Large-range high-speed dynamic-mode atomic force microscope imaging: adaptive tapping towards minimal force

In this paper, a software-hardware integrated approach is proposed for high-speed, large-range tapping mode imaging of atomic force microscope (AFM). High speed AFM imaging is needed in various applications, particularly in interrogating dynamic processes at nanoscale such as polymer crystallization process. Achieving high speed in tapping-mode AFM imaging is challenging as the probe-sample interaction during the imaging process is highly nonlinear, making the tapping motion highly sensitive to the probe sample spacing, and thereby, difficult to maintain at high speed. Increasing the speed via hardware bandwidth enlargement, however, leads to a substantially reduction of the imaging area. Contrarily, the imaging speed can be increased without loss of the scan size through control (algorithm)-based approach. For example, the recently-developed adaptive multiloop mode (AMLM) technique has demonstrated its efficacy in increasing the tapping-mode imaging speed without loss of scan size. Further improvement, however, has been limited by the hardware bandwidth and the online signal processing speed and computation complexity involved. Thus, in this paper, the AMLM technique is further enhanced to optimize the probe tapping regulation, and integrated with a field programmable gate array platform to further increase the imaging speed without loss of quality and scan range. Experimental implementation of the proposed approach demonstrates that high-quality imaging can be achieved at a high-speed scanning rate of 100 Hz and higher, and over a large imaging area of over 20 μm.


Introduction
In this paper, we present, through the developement of a controlbased imaging technique with adaptive tapping, a large-range, dynamic-mode atomic force microscope (AFM) imaging at scanning speeds significantly faster (4 to 5 times faster) than those reported in the literature.. Dynamicmode, particularly, tapping mode (TM) [1] and its extensions such as peakforce QNM [2,3], has become the de facto choice of AFM imaging technique for its highimaging quality and subdued sample distortion. The TM imaging speed, however, is significantly slower than that of contact mode (CM) [1], as it is much more challenging, due to the highly nonlinear probe sample contact [4], to maintain a stable probe-sample contact in TM imaging, especially when the scan size becomes large [5]. Although existing efforts have been made to increase the speed of TM imaging through hardware and software (algorithm) innovations [6][7][8], these efforts are limited in the imaging speed that can be achieved-without loss of imaging quality-or the sample size that can be scanned (per image). Thus, this work is motivated to substantially increase the TM imaging speed at large scan size.
High-speed TM imaging over a large scan size without loss of imaging quality faces challenges to overcome. Inherently, the imaging speed is limited by the highly nonlinear force-distance relation during the tapping of the probe on the sample surface when the probe scans across the sample surface [9]. As a result, the tapping amplitude (TA) is sensitive to the variation of the probe-sample distance. Thus, when the sample topography varies dramatically, the TA can quickly change significantly [10]. This sudden change of the TA, during the scanning can lead to loss of probe contactor annihilation of the tapping motion [10,11]. As the TA must be closely regulated, the loss of contact and/or tapping annihilation directly results in imaging quality degradation and sample and/or probe deformation [5,10]. Maintaining the TA during high-speed imaging is further complicated by the time-delay [12] in deciphering the TA as the tip is vibrating around the resonance of the cantilever [13]. Thus, maintaining the probe-sample distance upon sample topography variation is essential to high-speed TM imaging.
Limitations exist in current efforts to achieve high-speed TM imaging at large scan range. For example, the TM imaging speed can be increased through hardware improvements [12,14,15] by substantially increasing the bandwidth of the overall nanopositioning system along with high-speed data processing. The idea is that as such, the scanning rate can be increased accordingly while still staying well below the bandwidth, and the dynamics of the AFM system is not excited. This increase of scanning rate, however, is accompanied with a dramatic reduction of the imaging area-the sample area covered per image is reduced by over 2 orders of magnitude (e.g. from 100 × 100 μm 2 to around 2 × 2 μm 2 and less) [8], due to the inherent physical limitation-the actuator displacement range reduces as its bandwidth increases [15]. To increase the imaging speed without losing the scan size, more advanced control techniques (than the conventional PID control) [16][17][18] and scanning methods (than the conventional raster scanning) [27] have been developed. For example, the time-delay in deciphering the TA can be reduced, and thereby, the sample topography can be better estimated by observer-based techniques [19][20][21]. Recent efforts in improving the performance or functionality of tapping-mode or peak-force mode imaging also include the double-pass scanning method [22] to compensate for the cantilever deflection drift and environmental disturbance (e.g. hydrodynamic force in liquid imaging), and the peakforce quantitative nanomechanics technique [2,3] that combines peak force imaging with infrared reflection mapping to simultaneously map sample topography and chemical-mechanical properties of the sample. These techniques, however, are not focused on increasing the speed of TM imaging, and the challenges above in high-speed imaging still exist.
These limitations of control technique developments in improving TM imaging have been tackled in the recent-developed adaptive multi-loop mode (AMLM) [11,23] technique. The main idea is to introduce an additional feedback loop to regulate the mean value of the probe vibration (called the TM-deflection), and thereby, regulate the interaction force, and then, augment a data-driven online iterative feedforward control to enhance the tracking of the sample topography. Experimental results obtained on various polymer samples showed that over an order of magnitude increase of the imaging speed can be achieved in large-range imaging without loss of imaging quality (over 50 μm) [11]-at scanning rate at 20-25 Hz. Further increase of the imaging speed, however, has been limited by the hardware bandwidth, the online signal processing speed, and the computation complexity (in the frequency-domain iterative control algorithm involved). Therefore, we propose to address these limitations to further improve the technique.
We develop a hardware-software-integrated approach towards high-speed large-range TM imaging. First, to optimize the TA regulation, we propose to online regulate, via a local feedback control, the setpoint of the TA adaptively around the optimal value-in contrast, in all existing TM techniques, the setpoint of the TA is set at a pre-chosen constant. Then, a datadriven, time-domain, inversion-based iterative control is proposed to replace the frequency-domain one in the AMLM technique. As such, the complicated online computation in frequency-domain is eliminated. Moreover, to further improve the sample topography tracking, the estimation of the previousscan-line sample topography (used as the desired trajectory to be tracked on the current scan line) is improved by taking into account the tracking errors in both the TA and the TMdeflection regulation. This enhanced AMLM technique is implemented on a field programmable gate array (FPGA)based platform with high-speed online signal acquisition and processing. Methods to circumventhardware limitations of current FPGA system (e.g. limited onboard memory) are also discussed. This FPGA-based enhanced AMLM technique is applied to an AFM with higher bandwidth piezoelectric actuation system (nearly 10 times larger than that previously). Such an integrated approach merges, in a synergistic manner, the advantages of both hardware and software together for high-speed TM imaging at large scan size. Experimental implementation results are presented to show that TM imaging at large-range (scan size at over 21 μm) and high-speed (with scanning rate at 100 to 120 Hz) can be achieved while maintaining the image quality on samples of high aspect ratio. Preliminary results of this work has been reported in a recent conference [24]. Here we substantially expanded and extended the work with adaptive tapping modulation to minimize the tapping force, doubled the imaging speed, and enlarged the scanning area size.

