Design and Control Optimization for High-Speed
Jumping Mode Atomic Force Microscope
by
Fangzhou Xia
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2017
@
Massachusetts Institute of Technology 2017.
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Department of Mechanical Engineering
May 12, 2017
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Kamal Youcef-Toumi
Professor of Mechanical Engineering
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Rohan Abeyaratne
Chairman, Committee on Graduate Students
Design and Control Optimization for High-Speed Jumping
Mode Atomic Force Microscope
by
Fangzhou Xia
Submitted to the Department of Mechanical Engineering on May 12, 2017, in partial fulfillment of the
requirements for the degree of
Master of Science in Mechanical Engineering
Abstract
In this thesis, I improved the design of a high-speed Atomic Force Micrscope (AFM) for jumping mode operation. The relations between important imaging parameters and physical limitations of the system were established first to identify the aspects of improvement. Two control algorithms to improve the imaging speed and probe sample interaction force for jumping mode atomic force microscopy operation have been proposed and investigated both in simulation and experiment. A new gener-ation of multi-actuated sample scanner has been designed to address the dynamic coupling, thermal expansion and range issues in the previous design. Improvements to the optical beam deflection system, photodiode circuit, signal conditioning circuit and cantilever probe holder with actuators have been implemented. The combined optimization and design work improved the capability of the original custom made high-speed AFM setup in both subsystem performance and jumping mode operation. Thesis Supervisor: Kamal Youcef-Toumi
Acknowledgments
First of all, I would like to express my gratitude to my advisor Professor Kamal Youcef-Toumi for his support and guidance during my years at MIT. His knowledge and insights both in the area of engineering and in life have played an important role in my professional development. The friendly environment and freedom to explore a the Mechatronics Research Laboratory (MRL) helped me a lot in facing the challenges. It has truly been an honor and a memorable experience to work with Professor Youcef-Toumi at MRL.
Next, I want to thank my lab mate and mentor Iman Soltani Bozchalooi. It was his guidance and help that brings me up to speed with the project. I want to thank Jennifer Yu and Jesse Chang for their help to the project. I would also like to thank my lab mates Amith Somanath, Bo Jiang, You Wu and Ryan Fish for creating such a friendly and pleasant environment at MRL.
I feel grateful to Professor Harry Asada, Professor Ian Hunter, Professor David Trumper, and Prof. Ivo Rangelow for their advise and help. I have learned a lot from their insightful answers to my numerous questions.
I would also like to thank the staff members at the Mechanical Engineering De-partment of MIT, especially Ms. Catherine Anne Hogan and Ms. Leslie Regan for all their help in making the place running.
I also want to thank Synfuels China for their collaboration and financial support. I want to thank Mr. Stephen Truncale, Mr. Yi Wang for their support to this project. I have my deep gratitude to my family for their support and love in my life. I want to dedicate this work to my grandmother Fangnong Yan, my mother Ms. Yi Wang, my father Mr. Hai Xia. I would like to thank the love of my life, my wife Ms. Yao Tong, for bringing unlimited happiness and hope to my life.
Contents
1 Introduction 15
1.1 Background ... ... .. .. . .... .. ... .... ... ... 15
1.1.1 Speed Limitation for AFM . . . . 17
1.1.2 Importance of High Speed Imaging . . . . 18
1.2 Previous Approaches . . . . 18
1.2.1 High Speed Scanner Design . . . . 18
1.2.2 Specialized Small Size AFM Probes . . . . 19
1.2.3 Self Sensed and Actuated Cantilever Probes . . . . 19
1.2.4 Controller Design . . . . 19
1.2.5 Lateral Scan Control . . . . 19
1.2.6 Real Time Probe Deflection Regulation . . . . 20
1.3 Modes of Operations for AFM . . . . 20
1.3.1 Contact M ode . . . . 20
1.3.2 Non-Contact Mode . . . . 20
1.3.3 Dynam ic M ode . . . . 21
1.3.4 Jum ping M ode . . . . 21
1.4 Thesis Overview . . . . 22
1.4.1 Aspects of Improvement for High-speed AFM . . . . 22
1.4.2 Induced Vibration Contact Detection . . . . 23
1.4.3 Residue Vibration Suppression for Jumping Mode AFM . . . . 23
1.4.4 Multi-Actuated Nano-Positioner Design Optimization . . . . . 23
2 Aspects of Improvement for High-speed AFM 2.1 Impact of Imaging Parameters ...
2.1.1 Fram e Rate . . . . 2.1.2 In-Plane Resolution . . . . 2.1.3 In-Plane Imaging Range . . . . 2.1.4 Sharpness of Sample Topography Image 2.1.5 Relations Between Imaging Parameters 2.2 Physical System Limitations . . . .
2.2.1 Actuator Bandwidth . . . . 2.2.2 Y Axis Structure Bandwidth . . . . 2.2.3 X Axis Structure Bandwidth . . . . 2.2.4 Z Axis Structure Bandwidth . . . . 2.2.5 Cantilever Probe Resonance Frequency . . 2.3 Imaging Controller Bandwidth . . . . 2.3.1 Contact and Non-Contact Mode Controller 2.3.2 Dynamic Mode Controller Bandwidth . . . 2.3.3 Jumping Mode Controller Bandwidth . . . 2.4 Chapter Summary . . . .
3 Induced Vibration Contact Detection Method 3.1 Overview of Prior Art . . . .
3.1.1 Force-Volume Mode . . . . 3.1.2 Peak Force Tapping Mode . . . . 3.2 Contact Detection Working Mechanism . . . . 3.2.1 Coherence Contact Detection . . . . 3.2.2 Fast Fourier Transformation . . . . 3.2.3 Phase Locked Loop . . . . 3.2.4 Modified Lock-in Amplifier . . . . 3.2.5 Window Function . . . . 3.3 System Modeling . . . . 25 . . . . 25 . . . . 26 . . . . 27 . . . . 28 . . . . 29 . . . . 30 . . . . 35 . . . . 35 . . . . 35 . . . . 35 . . . . 36 . . . . 36 . . . . 36 Bandwidth . . . . 37 . . . . 37 . . . . 38 . . . . 38 41 42 42 43 47 48 51 51 52 54 55
3.3.1 Cantilever Probe Model with Two Modes of Vibration. 3.3.2 Visco-elastic Sample Modeling
3.3.3 3.3.4
Model Parameters . . . . Model Switching Between Contact and Non-contact 3.3.5 Cantilever Resonance Frequency Adjustment . . . . 3.4 Contact Detection Simulation . . . . 3.4.1 Matlab Simulation Implementation . . . . 3.4.2 Simulation Result . . . . 3.5 Experiment Verification . . . . 3.5.1 Test Setup . . . . 3.5.2 Experiment Results . . . . 3.6 Controller Design . . . . 3.6.1 Control Strategy . . . . 3.6.2 Regulated Variable . . . . 3.6.3 Controller Simulation Results . . . . 3.6.4 Prevention of "Parachuting Effect" . . . .. 3.7 Chapter Summary . . . .
