Thesis Organization

The dissertation consists of seven chapters. Chapter 2 introduces the basic structure and components of the AFM. In Chapter 3, the affection of the cantilever dimensions is discussed through theorems and experiments. Basing on the analysis, a mass sensing method by cantilever high order resonances in water is also demonstrated. In Chapter 4, different cantilever holder designs are developed. The points for reducing the complex acoustic interference are discussed according to the experimental results. The astigmatic detection method is studied in Chapter 5. The sensitivity of the astigmatic detection system is examined, and the optimum condition is proposed for operating in water.

Besides, the spring constant calibration process is presented by the astigmatic detection system. Chapter 6 displays the configuration and experimental results of a homemade AFM for liquid environment. In the final chapter, a summary of this dissertation is made.

Chapter 2 Preliminary

In this chapter, the AFM system is divided into the force sensing system, the actuator system, and the control system. The functions in these three sub-systems are introduced respectively. Besides, some typical phenomena and limitations of the AFM components are also presented.

2.1 AFM System Structure

The force sensing system, actuator system, and control system are three main components of an AFM. A system block diagram is shown in Figure 2.1. The force sensing system measures the interative force between the cantilever tip and the sample.

For the dynamic mode, an excitation source is essential to resonate the cantilever. When the cantilever deformation is small, the cantilever force sensor is equivalent to a linear spring. The cantilever deformation is detected by the cantilever detection system, and is usually transduced to the voltage signal for the controller. The actuator system is responsible to produce the precise relative displacement between the tip and the sample.

The surface image is scanned through the XYZ scanner. Because the maximum displacement range of the scanner is usually at micrometer scale, the tip and the sample must be brought closely by another Z-axis approaching system. The control system recieves the cantilever deformation signal from the force sensing system, and commands the actuator system for the scanning. For the dynamic mode, a lock-in amplifier or a phase lock loop (PLL) is required for driving the excitation source and

approaching function, the Z-axis approaching system is also controlled by the control system. The user interface, data processes are executed by the software in the computer.

Furthermore, some additional implements can also be combined in the AFM system. An optical microscope (OM) and a XY coarse stage are helpful to specify the scanning area on the sample, when the sample has some larger features. The combination of the Raman spectroscopy and the fluorescence imaging can also be realized on the OM-based AFM for molecular identification.

Figure 2.1 Force sensing system, actuator system, and control system

2.2 Force Sensing System

2.2.1 Cantilever force sensor

The force sensor is a critical element in the AFM, and includes the cantilever and the tip. Figures 2.2 show the scanning electron microscope (SEM) images of commercial cantilever tips. The cantilever is based on a chip for handling easily. A tiny tip sites on the front end of the cantilever and faces to the measured sample. The structure is made by the microelectromechanical systems (MEMS) process. The

cantilever geometry is designed for different requirements. Figure 2.2(a) and Figure 2.2(b) present a rectangular cantilever and a triangular cantilever, respectively. The rectangular cantilever has uniform cross-section, and its spring constant and resonant frequency can be evaluated simply. The triangular cantilever is less sensitive to the lateral force and disturbance.

(a) Rectangular cantilever tip (b) Triangular cantilever tip Figure 2.2 SEM images of commercial cantilevers (MikroMasch)

The sharpness of the tip influences the resolution in XY plane directly. Nowadays, the apex radius of the commercial tip is about several nanometers. However, large force between the tip and the sample could wear the tip. The tip could also be polluted due to adherent dust or biomolecules. For example, a typical artifact caused by the double tips is illustrated in Figure 2.3(a). Two tips contact with the sample alternately, and cause an error on the scanning trajectory. Figure 2.3(b) shows the pectin aggregates image captured by the double tips [37].

(a) Scheme of double tips trajectory (b) Pectin aggregates image of double tips [37]

Figure 2.3 Double tips artifact

The cantilever is another significant component, which affects the force sensitivity and the scanning speed directly. When the cantilever deformation is much smaller than its dimensions, the cantilever can be seen as a linear spring. On a homogeneous rectangular cantilever, the spring constant k and the fundamental resonant frequency fr

of the fundamental flexural mode can be approximated by following Equations (2.1) and (2.2) [38]: where E is the Young’s modules of cantilever, b, h, and L are the width, thickness, and length of the cantilever, and ρc is the cantilever density.