High-speed large-range dynamic-mode imaging: an integrated approach
We aim to address the challenges in high-speed TM imaging at large scan size. During TM imaging, the cantilever probe is excited by a dither piezo to vibrate near its resonance frequency, and tap on the surface constantly [25]. Then the TA is measured (e.g. through a lock-in amplifier) and regulated around a pre-chosen set-point value while the probe is scanning across the sample surface, and the sample topography can be quantified as the vertical displacement of the piezoelectrical actuator-provided that the TA is closely regulated. However, the speed of conventional TM imaging is inherently hampered by the slow response of the TA regulation feedback, and the tapping being sensitive to the probesample distance due to the highly nonlinearprobe-sample interaction force [10]. As the imaging speed increases, loss of probe-sample contact tends to occur when the topography suddenly drops, and the tapping can be completely annihilated around regions where the sample topography rises dramatically [24].
We propose, by extending the AMLM technique, [11] an adaptive tapping multi-loop mode (AT-MLM),depicted in figure 1, to adaptively tune the TA online towards the minimization of the tapping force (the 'Adaptive Tapping' part in figure 1). Moreover, the iterative feedforward control of the sample topography tracking in the AMLM method is further enhanced by accounting for both the TA and the mean value of the probe tapping vibration (called the TM-deflection below), and simplifying the online iterative control with a time-domain data-driven algorithm (the 'Iterative feedforward control of topography tracking' part in figure 1). As in the AMLM technique, a feedback control of inner-outer loop structure is integrated to regulate the TM-deflection (the 'TM-Deflection Feedback' part in figure 1). We start with introducing the adaptive tapping first.

