Blind Tip Reconstruction Research Articles

End-to-end differentiable blind tip reconstruction for noisy atomic force microscopy images

Observing the structural dynamics of biomolecules is vital to deepening our understanding of biomolecular functions. High-speed (HS) atomic force microscopy (AFM) is a powerful method to measure biomolecular behavior at near physiological conditions. In the AFM, measured image profiles on a molecular surface are distorted by the tip shape through the interactions between the tip and molecule. Once the tip shape is known, AFM images can be approximately deconvolved to reconstruct the surface geometry of the sample molecule. Thus, knowing the correct tip shape is an important issue in the AFM image analysis. The blind tip reconstruction (BTR) method developed by Villarrubia (J Res Natl Inst Stand Technol 102:425, 1997) is an algorithm that estimates tip shape only from AFM images using mathematical morphology operators. While the BTR works perfectly for noise-free AFM images, the algorithm is susceptible to noise. To overcome this issue, we here propose an alternative BTR method, called end-to-end differentiable BTR, based on a modern machine learning approach. In the method, we introduce a loss function including a regularization term to prevent overfitting to noise, and the tip shape is optimized with automatic differentiation and backpropagations developed in deep learning frameworks. Using noisy pseudo-AFM images of myosin V motor domain as test cases, we show that our end-to-end differentiable BTR is robust against noise in AFM images. The method can also detect a double-tip shape and deconvolve doubled molecular images. Finally, application to real HS-AFM data of myosin V walking on an actin filament shows that the method can reconstruct the accurate surface geometry of actomyosin consistent with the structural model. Our method serves as a general post-processing for reconstructing hidden molecular surfaces from any AFM images. Codes are available at https://github.com/matsunagalab/differentiable_BTR.

AFM‐Based Hamaker Constant Determination with Blind Tip Reconstruction

AbstractParticle contamination of extreme ultraviolet (EUV) photomasks is one of the numerous challenges in nanoscale semiconductor fabrication, since it can lead to systematic device failures when disturbing patterns are projected repeatedly onto wafers during EUV exposure. Understanding adhesion of particle contamination is key in devising a strategy for cleaning of photomasks. In this work, particle contamination is treated as a particle‐plane problem in which surface roughness and the interacting materials have major influences. For this purpose, vacuum atomic force microscopy (AFM) contact measurements to quantify the van der Waals (vdW) forces between tip and sample are performed. This as a vacuum AFM‐based methodology that combines numerical Hamaker theory and blind tip reconstruction is introduced. The Hamaker constants of 15 × 10−20 J and 13 × 10−20 J for the material systems of a silicon (Si) tip with both aluminum oxide (Al2O3) and native silicon dioxide (SiO2) on Si substrates, respectively have been determined. These methodology allows an alternative, quick and low‐cost approach to characterize the Hamaker constant within the right order of magnitude for any material combination.

Image reconstruction of TGZ3 grating by eliminating tip‐sample convolution effect in AFM

Accurate and meticulous measurement is an important prerequisite to obtain the real surface information of samples in atomic force microscopy (AFM). A severe problem is the frequent occurrence of measurement errors, which are mainly caused by the nonlinearity of the probe driver, the temperature drift of the system and the tip characteristics. The measurement errors caused by probe tip are the main source of errors in AFM nanoscale measurements. The shape and state of AFM tip will distort the AFM image from the actual sample morphology. If the information about the probe is known, the measurement error caused by the probe tip can be greatly reduced. In order to obtain accurate AFM images, a new method based on geometric measurement model and blind tip reconstruction is proposed to eliminate tip-sample convolution in the measurement of grating samples. The static and dynamic characteristics of the AFM tip are described by four parameters: cone angle, curvature radius, scanning inclination angle and mounting inclination angle. Finally, the feasibility and effectiveness of the new calibration method are verified by evaluating the image reconstruction quality. In conclusion, the proposed method can effectively reconstruct accurate AFM images of the grating.