4 Residue Vibration Suppression for Jumping Mode AFM 4.1 System Modeling . . . .
4.1.1 System Parameters . . . . . 4.1.2 Model Equations . . . . 4.2 Controller Selection . . . . 4.2.1 Control Law Design . . . . . 4.3 Sliding Mode Controller Simulation 4.3.1 System Parameters . . . . . 4.3.2 Simulation Results . . . . . 4.4 Implementation Consideration . . . 4.5 Chapter Summary . . . . . . . . 56 . . . . 56 . . . . 57 . . . . 58 . . . . 59 . . . . 60 . . . . 60 . . . . 62 . . . . 62 . . . . 63 . . . . 64 . . . . 64 . . . . 65 . . . . 65 . . . . 66 . . . . 67 69 . . . . 7 0 . . . . 7 0 . . . . 7 1 . . . . 7 2 . . . . 7 3 . . . . 7 4 . . . . 7 5 . . . . 7 5 . . . . 7 8 . . . . 7 8 55
5 Multi-Actuated Nano-Positioner Design Optimization 5.1 Existing Solutions ...
5.2 Previous Design . . . . 5.3 Issues for Improvement . . . . 5.4 System Identification Implementation . . . . 5.4.1 Random Binary Stochastic Signal Implementation . 5.4.2 Transfer Function Estimation . . . . 5.5 Flexure Based Scanner Design . . . . 5.6 Dual Actuated X Axis Scanner Design . . . . 5.7 Positioner Implementation . . . . 5.7.1 Structure Bandwidth . . . . 5.8 Chapter Summary . . . . 6 High-Speed and Large-Range AFM Instrumentation
6.1 Optical Beam Deflection System . . . . 6.2 Photodiode PCB Design . . . . 6.2.1 Design Requirement Overview . . . .
6.2.2 Trans-impedance Resistor Gain Calculation . . . .
6.2.3 Operational Amplifier Selection . . . . 6.3 Signal Conditioning PCB Design . . . . 6.4 Cantilever Probe Holder Design . . . . 6.4.1 Cantilever Holder for Air Operation . . . . 6.4.2 Cantilever Holder for Liquid Operation . . . . 6.5 Chapter Summary . . . . 7 Conclusion and Recommendations
7.1 C onclusion . . . . 7.2 Recommendations . . . . 7.2.1 Closed Loop High Speed X Axis Scanner . . . . 7.2.2 Adaptive Topography Tracking . . . . 7.2.3 Imaging of Dynamic Processes . . . .
79 . . . . 80 . . . . 83 . . . . 85 . . . . 87 . . . . 87 . . . . 88 . . . . 89 . . . . 90 . . . . 90 . . . . 91 . . . . 91 93 . . . . 93 . . . . 96 . . . . 97 . . . . 97 . . . . 98 . . . . 99 . . . . 101 . . . . 101 . . . . 101 . . . . 102 103 . . . . 103 . . . . 104 . . . . 104 . . . . 104 . . . . 105
List of Figures
1-1 AFM subsystem setup (a) optical beam deflection system (b) cantilever probe and sample environment control chamber (c) sample scanner . 2-1 2-2 2-3 3-1 3-2 3-3 3-4 3-5 3-6
Sine pattern with imaging system degradation . . . . Parameter definition for sawtooth and triangular waveform Parameter relation visualization at 25 FPS . . . . Probe tip and sample surface distance . . . .
Cantilever deflection signal measurement . . . . . Cantilever deflection background measurement Probe sample interaction force over cycles . . . . Tip-sample interaction force . . . . Jumping mode operation single cycle illustration .
16 29 31 34 . . . . 43 . . . . 44 . . . . 45 . . . . 45 . . . . 46 . . . . 47
3-7 High frequency noise superimposed on sinusoidal jumping signal . . . 49
3-8 Triangle window FIFO implementation . . . . 55
3-9 Cantilever and sample lumped parameter model . . . . 57
3-10 Bode plot for simulated cantilever dynamics . . . . 59
3-11 AFM jumping mode simulation and IVCD detection result . . . . 61
3-12 Jumping mode test system setup . . . . 62
3-13 IVCD method test results on a PS-LDPE-12M polymer sample . . . . 63
3-14 Regulated variable definition . . . . 65
3-15 Controller simulation result . . . . 66 4-1 Lumped parameter model for residue vibration compensation simulation 71
4-2 4-3 4-4 4-5 4-6 5-1 5-2 5-3 5-4 5-5 5-6 5-7 6-1 6-2 6-3 6-4 6-5 6-6 6-7 6-8 . . . 73 . . . 76 . . . 76 . . . 77 . . . 77
Control system paradigm . . . . Stage 3 controller displacement response . . . . . Stage 3 controller velocity response . . . . Stage 4 controller displacement response . . . . . Stage 4 controller velocity response . . . . Piezo tube scanner . . . . P-363 PicoCube piezo scanner . . . . High-speed large-range scanner original design . . X axis bode plot for dual actuated X axis scanner Flexure based scanner design . . . . Dual actuated X axis scanner design layout . . . Z and X1 axis positioner structure assembly . . . Schematic of optical beam deflection system setup Optical beam deflection system housing design . . Photodiode circuit design . . . . Photodiode PCB layout and assembly . . . . Signal conditioning PCB single channel schematic Signal conditioning PCB multi-channel assembly . Probe holder for air operation . . . . Probe holder for liquid operation . . . . 94 96 98 99 100 100 101 102 . . . . 80 . . . . 82 . . . . 83 design . . . . 88 . . . . 89 . . . . 90 . . . . 91
List of Tables
5.1 Original scanner parameter . . . . 84 5.2 Dual actuated scanner parameter . . . . 91
Chapter 1
Introduction
Atomic force microscopy (AFM) has been a great tool for nanotechnology research and high-tech industries since its invention [8]. The flexibility for imaging condition makes AFM a popular instrument for nano-scale measurement. AFM does not suffer from the visible light wave length limitation as optical microscopy so that nano-scale details can be obtained. AFM also does not require conductive samples as required by Scanning Electron Microscopy (SEM). Being able to image samples on a nanometer scale in ambient air, liquid and ultrahigh vacuum (UHV) makes AFM an ideal tool for a variety of applications in imaging semiconductors, chemical processes, biological samples, etc. In many cases, AFM has been used for both characterization and manipulation of sample surfaces [431 and nano-scale lithography [29].