Adaptive tapping towards force minimization
In contrast to other existing dynamic mode imaging methods where the TA-set point is pre-chosen and fixed, in the proposed AT-MLM approach the set-point of the TA is adjusted and tuned online during the scanning process. As such, it opens the door to optimize the cantilever tapping, e.g. minimizing the tapping force. The TA-set point is adjusted to ensure that loss of probe-sample contact or annihilation of tapping is avoided during the imaging process, making it more flexible, and thereby, potentially easier to track the sample topography, particularly when the scanning speed increases. Thus, this idea extends the adaptive adjustment of the deflection setpoint in contact mode imaging to minimize the normal force [4]. The TA-setpoint is adjusted through a gradient descend online adjustment: , with  s the total number of sampling points per scan line, A opt is the TA-setpoint corresponding to the minimal probe-sample interaction force, A p is the setpoint that ensures a stable probe tapping and maintains the image quality, ρ is the step size, and δ is the pre-chosen threshold, respectively. Thus in the above adaptive tapping, the TA-set-point is online adjusted towards the minimal tapping force when the fluctuation of the TA-error e k ( j) is small (within the threshold value δ). Other methods to adaptively adjust the TA might be utilized, for example, based on optimal control. The outerinner feedback control structure is proposed here for its ease of implementation, e.g. the existing tapping-amplitude feedback control is intacted.
When the normalized TA (with respect to the probe vibration amplitude without tapping on the sample surface) is smaller than 10%, the tip-sample interaction force increases significantly, while the probe-sample contact can be easily lost as scanning speed increases when the normalized TA is larger than 80% [9]. Therefore, the normalized TA A set shall be maintained within the range of 10%-30% to ensure the image quality and keep the interaction force small. If the TA is well maintained in this range, the setpoint can be increased to reduce the tapping force, or the setpoint is reset to ensure the imaging quality. The change of the TA-setpoint needs to be accounted in the sample topography quantification (discussed later in section 2.4.1).

TM-deflection regulation via inner-outer feedback control
As in the AMLM approach [11], a feedback loop is introduced to regulate the TM-deflection. Working together with the above TA feedback loop in concert, this TM-deflection feedback loop is to optimize and maintain a stable probe tapping during the imaging. Similar to the above TA-loop, the TM-deflection is regulated through an inner-outer feedback loop, where the outer loop is to adjust the TM-deflection setpoint through the following PID type of control (see figure 2) [24] where  s is the total number of sampling periods per scan line, and k p,m ,k i,m , and k d,m are the proportional, integral, and derivative coefficients, respectively. Initially the setpoint for the outer loop d TM_d is set as the mean TM deflection at the starting point of the imaging process.

Compensation for the lateral-to-vertical coupling
To integrate the above TM-deflection loop to state-of-the-art AFM systems using small-size cantilevers (e.g. the FAS-TSCAN system, Bruker Nano. Inc.), the deviation caused by the lateral-to-vertical coupling to the TM-deflection must be accounted for. The amplitude of the variation can be ten times larger than that caused by the sample topography variation.
An experiment-based decoupling method is employed to remove this lateral-to-vertical coupling effect. First, the coupling-caused TM-deflection is obtained by acquiring the signal through a so-called pseudo-imaging process during which the cantilever scans, without touching the surface, over the same imaging area at the same scanning speed as in the targeted imaging process. Then, during the targeted imaging process later, the acquired TM deflection signal will be subtracted from the measured one, and used in both the above TM-deflection feedback loop and the feedforward control, as well as in the topography construction, i.e.
is the raw deflection and d p ( j) is the TM deflection acquired by the pseudo-imaging process. Compared to other model-based methods, this procedure is more effective as the coupling can vary substantially in different cantilever condition but remains largely the same for the imaging process followed-the cantilever used and its mount and the environment condition are the same. where h k,z ( j) is the z-axis piezo displacement of k th scan line, k h,a and k h,m are the corresponding scale factors from TA error and deflection error to piezo displacement, e k,Amp ( j) and e k,TM ( j) are the TA error and deflection error of k th scan line, respectively, acquired during imaging process.