For the contact mode, smaller spring constant k is preferred. Therefore, long and thin cantilevers are usually adapted. On the other hand, the dynamic mode often uses shorter and thicker cantilevers, which have higher resonant frequency fr. The cantilever with high resonant frequency can reduce the response time, and improve the scanning

speed. However, the spring constant is also increased. This result causes larger interactive force between the tip and the sample. To overcome this conflict, the cantilever size trends to diminish in all dimensions, including the length, width, and thickness. Besides, the cantilever detection system also needs to be modified for the smaller cantilever.

2.2.2 Excitation source

In the dynamic mode, the cantilever has to be excited around its resonant frequency.

The most common method utilizes a piezoelectric actuator to generate the oscillation energy as shown in Figure 2.4. The energy transfers to the cantilever through the mechanical parts on the cantilever holder. In liquid environment, “forest of peaks”

phenomenon also appears generally. For avoiding this problem, different methods such as magnetic excitation and photothermal excitation are also developed.

Figure 2.4 Scheme of piezoelectric actuator excitation

The magnetic excitation method applies an AC magnetic field on a magnetic cantilever as shown in Figure 2.5 [39, 40]. The magnetic excitation force applies on the cantilever directly, and a pure peak can be got in the tuning spectrum in liquid.

Figure 2.5 Scheme of magnetic excitation method [39]

The Lorentz force excitation method is illustrated in Figure 2.6 [41, 42]. Unlike the magnetic excitation method, the magnetic field is constant. The AC current passes through a triangular cantilever, and generates the vertical force on the cantilever.

However, this method could also induce a coupling between the flexural mode and the torsion mode of the cantilever [43]. Besides, it could affect the imaging due to the immersed electrode in liquid buffer.

Figure 2.6 Scheme of Lorentz force excitation method [42]

Figure 2.7 displays a setup of the photothermal excitation method [44, 45]. Except the cantilever detection system, an additional laser is focused on the cantilever. The cantilever oscillation is induced by the heat expansion, and the oscillation frequency is controlled through the laser modulation.

Figure 2.7 Scheme of photothermal excitation method

Summarizing these methods, applying excitation force on the cantilever directly is an effective way to eliminate the spurious peaks. However, additional equipment is required and complicates the system design. Furthermore, the magnetic and Lorentz force excitation methods limit the available cantilevers, and involve magnetic field and current into the measured environment. Therefore, some modifications based on piezoelectric excitation are also proposed on the other hand. Adams et al. studied the contact surface between the cantilever chip and the holder [46]. Typically in air, adjusting the cantilever position on the holder can eliminate the spurious peaks. Basing on this observation, the affection of dust or silicon shards on the cantilever is considered.

Through modifying the chip surface by adding pattern, lowering the chip contact surface area decreased the occurrence of spurious peaks. This result can likely be attributed to a higher occurrence of particles trapped on larger contact area.

Figure 2.8 Cantilever holder design of Asakawa and Fukuma [47]

Asakawa and Fukuma considered the acoustic wave propagation from the piezoelectric actuator to the cantilever, and proposed a holder structure as shown in Figure 2.8 [47]. First, for suppressing the acoustic wave caused by the holder boundary stress, a PEEK holder body was placed between the piezoelectric actuator and the steel chip support. Second, the cantilever was excited by the flexure drive mechanism, which was achieved by a flexure hinge design as shown in Figure 2.8(c). Figure 2.9 shows the experimental results of their modified holder with two different holder materials. Figure 2.9(a) represents the bode plot with the steel holder body, and Figure 2.9(b) is the bode plot with the PEEK material. A single peak was captured on the PEEK holder successfully. However, the flexure drive mechanism caused the phase delay, which may need to be compensated for the FM-AFM and phase imaging.

(a) Bode plot on steel holder (b) Bode plot on PEEK holder Figure 2.9 Excitation spectrum comparison between two materials [47]

2.2.3 Cantilever detection system

The deformation of the cantilever has to be detected by a detection system. The resolution of the detection system affects the AFM force sensitivity directly. Besides, the bandwidth of the cantilever detection system also limits the scanning speed. Several detection methods are shown in Figure 2.10. The earliest method utilizes a STM tip to measure the tunneling current between the STM tip and the cantilever as shown in Figure 2.10(a) [4]. Utilizing the resistance variation of a piezoresistive cantilever, the cantilever deflection can be measured by a Wheatstone bridge as shown in Figure 2.10(b) [48]. This embedded piezoresistive sensor on the cantilever simplifies the alignment of the external detection sensor, but also complicates the cantilever

(a) Tunneling current (b) Piezoresistance (c) Capacitance

(d) Interference (e) Beam deflection (f) Astigmatism Figure 2.10 Cantilever detection methods

environment. Besides the electric methods, different optical methods are also utilized.