1.1
Background
Atomic force microscope operates by scanning over the sample with a micro-cantilever probe. The deflection of the cantilever probe is measured and utilized as feedback signal to the controller for tracking the sample surface topography in real time as well as creating a map of the sample surface. The probe scans in the lateral X - Y
plane and the vertical Z position of the sample is regulated to ensure the probe is tracking the sample topography without damaging the sample significantly. Several AFM operation modes for different imaging applications will be introduced later in
this chapter.
Conventional AFM system is composed mainly of three subsystem as shown in Figure 1-1 (Image source: [9]). The first subsystem is the optical beam deflection system the utilize an optical lever to amplify the nanometer level deflection of the cantilever probe tip for conversion to voltage signal. It also includes a camera for optical microscopy to help with the alignment of laser and sample probe. The second subsystem is the cantilever probe and the sample environment control chamber. The cantilever probe can be excited at its resonance frequency for dynamic mode imaging (introduced later) and the imaging environment such as ambient air or liquid pH value can be controlled using the chamber. The third subsystem is the sample scanner that performs the scanning and vertical position regulation of the sample for surface topography tracking. CA OA camera polarizing widwsample beamsplitter temperature 11 ~ ~control scne dichroic mirror , CA photodiode quarter-wave engagemen objective h fli mechanism % 7 exchange
OA photodiode electrical connections coarse
to sample and electrodes in-plane positioner
(a) (b) (c)
Figure 1-1: AFM subsystem setup (a) optical beam deflection system (b) cantilever probe and sample environment control chamber (c) sample scanner
Research efforts to improve the performance of AFM have been focusing on many aspects of imaging quality. The first major effort is to improve the imaging speed of AFM to look into dynamics processes [6, 5, 4, 13, 35, 18]. High-speed and large-range quasi-video rate imaging of chemical processes has been achieved before [9]. The second area of interest is to increase the resolution of AFM imaging [26, 48]. Utilizing AFM probe for material property estimation is another important area for research
[14,
46]. Different approaches have also been investigated for real-time control of tip-sample interaction force to reduce sample damage [33, 34].1.1.1
Speed Limitation for AFM
One of the main limitation to AFM is its operation speed. Depending on the imaging condition, it can take tens of seconds or even minutes to produce a single image, which means only static or very slow changing systems can be imaged using AFM. The speed limitation can be attribute to scanner bandwidth, cantilever probe dynamics and signal processing speed.
The scanner bandwidth is a fundamental limitation that determines the imaging range, resolution, and etc. The resonance frequency for traditional piezo tubes can be around 5 - 7 kHz in the Z axis direction, which limits the tracking bandwidth
of sample topography. The detailed relationship between imaging parameters and scanner bandwidth can be found in Chapter 2.
The cantilever probe dynamics is another limiting factor for high speed imaging. With the increase of imaging speed, probes with slow dynamics can lose contact with the sample surface easily and disrupt the image. To increase the resonance frequency of the cantilever probe, a higher spring constant of the probe is needed. However, the interaction force between the sample and probe will also increase at same level of indentation, which may even damage the sample. In tapping mode AFM, the quality factor of the probe also plays an important role in determining the maximum imaging speed.
The controller loop rate, signal processing circuits and data transmission rate can also limit the imaging speed in a complicated way. As the controller regulates the interaction force between the probe and sample, higher controller loop rate will help for regulation accuracy. The data acquisition and signal processing circuits should run at a rate much higher than the controller loop rate to reduce the discrete time effect of the digital controller. In addition, to maintain a good image resolution, the data throughput, logging and plotting system requirement also increase significantly at high speed.
1.1.2
Importance of High Speed Imaging
By increasing the imaging rate of AFM, we can begin to look into dynamic processes such as deposition, dissolution, crystallization and other chemical processes in real time. It also allows the study the real time change of protein dynamics [15], material property evolution of muscle cells and other biological processes . The techniques can also open up possibilities for high speed fabrication techniques in lithography.
1.2
Previous Approaches
Simultaneously achieving high speed, large range, and minimal tip-sample interac-tion is very challenging due to the contradicting requirements. As an illustrainterac-tion, in conventional setups, in order to achieve high-speed imaging, cantilevers with higher resonance frequencies are needed for high-speed sample topography tracking. How-ever, with conventional optical beam deflection setups, the size of cantilever should not be too small compared to the laser beam diameter for a photodiode detection. On the other hand, for the same cantilever size, higher resonance frequency leads to higher spring constant. Due to large interaction forces, such probes cannot be used on delicate samples. A number of approaches have been proposed for high- speed imaging and reduced sample damage.
1.2.1
High Speed Scanner Design
Flexure based mechanisms has been investigated as an alternative to the piezo tubes. By pre-loading the piezo stack actuators with flexure based design, the effects load-dependence and vulnerability to tensile stress of piezo actuators can be reduced sig-nificantly at a cost of having a smaller range. Flexure based design can typically reach a range of around 10 pm and achieving bandwidth at around 10 kHz. Multi-actuated scanners have also been investigated to address both the range and bandwidth issues [10].