Time-domain inversion-based iterative control (TDIIC).
Then, a data-driven iterative feedforward control is employed to track the sample topography, similar to the AMLM technique [11]. To enhance the online implementation efficacy-critical to the targeted high speed imaging in this work (e.g., at scanning rate of 120 Hz), the frequency-domain IIC algorithm in the AMLM method [11] is replaced with the following TDIIC algorithm = u j 0, 7 ff ,0 ( ) ( ) where, respectively, k inv ( j) is the iterative gain updated pointby-point, and h k+1,d ( · ) is the desired sample topography to track in the k + 1th iteration, estimated by using the kth estimation, h k,t ( · ) (see equation (6)). Moreover, the iterative gain k inv ( j) is updated by using the measured input-output data as where k inv,DC is the inverse DC-gain of the z-axis AFM piezoactuation system, and δh( j) is the velocity of the probe given by The online adjustment of the iterative gain k inv ( · ) is to account for the variation of the system gain with the saturation effect considered. The threshold value ò is chosen based on the probe velocity, as the variation of the gain k inv grows with the probe velocity due to its nonlinear dynamics [24].
At the beginning of the imaging process, the scheme described above is applied to scan on the first line repetitively until convergence is reached, (i.e. the difference of the z-piezo displacement between two consecutive iterations converges towards the noise level of the signal). Then the rest of the sample is scanned continuously without repetition [24].
A summary of the proposed method is presented as algorithm 1 in next page.

FPGA-based online implementation
An FPGA-based signal processing platform is utilized to materialize the proposed approach, providing the needed sampling rate and online computation capability for highspeed AFM imaging.
To implement control algorithms involving both feedforward and feedback loops for trajectory tracking (such as the tracking of the sample profile in the proposed approach), issues caused by limited onboard memory must be addressed, as the desired trajectory to track or the image data acquired online cannot be entirely stored onboard during the experiment process. For large-size data known a priori (e.g. a desired trajectory), the data are downsampled on the host computer before the transfer and then online recovered on the FPGA board via interpolation (see figure 2(a)) [24]. Contrarily, data generated or modified online, are transferred to the host computer simultaneously during the experiment process through a buffer-to-buffer structure implemented via the direct-memory-access (DMA) technique, without interfering with online operations (e.g. sampling and computation) (see figure 2(b)). Additional care shall also be taken to allocate and assign buffers along with the DMA channels to avoid data overlap or lost, as there are only few DMA channels onboard and that are half-duplex, too.
In implementation, the proposed technique is implemented as a project on the FPGA platform along with a computer (see figure 2). The project consists a 'host program', which ran on the host computer, and a 'main program' that was complied into the FPGA bit-code, and ran on the FPGA card. The 'host program' controls the data transfer between the host computer and the FPGA card (see figure 2), and the proposed technique is implemented in the 'main program', respectively.

Experimental example
The proposed technique was implemented in an AFM imaging experiments. The objective is to demonstrate that by using the proposed technique, high-quality, high-speed imaging can be achieved over a large scan size. We start with describing the experimental setup.  Comparison of (a) the z-axis piezoelectric actuator displacements obtained by using the AT-MLM in four repetitive scannings on the first line at the scan rate of 100 Hz to that obtained by the PI control at the scan rate of 2 Hz scan rate, and (b) displacement error of each scanning with respect to that obtained with PI control at 2 Hz as the reference, respectively.

Experimental setup
The experiments were performed on a state-of-the-art AFM system (Dimension FastScan, Bruker Inc), where, for implementing external control of AFM operation, the internal builtin control of the AFM can be bypassed, the piezoelectrical actuators can be directly controlled through external inputs, and the cantilever displacements in x-, y-and z-axes and the probe-sample interaction force (the cantilever deflection) can be directly measured (through a signal acquisition module box of the AFM system. Similar direct sensor access was applied in other commercial SPM systems). The bypass of the internal control and the direct sensor and drive signal accesses was provided by the AFM manufacturer (most AFM companies can provide such minor hardware modification at a small to no cost). A FPGA-based DAQ system (NI RIO Device, USB-7856R, National Instrument Inc.) was used along with a host PC (Asus G14 GA401 laptop with AMD Ryzen 7 4800HS CPU and 16 Gb RAM) to implement the proposed AT-MLM technique, and the data obtained were processed using Matlab-Simulink (Mathworks Inc.). The sampling rate was set at 200 kHz, and a calibration sample (STR3-1800P, Bruker Inc, with 180 nm step height and 1.5 μm pitches separated by 1.5 μm spacing) was imaged with a lateral scanning size at 21 μm. The displacement deviation caused by hysteresis at such a scan range was more than 22%. A blend of Polystyrene and Polyolefin Elastomer (PS-LDPE) sample was also imaged to further assess the proposed technique.

