonance frequency of oscillation through the z-feedback loop. Nearly ten years following the invention of the AFM, a few groups achieved true atomic resolution with a non-contact mode [35]. After that, several groups succeeded in obtaining true atomic-level resolution with non-contact mode on various surfaces. There still remain many important yet unresolved problems such as determining the tip-sample distance where atomic-level resolution can be achieved. Experimentally, atomic-level resolution can be achieved only between 0 – 0.4 nm. A stiff cantilever vibrates near resonance frequency (300 - 400 kHz) with amplitude of less than 10 nanometers.

In covalently bound materials, the charge distribution of surface atoms reflects their bonding to neighboring atoms [36]. These charge distributions have been imaged by non-contact mode with a light-atom probe such as a graphite atom. This process revealed features with a lateral distance of only 77 picometers (pm). However, all of the atomic scale images have been generated in ultrahigh vacuum, which has limited applications in biology. Recently, several groups have reported obtaining atomic scale images with FM mode in ambient conditions and liquid environments. In the near future, true atomic-level imaging by AFM will be commercially available in various environments.

2-Optical Beam Deflection