1.2.2
Specialized Small Size AFM Probes
To address the issue of cantilever probe bandwidth limitation, one approach is to reduce the size of cantilever probe to a width of 2 -6 ium, a length of 2.525 pum and a thickness of 0.11 pm [11, 36]. This gives a high bandwidth but maintaining a relatively low spring constant due to the reduced mass of the probe. However, smaller cantilever probes require modifying the optical beam deflection setup to focus the laser beam onto the small cantilever probe.
1.2.3
Self Sensed and Actuated Cantilever Probes
In this approach, the deflection sensing and actuation are both built into the cantilever probe using nano-fabrication techniques [37, 1]. This eliminates the need for an optical beam deflection system for capturing the probe deflection and opens up the possibility for using an array of individually sensed and actuated probes simultaneously for imaging large area [2].
1.2.4
Controller Design
Much research work has been conducted to increase the bandwidth of different AFM subsystems. Data driven controller design to improve the dynamics performance of scanner has been investigated. Another example involves designing controllers to modify the probe quality factor at various resonance frequencies for improved force sensitivity [22, 7]. Multiple eigenmodes of the cantilever probe can be utilized increase the imaging speed and better contrast without using stiffer cantilevers [38].
1.2.5
Lateral Scan Control
For positioning accuracy, and bandwidth improvement, both feedback and feed-forward control has been applied to tackle the non-linear behavior of piezo actuators such as hysteresis in the lateral direction.
as apposed to the unknown sample topography, adaptive controllers can be utilized to update the system model and controller parameters iteratively.
In addition, sinusoidal waveform have been utilized instead of triangular waveform to avoid exciting the higher order dynamics at the turning point. Although this approach adds another layer of complexity in sampling for image generation, this helps to improve the lateral scanning bandwidth performance of the scanner.
1.2.6
Real Time Probe Deflection Regulation
Another approach involves controlling the tip-sample interaction force actively during each contact [34, 32] to ensure the force is below a prescribed threshold. This approach helps to reduce sample damage during imaging.
1.3
Modes of Operations for AFM
In addition to modifications to AFM hardware setup for improved speed, range, and interaction forces, a variety of operating modes have been investigated to image samples with different topographies, different material properties and under different conditions
[30].
1.3.1
Contact Mode
Contact mode AFM is a straightforward method that regulates the deflection of the cantilever as it scans over the sample. Due to the lateral friction force caused by continuous mechanical contact, irreversible damage produced on delicate samples limits its usage. Examples include biological samples such as bacteria and DNA.
1.3.2
Non-Contact Mode
In this mode, the AFM probe is hovered over the sample surface without actually coming into contact with the sample. The probe is deflected by the Van der Waals
attraction force that is between the probe and the sample. By regulating the attrac-tion force, the topography informaattrac-tion can be obtained. However, this mode does not work very well with the presence of liquid and limits the application of AFM.
1.3.3
Dynamic Mode
To overcome the sample damage due to lateral forces, the dynamic mode AFM, some-times referred to as tapping mode was developed [27, 25]. This mode has been inves-tigated extensively in a variety of flavors e.g. amplitude (AM) and frequency (FM) modulation [3, 49]. In dynamic mode various modes of vibration of the probe are excited. The amplitude, frequency or phase of the resulting dynamics are regulated or acquired for image formation
[12].
As different eigenmodes of a cantilever have dif-ferent sensitivity to material property [161, they can be utilized to give contrast image for material properties [39]. Combined AM and FM mode has also been investigated for further sample damage reduction[42].
One main limitation for tapping mode is its imaging speed due to the cantilever resonance quality factor. When encountering a drop of topography, it takes several oscillations for energy to accumulate in the cantilever to give a larger oscillation amplitude and thus going too fast will cause a parachuting effect that yields inaccurate topography image. Research has been conducted to increase the speed and tackle this effect [21].The complexity of more advanced dynamic imaging mode also limits their application in routine imaging.1.3.4
Jumping Mode
To alleviate the complexity of dynamic mode imaging and at the same time benefit from its reduced lateral interaction forces jumping mode has been proposed [17]. In this mode, the sample is brought into contact with the probe intermittently by moving either the sample or the probe using the out of plane piezo(s). The difference from dynamic mode is that the cantilever probe in this case is not drive by a piezo at a specific frequency. This mode greatly reduces the friction force that is presented in contact mode and also does not suffer from the resonance quality factor limitation as
in the dynamic mode AFM. Based on this principle, the Peak Force Tapping mode
[40]
that regulates the maximum interaction force has been invented for imaging. With soft cantilevers, 150 pN of interaction force at 1 line per second [301 can be achieved for imaging. This level of interaction force demonstrated small damage to samples [31] which has been reported to reflect a reasonable performance on delicate samples such as live cells [28]. However, the reliance of the method on a single peak force detection, adversely influences the robustness of the method. As the imaging speed increases, the residual ripples associated cantilever dynamics can confuse the peak detection algorithm and thus requiring a higher peak force set point.Another main benefit of jumping mode imaging is its ability to cover a large range of imaging area. By jumping from one point to another for topography estimation, the need for tracking the sample topography variation between pixels is removed. This allows the scanning to be performed in larger range compared to other modes of operation.
1.4
Thesis Overview
In this thesis, the main focus of work is on the design optimization and control algo-rithm development to enable high speed jumping mode imaging with a custom made AFM. The system has adjusted optical beam deflection systems that is compatible with small size cantilevers with manual adjustable stages for alignment, high-speed multi-actuated piezo positioning scanner for both large range and high-speed opera-tions. In this section, we give a brief overview of the thesis work.
1.4.1
Aspects of Improvement for High-speed AFM
We start by looking into the relationships between imaging parameters and physi-cal constrains during AFM imaging. The frame rate, in-plane resolution, in-plane imaging range and sharpness of sample image are identified as the most important parameters. There relationship with the scanner bandwidths and controller band-width is also developed in this section. With a 3D visualization of the theoretical
performance limit for imaging parameters, we identified the aspects of improvcment for physical limitation.
1.4.2
Induced Vibration Contact Detection
With the aspects of improvement identified, we look at a new method named Induced Vibration Contact Detection (IVCD) as an alternative method for contact detection in jumping mode imaging
[20].