Figure 2.10(d) shows the interferometry method using an optical fiber, and this method has high sensitivity and provides absolute displacement measurement [50]. This technique needs the complex signal processing and implementation cost, and positioning the optical fiber is also a demanding task. The optical beam deflection method is the most popular method, and its principle is illustrated in Figure 2.10(e) [51, 52]. In this method, a laser beam is focused on the cantilever, and the reflective beam is detected by a position sensing detector (PSD). Beam deflection method is sensitive to the cantilever angular variation, and provides both the cantilever flexural and torsional deflection signals. The astigmatic detection method is widely used in the digital versatile disk (DVD) pickup head. Figure 2.10(f) is a schematic setup for the cantilever detection [53, 54]. The vertical displacement and two-dimensional angular tilts of the cantilever can be detected in this method. Utilizing the commercial astigmatic pickup

head, an astigmatic detection system can be compact and cheap. Furthermore, it has small laser spot size and high bandwidth. The detailed comparison between beam deflection and astigmatic detection methods is discussed in Chapter 5.

2.3 Actuator System

2.3.1 Scanner

The AFM scanner provides precise relative displacement between the cantilever tip and the sample. By moving either the tip or the sample, the AFM design can be classified to the scanning tip type or the scanning sample type roughly. For applications with small and light samples, the scanning sample type is prefered, because its bandwidth doesn’t reduces much due to the weight of sample. On the other hand, the scanning tip type is suitable for the large and heavy sample. However, the affection on the cantilever detection system due to the movement has to be avoided.

Most AFM scanners use the piezoelectric material to achieve precise displacement.

Piezoelectric ceramic material such as lead zirconate titanate (PZT) is a transducer between the electric charge and the mechanical force. The piezoelectric actuator can produce extension through applying voltage directly, and generates precise displacement.

On the contrary, high input voltage is required for larger displacement. The multilayer piezoelectric stack increases the displacement by stacking piezoelectric actuators as shown in Figure 2.11(a). A three-axes scanner can be achieved by collocating three piezoelectric stacks with an appropriate mechanism. The piezoelectric tube is another common design for the AFM scanner. The piezoelectric tube has upper and lower sections as shown in Figure 2.11(b). The outside electrode of the upper section is

electrodes provides one dimensional movement. Therefore, the upper section is responsible for the XY-axes movement, and the lower section controls the Z-axis extension. The tube scanner can provide the three-axes movement by one single structure, and simplifies the assembling problem. However, the XY-axes movement causes crosstalk on the Z-axis when the scanning area is far from the tube center.

Another drawback of the tube scanner is the spacial limitation. The tube scanner occupies the bottom space of the sample, and the invert OM is not compatible.

(a) Multilayer piezoelectric stack (b) Piezoelectric tube Figure 2.11 Piezoelectric scanner

Although the piezoelectric actuator is precise and easy to use, nonlinear and changeable properties of the piezoelectric actuator should be reminded. Similar to the electromagnetic actuator, the hysteresis phenomenon also exhibits on the piezoelectric actuator. In the piezoelectric material, hysteresis is caused by crystalline polarization effects and the molecular friction. Figure 2.12 illustrates the hysteresis phenomenon, where the X-axis and Y-axis are the input voltage and output displacement respectively.

The hysteresis effect is related to operation parameters such as input amplitude, load, temperature, etc. This nonlinear property causes the image distortion problem as shown in Figure 2.13(a). The sample is a square grating with 3 μm pitch and 20 nm height. The distortion of the square structures is obvious due to the hysteresis. Another issue is the scanner bandwidth, which limits the maximum scanning speed. Without the Z-axis feedback control, Figure 2.13(b) shows the cantilever deflection image of the same square grating with 800 line/sec scanning rate. Because the Z displacement of the scanner is constant, the deflection signal is proportional to the topography. The high scanning rate causes serious distortion and oscillation, and the scanning range also decreases. Except the scanner properties, the environmental temperature variation can induce a slow position drift due to the thermal expansion of the whole mechanism.

Figure 2.12 Piezoelectric hysteresis with different input amplitudes

(a) Topography image with scanning rate of 1 line/sec

(b) Deflection image with scanning rate of 800 line/sec Figure 2.13 AFM images of calibration grating with 3 μm pitch

Some nonlinear scanner properties can be solved by control methods. The open-loop control method calibrates the scanner displacement by adjusting the input driving signal. The upper diagram of Figure 2.14 is a typical calibrated driving waveform, and the output displacement becomes linear as the lower diagram. The open-loop calibration can solve the hysteresis phenomenon, but can’t deal with the thermal drift problem.

