Operation modes of AFM

There are various operation modes on the AFM with different features. The contact mode (stactic mode) is the first operation mode of the AFM. For explaining, the force-displacement curve (force curve) is illustrated in Figure 1.4. The y-axis represents the flexural deflection of the cantilever, and the x-axis is the z displacement of the piezoelectric scanner. At the initial position (index 1), the tip is far from the sample, and there is no force acting on the cantilever. Next, the sample is brought close to the tip continuously. Until the tip is very close to the sample (index 2), the capillary force caused by the thin water layer on the sample and the Van der Waals force attract the cantilever to the sample. Following the closer distance, the tip will contact with the sample, then the repulsive force between atoms will bend the cantilever upward linearly (index 3). The contact mode AFM is operated in this repulsive region. When the cantilever removes from the sample, the capillary force still grabs the tip until the cantilever spring force exceeds the attractive force. This curve presents the relation between the cantilever flexural deflection and the scanner displacement. Therefore, the curve is called the force-displacement curve or the force curve. For capturing the topography of the sample, the tip will scan the sample surface along the X-Y axes by the piezoelectric scanner, and a feedback controller is used to keep the cantilever deflection constant by adjusting the Z axis of the scanner. Therefore, the tip-sample interactive force is maintained constant during scanning. The recorded 3-D displacement of the scanner represents the acquisitive topography that will be showed on the computer. In the contact mode, the cantilever tip is always kept contact with the sample. Some techniques must be operated in the contact mode like the FFM and the conductive AFM (CAFM). However, the contact mode induces larger lateral force, and could damage soft samples easily.

Figure 1.4 Force-displacement curve of contact mode

The tapping mode (intermittent contact mode) is the most common mode in the AFM today. This mode improves the resolution and reduces damage to soft samples [21, 22]. In the tapping mode, the cantilever tip is oscillated around its resonant frequency, and lightly taps on the sample surface. Since the tip is no longer continuously in contact with the sample, the lateral friction between the tip and the sample is reduced significantly. Similar to the contact mode, the force-displacement curve illustrates the operating region of the reference signal. An experimental force-displacement curve on a hard substrate is shown in Figure 1.5 [23]. Figure 1.5(a) shows the relation between the cantilever oscillation amplitude and the z-axis scanner displacement. The amplitude doesn’t change when the cantilever tip is still far from the sample. A small amplitude reduction occurs when the tip falls in the attractive region intermittently, and the repulsive force keeps reducing the amplitude to zero with the tip-sample distance decreasing. Substituting the cantilever deflection signal, the amplitude signal is chosen as the reference signal for z-axis feedback control. Therefore, the tapping mode is also

phase signal represents the phase shift between the excitation signal and the cantilever oscillation. The phase signal is very sensitive to the material properties, and provides an intense contrast between different materials [24]. The phase signal also varies with the z-axis displacement as shown in Figure. 1.5(b). Through the amplitude and phase signals, the total energy transmission on the cantilever can be calculated, and the tip-sample energy dissipation is evaluated as shown in Figure. 1.5(c). Similarly, the phase modulation AFM (PM-AFM) utilizes the phase signal as the feedback reference signal [25]. The PM-AFM is claimed to be more suitable for high speed imaging, because its time response is not influenced by the Q-factor of the cantilever. Except the AM-AFM and the PM-AFM, the mode used the frequency shift of the cantilever resonant frequency is so called the frequency modulation AFM (FM-AFM) [26].

Besides the high resolution imaging ability [27], the measurement of dissipative energy is also proposed by the FM-AFM [28]. However, the FM-AFM also requires a stable cantilever deflection signal, and could be disrupted by occasional disturbance such as the tip crash, adhesion and environmental thermal variation. In contrast with the contact mode, these modes with the oscillation are classified into the dynamic mode.

Figure 1.5 Force-displacement curves of tapping mode [23]

The dynamic mode mentioned above is associated with the electric signal modulation. From the point of mechanics, the cantilever tip has infinite different resonant modes itself. Figure 1.6 shows several modes of a retangular cantilever tip.

Most often, the fundamental flexural mode is used for the dynamic mode. Some higher order resonant modes of the cantilever can also get stable images, and their phase images have high contrast on differet materials [29]. Another associated method detects the higher harmonics of the fundamental resonance [30, 31]. In this method, the force-displacement curve is constructed from higher harmonic signals, and the material mechanical properties can be evaluted by theoretic equations. In the torsion mode AFM (TR-AFM), the cantilever executes a small torsion resonant oscillation on its long axis

such as friction and elasticity [32], and the AM and FM techniques can also adapt to the TR-AFM [33]. Comparing with the fundamental flexural mode, the Q-factor of the torsion mode is higher, and the long-range normal force has less influence on the frequency shift [34].

(a) Fundamental flexural mode (b) Second flexural mode

(c) Third flexural mode (d) Torsion mode Figure 1.6 Cantilever resonant modes