Self-Adaptive Grinding for Blind Tip Reconstruction of AFM Diamond Probe

Blind tip reconstruction (BTR) method is one of the favorable methods to estimate the atomic force microscopy (AFM) probe shape. The exact shape of the characterizer is not required for BTR, while the geometry of the sample may affect the reconstruction significantly. A cone-shaped array sample was chosen as a characterizer to be evaluated. The target AFM probe to be reconstructed was a diamond triangular pyramid probe with two feature angles, namely front angle (FA) and back angle (BA). Four conical structures with different semi-angles were dilated by the pyramid probe. Simulation of scanning process demonstrates that it is easy to judge from the images of the isolated rotary structure, cone-shaped, the suitability of the sample to be a tip characterizer for a pyramid probe. The cone-shaped array sample was repeatedly scanned 50 times by the diamond probe using an AFM. The series of scanning images shrank gradually and more information of the probe was exhibited in the images, indicating that the characterizer has been more suitable for BTR. The feature angle FA of the characterizer increasingly reduces during the scanning process. A self-adaptive grinding between the probe and the characterizer contributes to BTR of the diamond pyramid probe.

Fabrication of nanochannels on polyimide films using dynamic plowing lithography

Three distinct polyimide films were analyzed from the point of view of their morphology in order to determine if their surface features can be adapted for applications where surface anisotropy is mandatory. Channels of nanometric dimensions were created on surface of the specimens by using a less common atomic force microscopy (AFM) method, namely Dynamic Plowing Lithography (DPL). The changes generated by DPL procedure were monitored through the surface texture and other functional parameters, denoting the surface orientation degree and also bearing and fluid retention properties. The results revealed that in the same nanolithography conditions, the diamine and dianhydride moieties have affected the characteristics of the nanochannels. This was explained based on the aliphatic/aromatic nature of the monomers and the backbone flexibility. The reported data are of great importance in designing custom nanostructures with enhanced anisotropy on surface of polyimide films for liquid crystal orientation or guided cell growth purposes. At the end, to track the effect of the nanolithography process on the tip sharpness, degradation and contamination, the blind tip reconstruction was performed on AFM probe, before and after lithography experiments, using TGT1 test grating AFM image.

Noise reduction by sparse representation in learned dictionaries for application to blind tip reconstruction problem

Scanning probe microscopy (SPM) is a well known tool used for the investigation of phenomena in objects in the nanometer size range. However, quantitative results are limited by the size and the shape of the nanoprobe used in experiments. Blind tip reconstruction (BTR) is a very popular method used to reconstruct the upper boundary on the shape of the probe. This method is known to be very sensitive to all kinds of interference in the atomic force microscopy (AFM) image. Due to mathematical morphology calculus, the interference makes the BTR results biased rather than randomly disrupted. For this reason, the careful choice of methods used for image enhancement and denoising, as well as the shape of a calibration sample are very important.In the paper, the results of thorough investigations on the shape of a calibration standard are shown. A novel shape is proposed and a tool for the simulation of AFM images of this calibration standard was designed. It was shown that careful choice of the initial tip allows us to use images of hole structures to blindly reconstruct the shape of a probe. The simulator was used to test the impact of modern filtration algorithms on the BTR process. These techniques are based on sparse approximation with function dictionaries learned on the basis of an image itself. Various learning algorithms and parameters were tested to determine the optimal combination for sparse representation.It was observed that the strong reduction of noise does not guarantee strong reduction in reconstruction errors. It seems that further improvements will be possible by the combination of BTR and a noise reduction procedure.

Controlled tip wear on high roughness surfaces yields gradual broadening and rounding of cantilever tips.

Tip size in atomic force microscopy (AFM) has a major impact on the resolution of images and on the results of nanoindentation experiments. Tip wear is therefore a key limitation in the application of AFM. Here we show, however, how wear can be turned into an advantage as it allows for directed tip shaping. We studied tip wear on high roughness polycrystalline titanium and diamond surfaces and show that tip wear on these surfaces leads to an increased tip size with a rounded shape of the apex. Next, we fitted single peaks from AFM images in order to track the changes in tip radius over time. This method is in excellent agreement with the conventional blind tip reconstruction method with the additional advantage that we could use it to demonstrate that the increase in tip size is gradual. Moreover, with our approach we can shape and control the tip size, while retaining identical chemical and cantilever properties. This significantly expands the reproducibility of AFM force spectroscopy data and is therefore expected to find a wide applicability.