The IVCD method helps to reduce the probe sample interaction force by detecting the contact faster using superimposed oscillation on the cantilever probe. A control algorithm design is also proposed for utilizing this method for imaging.1.4.3
Residue Vibration Suppression for Jumping Mode AFM
In this section, another method for increasing the speed of jumping mode is inves-tigated. By regulating the cantilever probe dynamics in real time using non-linear control techniques, the residue vibration of the probe can be effectively attenuated in a short time, which reduce the time between sampling of pixels. A sliding model controller is designed and simulated to yield ideal performance. This method is suit-able for imaging in air with the direct control of cantilever probe base movement accessible, but it is harder to implement for imaging in liquid as the probe is usually driven acoustically.1.4.4
Multi-Actuated Nano-Positioner Design Optimization
Apart from the control algorithms, the design optimization of the multi-actuated sample scanner plays an important role in the AFM setup. In the new design, We ad-dress the numerous issues presented with the original design such as dynamic coupling, heating, range limitation and etc. Both the flexure based design and dual-actuated design are presented and compared. A testing method for structure dynamics using stochastic binary signal is also presented in this section. The resulting new scannerhas a higher X axis bandwidth (10 kHz) compared to the original design (5 kHz) and resolved a number of other issues as mentioned before.
1.4.5
High-Speed and Large-Range AFM Instrumentation
In chapter 6, the design improvements for optical beam deflection system, photodiode circuit, signal conditioning circuit and actuated cantilever probe holder are discussed. In addition to speed improvement, the instrumentation of each subsystem helps to ensure the quality of the image in terms of Z axis resolution and positioning accuracy to avoid image scaling error.
Chapter
2
Aspects of Improvement for
High-speed AFM
In this chapter, we discuss the different imaging parameters and their effects on the design and instrumentation of AFM components. There are many differences between the effects of imaging parameters of AFM imaging as compared to optical microscopy imaging or traditional video recording with Charge Coupled Device (CCD) cameras. The mechanical process of scanning the sample topography on the nano-scale presents major challenges in actuator bandwidth, structure dynamics, electronics and etc. when operating at high speed. We will also discuss how improving certain aspects of the design such as the structure bandwidth, operational modes would help to better meet the imaging requirements.
2.1
Impact of Imaging Parameters
During the creation of a video, there are numerous criteria that can be utilized for characterizing its quality such as dynamic range, noise, color accuracy and many others. In the case for taking video with high speed atomic force microscopy, the frame rate, imaging range, resolution and sharpness are key parameters. Given a fixed amount of resources such as the processing speed for each pixel and the number of processing units, a lot of the imaging parameters contradicts each other as increasing
one parameter would result in the decrease of other parameters. Therefore, to achieve a reasonable compromise between the parameters and take videos to gain more insight into the nano-world, we need to identify the relationship between the parameters and the aspects of improvement that can push the boundary that we can achieve through high speed imaging.
2.1.1
Frame Rate
The frame rate, denoted as F, is one of the most fundamental requirement for a video. The unit of frame rate is often given as Frames Per Second (FPS). As videos are composed of a sequence of images taken at different time instant, the time between two different images gives the period of imaging. Taking the reciprocal of period gives us the number of periods that are contained in each second, which is equal to the frame rate. Assuming that the processing time for recording or playing each image is fixed, a higher frame rate requires higher processing speed.
There are different standards for traditional videos taking with CCD cameras. The common standards for commercial television display systems include PAL (commonly used in Europe and Asia), which gives 25 FPS at 625 lines in each image and NTSC (commonly used in the U.S.), which gives 30 FPS at 525 lines in each image. We can see that there is some compromise between the frame rate and the lines in each image.
The frame rate in the range of 25-30 has good enough performance when con-sidering the persistence of vision effect, which fills the gap between image changes, and the Phi phenomenon, which helps human to perceive a series of still images as motion. However, for capturing details of events happening at a higher speed, the frame rate needs to be increased to be at least comparable with the time scale of the events.
A fundamental difference between atomic force microscopy and traditional CCD cameras in taking a single frame of frame lies in the number of sensors available. In CCD camera, a grid of light sensitive CCD components captures the light simultane-ously with each pixel of the image corresponds to an integrated circuit that can sense
the light. For conventional AFM, only 1 probe can be used to measured the topogra-phy of the sample at a single instance. This means that the topogratopogra-phy image taken by an AFM is not a snapshot of the sample surface at a single time instance. Instead a single frame is created gradually with the scanning motion of the sample tip. In some variation design, we might have multiple cantilever probes scanning simultaneously to achieve higher speed and larger range but the number of probes are still on the order of 10, which is much less than the CCD components. The scanning operation directly cause the first pixel in the image is taken at roughly T seconds before the last pixel in the same frame with T being the time to take a single frame. This difference in time makes taking video with AFM challenging as the changing of process must happen in a time scale smaller compared to the period T for taking a single images. While an optical blur will happen for fast moving objects if the shutter of a CCD camera is opened too long for a single frame, a fast changing sample topography in AFM image will become distorted and does not capture the actual topography of the sample. We need appropriate frame rate selection for different applications. This in some cases can be very challenging as it has an overall impact on all the imaging components. It would be clear when we combine the different imaging parameters and address their individual effect on the design later in this chapter.
2.1.2
In-Plane Resolution
The in-plane resolution of a video or an image, denoted as R, and RY respectively for each in plane direction, is another important parameter during the creating of an image. As most of the images are usually displayed on a 2D rectangular screen, the characterization of resolution is given as R. x Ry pixels. For traditional CCD camera, each pixel corresponds to a single integrated circuit component. In terms of AFM imaging, the resolution usually means the number of sample points taken as the estimation for the sample topography in a single image.
In conventional video specification, aspect ratios of 4 : 3 or 16 : 9 are commonly used for human visual considerations. A resolution of 1280 x 720 is common numbers for a video with relatively good resolution.
In terms of AFM imaging, the resolution of an image directly depend on the bandwidth of the fast in-plane X axis (horizontal axis when looking from top). This assumes that we are scanning each line in the X direction and moving the probe gradually in the Y direction. To understand the relationship, let us for simplicity assume that we are taking a video with 1280 x 720 resolution at 1 frame per second. For the slower Y axis, it only needs to travel once from top to bottom. However, for the X axis, the scanner needs to move from one end to another for at least 720 times in total (assuming we do not measure forward and backward twice to take average, which is used to get better estimation). In the mean time, the topography estimator needs to record 1280 data points during each sweep of the fast X axis to achieve the desired resolution.