Experimental implementation
First, the lateral-coupling effect was accounted for by using the proposed pseudo-imaging technique (see section 3.2). The TM-deflection signal was acquired without sample-probe contact, and the lateral scanning size was kept the same as those used in later imaging experiment. The scanning speed was set at 50 Hz and the TM-deflection signal acquired through the pseudo-imaging process was used as the baseline TM-deflection signal d p ( j) (in equation (5)) to be subtracted to remove the lateral-coupling from the measured TM deflection in all the experiments at three different scanning speeds (50, 100 and 120 Hz). Then, the proposed AT-MLM technique was applied. First, the PID parameters of the TMamplitude loop and the cut-off frequency of the low pass filter were adjusted under the conventional TM (i.e. with only the TM-amplitude feedback and a constant TM-amplitude setpoint value), through the step response of the TM-amplitude closed-loop system, under a stable tapping on a hard sample (e.g. the calibration sample above) without lateral scanning. The experimentally-tuned optimal settling time and the optimal overshoot obtained were 0.56 milliseconds with 12% overshoot, respectively, and the desired topography h k,d ( j) was filtered by low pass filter whose cut-off frequency was chosen at 3000 Hz based on the estimated spectrum of the topography signal at the scan rate of 100 Hz. Then, the coefficients of both the TM-amplitude and the TM-deflection loop were tuned experimentally, respectively, by following the same procedure and the similar criteria. Once these three loops worked together properly, the TDIIC feedforward control was augmented (see equation (6)), where the scaling factors of the TM-amplitude error and the TM-deflection error, respectively, were adjusted by using the calibration sample above.
During the implementation of the AT-MLM method, the sample was first scanned by using the TM-ampltitude feedback alone at low scan rate of 2 Hz on the first scan line, i.e. without augmenting the iterative feedforward control and the TM-deflection loop, to obtain an accurate tracking of the sample topography profile of the first scan line. Then the time-domain iterative feedforward control was augmented, along with the TM-deflection feedback loop and the adaptive TM amplitude regulation loop, where the sample topography obtained via at 2 Hz was used as the initial desired trajectory. The sample was then imaged at the chosen high-speed scan rate repetitively on the first line for four times (see figure 5) to ensure the convergence and thereby, accurate in tracking of the sample topography. Next, the rest of the sample area was imaged without repetitive scanning, with the desired trajectory for the TDIIC feedforward constructed by using the signals acquired in the previous scanline (see equation (6)). Precision scanning in the lateral x-and y-axes were obtained by using the MIIC technique [26], where the lateral scanning tracking error was maintained below 1.2% (measured in the relative 2-norm sense), respectively. For comparison, images of both the calibration sample and the PS-LDPE sample were also obtained by using the conventional TM-imaging at the three scanning rates of 50 Hz, 100 Hz, and 120 Hz, respectively.