Investigation on blind tip reconstruction errors caused by sample features.

Precision measurements of a nanoscale sample surface using an atomic force microscope (AFM) require a precise quantitative knowledge of the 3D tip shape. Blind tip reconstruction (BTR), established by Villarrubia, gives an outer bound with larger errors if the tip characterizer is not appropriate. In order to explore the errors of BTR, a series of simulation experiments based on a conical model were carried out. The results show that, to reconstruct the tip precisely, the cone angle of the tip characterizer must be smaller than that of the tip. Furthermore, the errors decrease as a function of the tip cone angle and increase linearly with the sample radius of curvature, irrespective of the tip radius of curvature. In particular, for sharp (20 nm radius) and blunt (80 nm radius) tips, the radius of curvature of the tip characterizer must be smaller than 5 nm. Based on these simulation results, a local error model of BTR was established. The maximum deviation between the errors derived from the model and the simulated experiments is 1.22 nm. Compared with the lateral resolution used in the above simulated experiments (4 nm/pixel), it is valid to ignore the deviations and consider the local error model of BTR is indeed in quantitative agreement with the simulation results. Finally, two simulated ideal structures are proposed here, together with their corresponding real samples. The simulation results show they are suitable for BTR.

Towards easy and reliable AFM tip shape determination using blind tip reconstruction.

Quantitative determination of the geometry of an atomic force microscope (AFM) probe tip is critical for robust measurements of the nanoscale properties of surfaces, including accurate measurement of sample features and quantification of tribological characteristics. Blind tip reconstruction, which determines tip shape from an AFM image scan without knowledge of tip or sample shape, was established most notably by Villarrubia [J. Res. Natl. Inst. Stand. Tech. 102 (1997)] and has been further developed since that time. Nevertheless, the implementation of blind tip reconstruction for the general user to produce reliable and consistent estimates of tip shape has been hindered due to ambiguity about how to choose the key input parameters, such as tip matrix size and threshold value, which strongly impact the results of the tip reconstruction. These key parameters are investigated here via Villarrubia's blind tip reconstruction algorithms in which we have added the capability for users to systematically vary the key tip reconstruction parameters, evaluate the set of possible tip reconstructions, and determine the optimal tip reconstruction for a given sample. We demonstrate the capabilities of these algorithms through analysis of a set of simulated AFM images and provide practical guidelines for users of the blind tip reconstruction method. We present a reliable method to choose the threshold parameter corresponding to an optimal reconstructed tip shape for a given image. Specifically, we show that the trend in how the reconstructed tip shape varies with threshold number is so regular that the optimal, or Goldilocks, threshold value corresponds with the peak in the derivative of the RMS difference with respect to the zero threshold curve vs. threshold number.

Mechanics of Interaction and Atomic-Scale Wear of Amplitude Modulation Atomic Force Microscopy Probes

Wear is one of the main factors that hinders the performance of probes for atomic force microscopy (AFM), including for the widely used amplitude modulation (AM-AFM) mode. Unfortunately, a comprehensive scientific understanding of nanoscale wear is lacking. We have developed a protocol for conducting consistent and quantitative AM-AFM wear experiments. The protocol involves controlling the tip-sample interaction regime during AM-AFM scanning, determining the tip-sample contact geometry, calculating the peak repulsive force and normal stress over the course of the wear test, and quantifying the wear volume using high-resolution transmission electron microscopy imaging. The peak repulsive tip-sample interaction force is estimated from a closed-form equation accompanied by an effective tip radius measurement procedure, which combines transmission electron microscopy and blind tip reconstruction. The contact stress is estimated by applying Derjaguin-Müller-Toporov contact mechanics model and also numerically solving a general contact mechanics model recently developed for the adhesive contact of arbitrary axisymmetric punch shapes. We discuss the important role that the assumed tip shape geometry plays in calculating both the interaction forces and the contact stresses. Contact stresses are significantly affected by the tip geometry while the peak repulsive force is mainly determined by experimentally controlled parameters, specifically, the free oscillation amplitude and amplitude ratio. The applicability of this protocol is demonstrated experimentally by assessing the performance of diamond-like carbon-coated and silicon-nitride-coated silicon probes scanned over ultrananocrystalline diamond substrates in repulsive mode AM-AFM. There is no sign of fracture or plastic deformation in the case of diamond-like carbon; wear could be characterized as a gradual atom-by-atom process. In contrast, silicon nitride wears through removal of the cluster of atoms and plastic deformation.