2.1.3
In-Plane Imaging Range
The in-plane range of a video or an image, denoted as L, and LY respectively for each in plane direction, is defined specifically for AFM imaging. The definition of imaging range here is different from the dynamic range, which captures the range of exposure with good contrast and signal to noise ratio for a camera. Imaging range here refers to the physical range in the XY plane that the probe will scan across to create the topography image of the sample. The range of an image is particularly important for majorly three reasons as discussed below.
First, the deflection of the cantilever probe that is scanning across the sample needs to be controlled at all time regardless of whether we capture the topography estima-tion to form an image or not. With the rest of the imaging parameters unchanged, covering a larger area requires higher control loop rate and structure bandwidth to keep up with the cantilever deflection regulation.
Second, the range of scanning affects the mechanical design of the scanner due to the roughly 1 to 1000 ratio of piezo actuators (i.e. 1 pm of positioning range corresponds to 1 mm length of piezo actuator). In general, piezo actuators with larger range have bigger mass, which reduce the structure bandwidth.
resolution is also usually needed. For example, assuming that we are taking an image with 1 nm distance between to pixels. Using a range of L_ = 1pm LY = 1pm requires a resolution of R, = 1000 and R. = 1000. We see that when we keep the pixel distance fixed at 1 nm, the fast X axis bandwidth increase linearly with the imaging range but the out-of-plane Z axis bandwidth is proportional to the square of the imaging range. This makes covering larger area at high speed particularly hard in AFM imaging.
2.1.4
Sharpness of Sample Topography Image
The definition of sharpness is more complicated as compared to the frame rate and resolution as defined before. The sharpness determines the amount of details that can be captured in an image. A common approach to quantify the sharpness is to use the spatial frequency measured in units of cycles per pixel. In Figure 2-1 (Image source:
[44]),
a sine wave pattern of an increasing spatial frequency from left to right is shown. The upper half of the image represents an ideal spatial sine waveform of the actual object while the lower half of the image represents the image captured by an imaging system (e.g. optical lens and CCD components and etc.). We can observe visually that at higher spatial frequency, the image become blurry as the contrast between lines is not as good as the lower spatial frequency image. Therefore, the ability in capturing details of an image can be quantified by the largest spatial frequency that an imaging system can produce. Techniques of Fourier transformation can be applied to decompose different patterns of images into spatial frequency components.* I IIIIUiNII
Figure 2-1: Sine pattern with imaging system degradation
In the case for AFM imaging, we characterize the sharpness, by using the spatial wavelength A, which is the reciprocal of the spatial frequency. The units for the
spatial wavelength is measured in the unit of nm for AFM images.
Since AFM imaging is a scanning process that produce the topography estimation of the sample line by line, it would be sufficient if the imaging system can follow the sample topography reasonably along the fast moving X axis. If we assume that the sampling rate for topography estimation is unlimited, which is usually true with fast analog to digital conversion circuits, the spatial wave length that an AFM can capture is affect by the out-of-plane Z axis positioning bandwidth, imaging resolution, range and frame rate.
2.1.5
Relations Between Imaging Parameters
As we have discussed the 4 important parameters in creating AFM videos, namely, frame rate F, in plane resolution R, and RY, in plane range L. and LY, and spatial frequency A for characterizing of sharpness. We will illustrate three fundamental relationships between the imaging parameters and the structure bandwidth of the three axis in the order from slowest to fastest. For all the analysis in this section, a sine wave pattern is assumed unless otherwise specified.
(a) In AFM imaging, the slowest axis is the Y axis since it only provides the scanning frequency comparable to the frame rate. The governing equation is given in Equation (2.1).
Ky - F < BW (2.1)
where Ky is a dimensionless proportionality factor, F, is the frame rate of the video and BWy is the Y axis bandwidth of the structure. If we assume that we scan from top to bottom each time, we have K, = 1. If the scanning can go from top to bottom for the first image and from bottom to top for the consecutive image, we have Ky = 1/2. The units for both sides of the equation are in Hz. To achieve a typical standard video at 25 frames per second, if we utilize a sinusoidal scanning waveform the Y axis can move as slow as 25 Hz to satisfy
the needs of bandwidth for the K, = 1 case or 12.5 Hz for the Ky = 1/2 case. We can also use other types of waveform such as the sawtooth waveform or the triangular waveform as shown in Figure 2-2.
Amplitude
ItTriangular
Waveform
Ampli
Sawtooth
Waveform
\77N\
A--tZ-A'
Tin
tude
- ~~2r
T=
'
Figure 2-2: Parameter definition for sawtooth and triangular waveform
If we use a linear scan pattern for scanning to start from top to bottom each time with sawtooth waveform , we can use Fourier series expansion to have the result in Equation (2.2).
A A sin(27rnf t)
Xsawtooth(t) = _ _ Z(l)nn (2.2)
2 7r n=1 n
where xsawtooth(t) is the sawtooth waveform, A is the amplitude and
f
is thefrequency in Hz of the waveform. Taking the first 6 to 10 terms would be sufficient to capture the sawtooth waveform with reasonable accuracy.
In the case where we are scanning from top to bottom and bottom to top for
e
Time
b I
consecutive images, a triangular waveform is needed for the Y axis scanner. Using Fourier series expansion, we have the result in Equation (2.3).
8A
Z(
sin(27rf (2n + 1)t)Xtriangle ) = 2 (n 2 (2.3)
k=O
where Xtriangle(t) is the triangular waveform, A is the amplitude and
f
is thefrequency in Hz of the waveform. Similarly, taking the first 6 to 10 terms would be sufficient for constructing the waveform. Notice that the frequency spacing of the wave form is a series of odd number multiples at frequencies
f,
3f, 5f andso on. However, for sawtooth wave, the frequencies are integer multiples at
f,
2f, 3f and etc. Taking the same number of terms to approximate the waveform,
for example 10, we will have the highest frequency component being 19f of the triangular wave form and 10f for the sawtooth waveform.