Figure 2.14 Open-loop scanner calibration

The closed-loop method performs an accurate positioning by a feedback control loop as shown in Figure 2.15(a). In this method, a position sensor detects the accurate displacement of the actuator. Then, the actuator displacement signal is compared with the target signal, and a controller compensates the driving signal to minimize the error signal. The proportional-integral-derivation (PID) controller is used in the AFM generally. For optimizing the performance, the PID gains should be adjusted for applications. Figure 2.15(b) demonstrates the step response with different controller gains setting. If the gains are too high, the overshooting occurs and causes an oscillation.

On the contrast, the settling time will be extended when the gains are reduced. The closed-loop is helpful for the applications that need accurate positioning. However, the essential position sensor also complicates the scanner design, and the sensor noise restricts the scanning resolution.

(a) System block diagram

(b) Step response with different controller gains Figure 2.15 Closed-loop scanner control

2.3.2 Z-axis approaching system

Before scanning, the cantilever tip must approach the sample surface into the scanner range. This step can be achieved by manual operation or a motorized system.

The stepper motor system is easy to control the displacement, and is widely used for approaching. Two considerations here are the tip colliding and time consumption, and two tactics are introduced as follows.

In the continuous approaching method, the Z-axis scanner and the stepper motor work simultaneously. The Z-axis feedback controller monitors the tip-sample interactive force during the stepper motor running. When the tip contacts with the sample, the scanner will draw back. After the scanner retracting to its half range, the stepper motor stops. In this method, the motor speed and feedback parameters must be adjusted

appropriately. Otherwise, the impact force could damage the tip at the contact instant.

In the alternate approaching method, the Z-axis scanner and the stepper motor work alternately. After the stepper motor running a small distance, the force-displacement curve is performed to detect the tip-sample distance. Similarly, this loop stops when the sample is located around the half range of the scanner. The alternate approaching method can avoid large interactive force during approaching. However, it cost more time than the continuous approaching method. For improving the approaching efficiency, an OM can monitor the tip-sample distance roughly. First, the tip is brought close to the sample rapidly with the OM monitor. Then, the alternate approaching method is adopted.

2.4 Control System

Various functions such as the scanning and the force-displacement curve measurement are controlled by the control system. The digital control system is flexible for adjusting parameters, and is adopted in most AFM systems. In the tapping mode AFM, the lock-in amplifier is necessary for getting the cantilever amplitude and phase signals. The Z-axis feedback control collaborates with the XY-axes scanning function for measuring the surface image.

2.4.1 Lock-in amplifier

Figure 2.16 illustrates the principle of a digital lock-in amplifier. The sinusoidal driving signal with frequency ω is generated by a direct digital synthesizer (DDS), and transferred to the excitation source after a digital-to-analog converter (DAC). For simplification, the supposed cantilever response is an ideal sinusoidal wave with

multiplied by sin(ωt) and cos(ωt), respectively. After a low pass filter (LPF), the remaining dc terms x and y represent the Cartesian coordinates of the point on the unit circle. Therefore, A and θ can be calculated by trigonometric functions. In practice, these signal processing can be realized by the field-programmable gate array (FPGA) or the digital signal processor (DSP). During scanning, the cantilever response could not be an ideal sinusoidal wave due to the complex interactive force with the sample.

Lowering the cutoff frequency of LPF can reduce the noise, but the bandwidth is also reduced.

Figure 2.16 Digital lock-in amplifier diagram

2.4.2 Z-axis feedback control

The Z-axis feedback controller is responsible for adjusting the interactive force between the tip and the sample. Figure 2.17 presents a Z-axis feedback loop. At first, user determines the setpoint, which is the tracking value of the reference signal. The

reference signal depends on the operation mode. In the contact mode, the cantilever deflection signal is selected for reference. In the dynamic mode, the amplitude, the phase, or the frequency signal can be adopted. The error between the setpoint and the reference signal is inputted to a PID controller, and the driving signal to the Z-axis scanner is generated. The Z-axis displacement of the scanner is adjusted to minimize the error signal. During the scanning, the tip-sample distance can be kept constant, and the

reference signal depends on the operation mode. In the contact mode, the cantilever deflection signal is selected for reference. In the dynamic mode, the amplitude, the phase, or the frequency signal can be adopted. The error between the setpoint and the reference signal is inputted to a PID controller, and the driving signal to the Z-axis scanner is generated. The Z-axis displacement of the scanner is adjusted to minimize the error signal. During the scanning, the tip-sample distance can be kept constant, and the