In the simplest AFM set up there is, which was developed in 1986,1 a micro-machined cantilever is scanned across the surface of a sample by a piezoelectric tube.
In this set up topographical features cause the fine cantilever tip to be deflected, and this deflection is detected using the deflection of a laser beam off the top of the cantilever.
Laser deflection is measured using a position-sensitive photo detector (PSPD) and the information is collected to provide a map of the sample surface. This configuration is shown in Figure 1.
Figure 1. Schematic of AFM operation
The extent by which the cantilever is deflected depends on the Van der Waals (VdW) interactions between the sample and the cantilever tip. The magnitude of the VdW force is significantly impacted by the attractive forces between ion cores and valence electrons (Fel) and the repulsive forces between the positive nuclear cores (Fion). The distance dependence of these two different forces is shown in Figure 2.
Figure 2. Interatomic force vs. distance
If the AFM is held several nanometers away from the surface of the sample Fel is more significant, however as the tip approaches the sample surface Fion becomes increasingly dominant. In contact mode AFM, first used in 1986, the cantilever tip is always in contact with the surface of the sample, meaning close-range repulsive deflections are used to trace the samples features.
Non-contact mode AFM (NC-AFM) was developed one year later and in this set up the tip remains close above the surface of the sample as it is scanned over it. In NC-AFM the features of the sample surface are traced using deflections as a result of longer-range attractive interactions.
The attractive deflections used in NC-AFM methods tend to be of too low a magnitude to measure sample surfaces using a direct current (DC). One way around this is vibrating the cantilever at its resonant frequency (using a piezoelectric modulator), which allows changes in this resonance to be correlated to surface features of the sample. This alternation current (AC) method provides a greater level of sensitivity and resolution than DC NC-AFM methods.
The original NC-AFM was developed in 1987 by Martin et al. one year after the development of non-contact mode in standard AFMs.3 An NC-AFM vibrates the cantilever close to its intrinsic frequency of resonance (f0) with a piezoelectric bimorph. This frequency tends to lie between 100 – 400 kHz, with Park System’s True Non-Contact Mode AFM having a resonance frequency of 350 kHz, with an oscillation amplitude of 1-5 nm.
The resonance frequency of the cantilever can be determined by scanning through the frequencies by varying the voltage supplied to the bimorph (Figure 3). This resonant vibration is described using a spring constant (k0) as in Equation 1, shown below.
When the tip approaches the sample the VdW interactions between the sample surface and tip result in fluctuations in the phase and amplitude of the cantilever’s resonance, which results in a new effective resonant frequency (feff) and a new effective spring constant (keff).
If the force gradient is positive (i.e. an attractive force is present) the effective spring constant (keff) becomes smaller as the tip moves closer to the surface, this also results in the new effective resonance frequency (feff) becoming smaller than the intrinsic resonance frequency (f0). This is illustrated in Figure 4.
Fluctuations in the vibration amplitude result in changes in the distance between the sample surface and the tip (Δd). Measurement of Δd whilst keeping the distance (d0) and amplitude (A0) the same allows the NC-AFM to map a sample’s topography by controlling movement of the Z-scanner in response to frequency changes. A rapid Z-servo feedback loop is used to oversee this process.
Figure 3. Resonant frequency of a cantilever
Figure 4. Resonant frequency shift
Figure 5. Resonant frequency shift
Challenges of Non-Contact AFM in Ambient Atmosphere: Fast Z-Servo Feedback
Mechanisms of feedback modulation can work in both the repulsive and attractive interaction zones. In the attractive interaction zone, the overall attraction between the sample surface and the cantilever tip dominates the reduction of the amplitude when there is no real contact between the sample and the tip.
If there is not enough mechanical control it is possible for the longer range attractive forces to overcome the short-range repulsion, which results in contact between the sample and the tip at the end of each cantilever oscillation cycle.
As illustrated in the Amplitude vs. Distance plot in Figure 6 only a small amount of the tips motion is in the attractive force zone for tips that oscillate with large free air amplitudes. For this reason, it is hard to hold the tip within a strict region.
At smaller free air amplitudes (Figure 7, Figure 8) more of the tips motion sits within the attractive force zone. However, to have such a small free air amplitude a high degree of mechanical control, with rapid Z-servo feedback, is needed to identify any permutations in tip amplitude, which occur when the interaction forces change as the tip passes over the sample’s surface.
Figure 6. Amplitude vs. distance plot of a tip oscillating with large free air amplitude
Figure 7. Amplitude vs. distance plot of a tip oscillating with small free air amplitude
Figure 8. Amplitude vs. distance plot under the net attractive force regime
True Non-Contact Mode by High Force Z-scanner in Crosstalk Eliminated (XE) AFM
The majority of ambient AFM manufacturers do not have Z scan actuators that can hold the tip in the attractive zone, so instead they work in the repulsive zone. However, this means that their tips often come into physical contact with surface of the sample, which results in damage to both the sample and the cantilever tip.
Crosstalk eliminated AFMs (XE-AFMs) from Park systems use a flexure guided high-force Z-scanner (Figure 9) to provide highly sensitive responses to tiny fluctuations in cantilever amplitude caused by small changes in the amplitude of the attractive force.
Figure 9. The crosstalk eliminated (XE) AFM with high force Z-scanner
The rapid response of this Z-scanner means movement of the end and side of the cantilever tip is tracked with precision. This means the tip can quickly move away from the surface when in the presence of quickly rising sample features (Figure 10, Figure 11) and remain within the attractive zone without hitting the surface of the sample.
Figure 10. Tip-sample interaction at the end and side of the tip
Figure 11. 3D rendering of 1 um scan image of 50 nm wide, 100 nm deep trenches, measured by True Non-Contact Mode of the XE-100, is shown in 1:1 aspect. True Non-Contact Mode from the XE-series with high Z-servo performance can accurately trace the steep walls of the trenches.
Park Systems’ XE AFMs, equipped with high-frequency cantilevers, decoupled Z and XY scanners and novel multiple-stacked piezos can provide both the control and speed required to carry out True Non-Contact Mode AFM.
References and Further Reading
- G. Binnig, C. Quate, and Ch. Gerber, Phys. Rev. Lett. 56, 930 (1986).
- G. Meyer and N. M. Amer, Appl. Phys. Lett. 53, 2400 (1988).
- Y. Martin, C.C. Williams, H.K. Wickramasinghe, J. Appl. Phys. 61, 4723 (1987).
- R. Garcia, and A. San Paulo, Phys. Rev. B. 60, 4961 (1999).
This information has been sourced, reviewed and adapted from materials provided by Park Systems Inc.
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