Combining this observation with the 25 Hz used with sawtooth waveform and 12.5 Hz used with triangular waveform as in the example above, the highest frequency needed are 250 Hz or 237.5 Hz respectively.
(b) The axis with middle range bandwidth requirement in AFM imaging is the X axis. The governing equation for the bandwidth requirement can be written as is
(2.4).
Kx . Fr -Ry < BW (2.4)
where Kx is a proportionality factor, Fr is the frame rate of the video and, RY is the resolution in terms of pixels along the Y direction, and BWx is the X axis bandwidth of the structure. If we assume that a line is scanned twice (often called trace and retrace) to taking the average for topography estimation, we have
K, = 1. If each line is only scanned once, we have K. = 1/2. The units for both sides of the equation are in Hz.
We see that the bandwidth required for the X axis is RY times the bandwidth of the Y axis. Similar to the discussion before for the Y axis, we can approximate different waveforms using Fourier transformation. However, in order to scan at
higher frequencies, scanning with sinusoidal waveform is preferred as it allows the scanning frequencies to be pushed up by one order of magnitude compared to triangular waveform or sawtooth waveform.
(c) For the fastest Z axis in AFM imaging, the equation is more involved with the parameters as shown in Equation (2.5).
FrRYLxCz - BWz (2.5)
Amin
where Fr is the frame rate of the video with unit of Hz, RY is the resolution in terms of pixels along the Y direction which captures the number of lines to scan,
Lx is the imaging range in the X axis direction in nm, A is the smallest spatial
wavelength of the sample topography that can be captured in nm, BWac is the Z axis controller bandwidth, and Cz is a dimensionless proportionality constant that depends on the imaging condition, for example in tapping mode, C, is sometimes chosen as C = 2G with 6m being the maximum phase lag allowed for the sample (e.g. 7r/9 for most protein AFM imaging)[5]. We see that the overall units for both of sides of the equations are again in Hz.
To understand the equation, notice that the product of F, .RY * L,, gives the in
plane velocity of the cantilever probe tip during scanning. Dividing the product by the minimum spatial wavelength Amin yields the bandwidth requirement in the Z axis.
Notice that the differences between controller bandwidth used for the Z axis case and structure bandwidth used for X and Y axis. This is because in different imag-ing modes such as tappimag-ing mode or jumpimag-ing mode, the controller bandwidth is often smaller than the structure bandwidth. More importantly, it is the controller bandwidth that determines the tracking of the sample topography.
(d) During actual imaging, the bandwidth of structure or controllers are usually fixed. If we also chose the frame rate, we can create a 3D surface to see the relationship between imaging range, resolution and sharpness.
A visualization for the relation is shown in Figure 2-3. We choose BW' = 10 kHz,
BWy = 300Hz, BWzc = 100 kHz, K, = 1, Ky = 1, Cz = 1. We assume the range and resolution are same in the X and Y direction, which gives L. = LY
and R. = RY. The sharpness is represented by the spatial frequency 1/A for
visualization purpose. 0.1 E 0.08, c 0.06, :30 LO 0.04, UUZ 0~ 30 30000 1000 2W WO 100
Range (nm) 0 0 Resolution (pixels)
Figure 2-3: Parameter relation visualization at 25 FPS
We see that the maximum resolution that can be achieved is R = R,= BWF,
10000 = 400 due to the limitation in X axis bandwidth. In addition, although
the-25
oretically the range can be increased with small spatial frequency (think of making an image of an ideal flat surface, the Z axis does not need to move), in practise it is limited by the range of actuation. The plot utilize a range of 3pum, which is typical range for the high bandwidth actuator used for positioning.
2.2
Physical System Limitations
In the previous section, we discussed the details for the imaging parameters (left hand side parameters of governing equations for the three axis). We now look into the scanner bandwidth limiting factors (right hand side parameters).
2.2.1
Actuator Bandwidth
The actuator bandwidth is a specifications given by the manufacturer. As piezo electric actuators are commonly used in high speed positioning applications, their bandwidths are usually tested when unloaded or fixed at one end. The typical actua-tor bandwidth is in the kilo hertz range. On the other hand, piezo actuaactua-tors in general work better when constrained in mechanical structure so that the structure can exert spring back force to act as the pulling force (relying on permanent attachment of glue sometimes introduce visco-elastic dynamics that is hard to deal with). On the other hand, the additional of mechanical constrain makes the assembled structure dynamics smaller than the actuator bandwidth.
2.2.2
Y Axis Structure Bandwidth
The Y-axis structure bandwidth requirement is the smallest among all three axes. A bandwidth of 200 to 300 Hz is usually sufficient for most applications. Many com-mercially available piezo nano-positioner can operate at this frequency with relatively large range on the order of 100 pm.
2.2.3
X Axis Structure Bandwidth
The X axis structure bandwidth requirement is a lot higher than the Y axis bandwidth as it is multiplied by the resolution in the Y axis direction. In practise, custom made nano-positioner using piezo actuators can achieve a bandwidth around 10 kHz with a range around 5 pm. Details of the design of the scanner can be found in Chapter 5.
2.2.4
Z
Axis Structure Bandwidth
The Z axis structure bandwidth has the highest requirement among all three axis. In actual implementation, structure bandwidth over 100 kHz can be realized be con-straining small range piezo actuators in caps. On the other hand, the range of travel is usually smaller for such high frequency operation. Common values for the Z axis travel range are around 1 - 2 tum. Multi-actuation techniques can be utilized to cover small range at high frequencies and large range at low frequencies with careful structure design to avoid dynamic coupling and controller design for assigning control efforts.
In many cases, the Z axis structure is designed to have small geometry and placed on top of structures for other axis to reduce the mass to be carried for bandwidth con-sideration. Simple structure formed by constraining piezo actuators between a rigid surface and a thin metal membrane (typically around half of a millimeter thickness). Due to the bandwidth limitation under constrained operation for available piezo ac-tuators, further improving the bandwidth of the Z axis can be very challenging.
2.2.5
Cantilever Probe Resonance Frequency
Another important factor in AFM imaging is the cantilever probe bandwidth. From the Euler-Bernoulli beam equation, we know that there is an infinite number of eigen-modes that provides resonance peaks. Depending on the size, stiffness and imaging condition, the resonance of cantilever probes are usually different. The first resonance frequencies of cantilever probes can vary from several kHz to the MHz range, which is chosen based on the requirement of imaging.