Regularization mechanism in blind tip reconstruction procedure

In quantitative investigations of mechanical and chemical surface parameters using atomic force microscopy (AFM) techniques the determination of the probe radius and shape is required. To the most favorable methods of the microprobe characterization belongs the blind tip reconstruction method (BTR). The BTR similar to many other inverse problems is sensitive to noise and needs the so-called regularization mechanism. In this article we describe and investigate two the most popular regularization schemes, which were proposed in Villarubia et al. (1997) [30] and Tian et al. (2008) [31]. We have shown that the procedure described in Tian et al. (2008) [31] enables very effective probe shape reconstruction if we know the statistics of noise present in the AFM system. The increase of effectiveness with relation to the procedure described in Villarubia (1997) [30] is so significant that makes it possible to reconstruct probes with much larger resolution. We have also noticed the fact, that probes reconstructed by means of the procedure presented in Tian et al. (2008) [31] have flat apexes for AFM images with low signal to noise ratio (SNR). We propose procedure, which can improve the probe apex reconstruction. It uses the AFM image to estimate the initial shape of the reconstructed probe. This shape may be further improved by the BTR algorithm. We have shown that it is possible only for the procedure described in Tian et al. (2008) [31].

Use of biaxially oriented polypropylene film for evaluating and cleaning contaminated atomic force microscopy probe tips: An application to blind tip reconstruction

An atomic force microscopy (AFM) image of a surface is basically a convolution of the probe tip geometry and the surface features; it is important to know this tip effect to ensure that an image truly reflects the surface features. We have found that a biaxially oriented polypropylene (BOPP) film is suitable for checking tip performance and for cleaning contaminated tips, thus making it possible to collect images of the same area of a BOPP film surface before and after the tip was cleaned. Therefore, the difference between the two different images is solely due to the contamination of the tip. We took advantage of our ability to collect AFM images of the same area using the same tip, in one instance, contaminated and, in the other, after being cleaned. First we used blind reconstruction on the image collected using the contaminated tip. Blind tip reconstruction allows one to extract the geometry of the tip from a given image. Once we had estimated the geometry of the contaminated tip, we used it to simulate the tip effect using the image collected using the cleaned tip. By comparing the simulation result with the image collected using the contaminated tip we showed that the blind reconstruction routine works well. Prior to this, there was no de facto method for testing blind reconstruction algorithms.

Pull-off forces measured between hexadecanethiol self-assembled monolayers in air using an atomic force microscope: analysis of surface free energy

The pull-off forces were measured between hexadecanethiol monolayers, self-assembled on gold-coated silicon nitride cantilever tip and silicon wafer, using atomic force microscopy (AFM). The blind tip reconstruction technique was used for determination of the curvature of the AFM tip. The measured pull-off force value remained practically unaffected by a variation of the maximum applied load in a range of 5–80 nN. This result suggests that the use of continuum elastic contact mechanics in the analysis of AFM pull-off force measurements is not as straightforward as usually assumed in the literature reports on similar systems. The surface free energy of hexadecanethiol monolayer on a gold film of γ = 24–27 mJ/m2 was calculated based on the pull-off forces (F), measured using R = 60–80 nm radius tips, and next applying the Derjaguin approximation: F = 4πRγ. These γ-values were found to match the surface free energy value calculated from contact angle data and using Lewis acid–base interfacial free energy theory.