Experimental results and discussion
The experimental results obtained are presented in figures 3-10. The lateral-coupling-caused TM-deflection variation measured at the scan rate of 50 Hz is shown in figure 3(a), compared to that after the coupling removal in figure 3(b), respectively. To examine the convergence of the TD-IIC in the proposed AT-MLM approach, the z-axis tracking results obtained in the four online repetitive scannings on the first scan line (scan rate: 100 Hz) are shown in figure 4, compared to that obtained by using the PI-feedback control at low speed (scan rate of 2 Hz). The relative 2-norm of the tracking error with respect to the 2 Hz PItracking in each iteration, E k,2 (%), is shown in figure 5. To assess the effectiveness of the adaptive adjustment of the TMampltiude set-point, A set ( j), the online adjusted A set ( j) and the TA ratio A( j)/A free (A free is the free TA) are shown in figure 6. The topography images obtained by using the proposed AT-MLM technique at the scan rate of 100 Hz is compared to that by using the PI-control at the scan rate of 2 Hz and 100 Hz in figure 7, respectively, where the image obtained by using the adaptive tapping technique and TD-IIC feedforward control (figure 7(c)) is also shown to evaluate the effectiveness of the proposed adaptive adjustment of TM-amplitude set-point. To further validate the proposed approach, the topography images obtained at other two scan rates (50 Hz and 120 Hz) are compared to the PI-control results in figure 8, and the images of the LDPE sample obtained by these two methods are also compared in figure 9 for all the three scan rates, respectively. The relative 2-norm errors over the entire image for the proposed technique are compared to those by the PI-control for the three scan rates in figure 10, respectively, where the low-speed 2 Hz scan image was used as the reference.
The experimental results showed the efficacy of the proposed approach in improving the topography tracking in high-speed TM imaging. First, by using the proposed experimental-based on-site free-scanning method (see section 2.3), the lateral-coupling-caused deflection deviation was effectively removed. As shown in figure 3, the lateral-couplingcaused TM-deflection fluctuation was pronounced-the envelop change of the TM-deflection in figure 3 (a) caused by the lateral coupling effect was as large as 2 V, 10 times larger of that due to the topography variation of the calibration sample. By using the proposed method, this lateral coupling effect was completely removed-the fluctuation of the TMdeflection was now around the noise level with a small mean value around 20 mV. Secondly, online convergence was achieved by using the proposed TD-IIC algorithm in the AT-MLM control. As shown in figure 4, tracking of the sample topography on the first scanline converged in only 3-4 iterations, with the relative tracking error reduced by 84.7%. These three improvements in lateral-coupling removal, rapid convergence and accurate topography tracking in the repetitive scanning on the first line, and the adaptive TM-amplitude set-point adjustment directly contributed to the performance of the proposed AT-MLM technique.
The imaging results obtained in the experiment demonstrated that the speed of tapping-mode, large range AFM imaging can be significantly increased by using the proposed approach. It can be seen that the image quality of the topography obtained by using the AT-MLM technique at 100 Hz Figure 8. Comparison of the topography image of the calibration sample obtained by using the AT-MLM technique at the scan rate of (a3) 50 Hz, (a4) 120 Hz, to those by using the PI-feedback alone at the scan rate of (a1) 50 Hz, (a2) 120 Hz, respectively. Figure 9. Comparison of the topography image of the LDPE obtained by using the AT-MLM technique at the scan rate of (b5) 50 Hz, (b6) 100 Hz, and (b7) 120 Hz, to those by using the PI-feedback alone at the scan rate of (b2) 50 Hz, (b3) 100 Hz, and (b4) 120 Hz, respectively. compared well to that obtained by TM imaging at 2 Hz (compare figures 7(a)-(d)). Both images presented sharp edges of the square-shaped pitches in figure 8, whereas these topography characteristics of the sample was severely distorted in the conventional TM imaging result at 100 Hz scan rate. The overall imaging error was reduced from 73% to 14% (see figure 10(a)). Moreover, the experimental results also showed the efficacy of the proposed adaptive set-point adjustment in imaging quality improvement-resulting in sharper edges of the pitches captured in the topography image (compare figures 7(c), (d)). These improvements in highspeed, large-range imaging was consistent across all three scan rates tested in the experiment, as shown in figure 8. The overall imaging error was reduced from the conventional TM imaging by 80% and 75% for the scan rate of 50 Hz and 120 Hz, respectively (see figure 10(a)). This significant increase of imaging speed while maintaining the imaging quality can also been clearly seen in the imaging results for the LDPE sample (see figure 9).
Two features of the proposed AT-MLM technique were illustrated through the experimental results. At the scan size of 20 μm, the probe scanning speed on the sample surface reached 4 mm s^{-1} and 4.8 mm s −1 for the scan rate of 100 and 120 Hz, respectively Such a high-speed probe scanning has not yet been reported in the literature (with the imaging quality maintained). As a comparison, the probe scanning speed in the high-speed TM imaging reported in [15] was at 0.48 mm s −1 for the scan size of 150 nm, 10 times slower than that achieved in this work. Another feature is that the proposed AT-MLM was capable of imaging samples of high aspect ratio. With vertical edges and sample height at 180 nm, the calibration sample was challenging to image at high speed, whereas in the high-speed TM imaging in [15], the sample height was below 18 nm, also 10 times smaller than that imaged in this work, and the sample topography was smooth. Therefore, the experimental results demonstrated the efficacy of the proposed approach in achieving high-speed large-range tapping-mode AFM imaging.

Conclusion
A hardware-software integrated approach is proposed for high-speed, large-range tapping-mode AFM imaging. The recently developed AMLM technique was further extended and integrated with a FPGA high-speed data processing platform on an AFM system with an nanopositioning system of increased bandwidth. Moreover, an AT-MLM was proposed to adaptively minimize the tapping force while maintaining the imaging quality during high speed scanning. The efficacy of the proposed AT-AMLM imaging technique was demonstrated through experiments of imaging a calibration sample and a LDPE sample at different scanning speeds (50-120 Hz). The experiment results showed that by using the proposed technique, the imaging speed was significantly increased while the imaging quality was maintained.