2.3
Imaging Controller Bandwidth
The controller bandwidth is related not only to the component bandwidth but also the required movement of sample and cantilever probe. In this section, we look into different modes of operation commonly used in AFM imaging.
2.3.1
Contact and Non-Contact Mode Controller Bandwidth
In this imaging mode, the cantilever probe is not excited but maintained at a certain deflection value. The controller bandwidth depends on the sample rate, electronics processing speed and most importantly the Z axis bandwidth. With modern day Field Programmable Gate Array (FPGA), the sample rate and control loop can run in the MHz range, which would be sufficient in most cases. If the cantilever probe bandwidth is chosen to be higher than the Z axis structure bandwidth, the main limitation for this imaging mode would be the Z axis structure bandwidth.2.3.2
Dynamic Mode Controller Bandwidth
For dynamic mode operation, the cantilever probe is excited at its first resonance frequency. A sinusoidal waveform demodulation loop is used to extract the the am-plitude and phase of the excited cantilever oscillation. The bandwidth of the control loop depends on three aspects as discussed below.
First, since the cantilever is excited at its first resonance frequency, the cantilever probe bandwidth is important as it determines the fundamental period of each oscil-lation.
Second, a common method for sinusoidal waveform demodulation is through the use of lock-in amplifier. Although the detailed operation of a lock-in amplifier is beyond the scope of the discussion here, we need to take average of several cycles of sinusoidal waveform excited deflection signal measurement to accurately extract the amplitude and phase information. The number of cycles of sine wave needed for averaging to extract amplitude or phase depends on the signal to noise ratio and algorithm used.
Third, after the-cantilever probe oscillation amplitude is decreased after coming close into the sample surface, it takes several cycles for the amplitude of oscillation to grow back when we have a decreased height in the topography. Scanning too fast would results in the well known "parachuting" effect that cause inaccurate topography estimation. The number of cycles needed for the oscillation to build up is related to the
quality factor of the resonance peak, which is a cantilever probe mechanical property and also depends on imaging condition.
2.3.3
Jumping Mode Controller Bandwidth
In jumping mode imaging, the sample is brought up and down and come into contact with the cantilever intermittently. One important consideration is that the frequency of the sample motion needs to be small compared to the first resonance frequency so that the residue vibration from the cantilever probe have enough time to damp out before making another contact. Therefore, the jumping mode controller is affected by both the cantilever bandwidth, the Z axis structure bandwidth and the damping of the cantilever probe.
Notice that the jumping mode topography estimation can only estimate sample topography at each time the cantilever probe and sample come into contact. The resolution an image taken in this mode is directly related to the jumping frequency. This is different from the other modes as the surface topography is continuously tracked in the other imaging modes. However, jumping mode allows the AFM to cover larger area as the cantilever probe does not need to track the sample topography at all time.
In jumping mode imaging, if an actuator is installed on the cantilever probe, active residue vibration suppression algorithm can be utilized to reduce the time needed for the first mode residue vibration to damp out. This allows the jumping frequency to be increased. However, due to the complicated non-linearity involved during the process, careful design of the controller is needed for vibration suppression. This is investigated in details in Chapter 4.
2.4
Chapter Summary
In this chapter, we discussed four important parameters for taking AFM video, namely, frame rate, resolution, range, and sharpness. The physical limitations of actuators and structures are also investigated. Relations between imaging
parame-ters and physical limitations are presented in terms of three inequalities. In addition, considerations for different AFM imaging modes are introduced to see the different level of importance of individual component limitation has in different imaging modes. After identifying the limitation and there importance in different modes of imag-ing, we can start to address the aspects that helps to improve the imaging bandwidth.
Chapter 3
Induced Vibration Contact Detection
Method
+ Jumping mode operation allows the AFM probe to come into contact with the sample surface intermittently. As introduced in subsection 1.3.4, jumping mode op-eration combines the benefits of both contact mode in direct interaction force control and dynamic mode AFM in reducing friction force in tip-sample interaction.
One of the important performance factor of jumping mode AFM imaging is the tip-sample interaction force. Different methods have been developed to address this issue. In low speed operation for static imaging, the Force-Volume mode is utilized. For higher speed imaging, the peak force tapping mode is developed. This mode aims to directly regulate the interaction force by controlling the maximum cantilever de-flection at each cycle to a set-point value. However, due to the presence of drag forces (in aqueous environments), noises and cantilever dynamics, the minimal detectable peak force can be large. This results in large tip-sample interaction forces and hence sample damage.
To minimize the interaction force, we propose an alternative Induced Vibration Contact Detection (IVCD) method. This method is based on induction of surface or probe vibrations to detect contact between cantilever probe tip and sample substrate. A transfer function model for the cantilever probe and sample was first developed for simulation in Matlab. Different algorithms for contact detection were investigated
and compared against each other. To illustrate the effectiveness of the method, we conducted experiments for contact detection on a PS-LDPE-12M polymer sample. The results of contact detection proves the feasibility of the detection method. A to-pography tracking control algorithm based on the proposed contact detection method has also been investigated and simulated.
3.1
Overview of Prior Art
In this section, we take a look at the previous operational mode being used in jumping mode imaging. By understanding their principle of operation, we can address the limitations directly.
3.1.1
Force-Volume Mode
For static imaging, a force versus distance curve can be obtained at each imaging pixel. With the stiffness of the cantilever known after calibration, the interaction force between the sample and the probe can be directly calculated from the cantilever deflection. To avoid sample damage, we can simply regulate the maximum interaction force to be smaller than a certain threshold.
In addition, with the measured cantilever deflection and positioning command of the sample stage known, the deformation of the sample surface can be obtained. The force versus deformation of the sample provides additional material property information at each pixel.
However, despite good control of interaction fore and obtaining additional infor-mation for material properties, the imaging speed becomes a major limitation for the force-volume mode. For accurate mapping of force to deflection, a quasi-static situation where the acceleration of the cantilever probe tip is negligible. This imag-ing requirement is very hard to satisfy at high speed where the probe and sample is brought into contact at high speed.
