The scanning tunneling microscope STM is widely used in both industrial and fundamental research to obtain atomic-scale images of metal surfaces. It provides a three-dimensional profile of the surface which is very useful for characterizing surface roughness, observing surface defects, and determining the size and conformation of molecules and aggregates on the surface.
Scanning tunneling microscope
Several other recently developed scanning microscopies also use the scanning technology developed for the STM. The electron cloud associated with metal atoms at a surface extends a very small distance above the surface. When a very sharp tip--in practice, a needle which has been treated so that a single atom projects from its end--is brought sufficiently close to such a surface, there is a strong interaction between the electron cloud on the surface and that of the tip atom, and an electric tunneling current flows when a small voltage is applied.
At a separation of a few atomic diameters, the tunneling current rapidly increases as the distance between the tip and the surface decreases. This rapid change of tunneling current with distance results in atomic resolution if the tip is scanned over the surface to produce an image. Russell D. Young , of the National Bureau of Standards, was the first person to combine the detection of this tunneling current with a scanning device in order to obtain information about the nature of metal surfaces.
The instrument which he developed between and , the Topografiner , altered the separation between the tip and the surface z so that, at constant voltage, the tunneling current or, at constant current, the tunneling voltage remained constant as the tip was scanned over the surface. The x, y, and z coordinates of the tip were recorded. For details of the design and operation of the Topografiner, see the references given in the Bibliography. The same principle was later used in the scanning tunneling microscope.
To achieve this, we estimate the value of the background at point x , g x , by a weighted least mean-square linear fit to a segment of the line centered at x with length L :. It is a numerically efficient alternative to robust least mean-square fits. The corrected image is given by. This means that on average the corrected image intensity is close to zero.
This removes most of the background and brings all lines to about the same intensity close to zero. An additional minor improvement to the background removal process is to remove the small remnant slope at the two edges by fitting a small part of the line at two ends to a linear background with slopes of the same magnitude but opposite sign so that the two lines meet at the same height in the middle and removing this background from the corresponding halves of the line.
This step makes the intensity somewhat more uniform across the whole line. The value of L is determined by searching for the maximum correlation coefficient after image registration, a process that we will describe below. The effect of the background removal step using linear regression allows the subsequent two steps to be carried out which produced Figure 4 a , whereas without this step the steps described in the following two subsections are ineffective to process the original image in Figure 1 due to the overwhelming noise.
Our goal is to combine data from forward and backward scans to obtain a more accurate image. Because there is always a small registration difference between the forward and backward scans, a simple combination of the unprocessed data e. Indeed, the difference between the forward and backward scans is large near the features in the image Figure 6 a. Therefore it is necessary to first match the two scans via a process of image registration before combining them. The method for image registration is improved significantly from the one used in [ 14 ].
The main differences are that we now use a new global registration method different than the one used in [ 14 ] and that we no longer use a deformation based local registration method. The latter tends to lock onto the noise thus magnifying the effects of noise. Although the images are two-dimensional, the data is acquired in a line-by-line manner.
Therefore the image registration method is applied separately to each line of the forward and the backward scans, F a and B a.
In the registration procedure, each pair of corresponding lines from F a and B a are adjusted by a line shift to minimize their difference. In [ 14 ], the condition is expressed as the following model:. The small searching space for c in practice allows one to solve this minimization through a heuristic search. However, this method is susceptible to noise, especially for atomic resolution data in which presence of noise signal may have the same magnitude as images of atoms.
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Therefore we need a more robust approach to image registration. The improved approach is to treat the pair of data sets F a and B a as linearly correlated data and find the constant c such that the correlation coefficient is maximized:. The benefit of image registration is clearly visible in Figure 5 b , which shows the simple average of the aligned data F a and B a. The average image is much sharper compared to Figure 5 a.favwaggmasscentve.ga
Postprocessing Algorithm for Driving Conventional Scanning Tunneling Microscope at Fast Scan Rates
However, even with the aligned data, the spurious oscillations still exist. In fact, in the best case scenario, a simple average would only reduce the spurious oscillations by about half. A better algorithm is needed to eliminate these oscillations, as we will present next. Using the aligned forward scan F a and backward scan B a , we wish to find an approximate image that is as close to the true image S as possible. Our main goal is to eliminate any noise and spurious signals in the image, while keeping all features in the image.
We consider any feature that exists only in one forward or backward scan but is not matched in the other scan as spurious and must be removed. Mathematically, let s denote one row of S while f and b represent the corresponding rows of F a and B a. The associated model for this pair of lines is given by. This model can be solved in an efficient manner by repeatedly smoothing a candidate signal inserted between the two curves F a and B a via a constrained signal filtering that maintains the filtered value within the bounds set by F a and B a until convergence.
The existence of the solution is guaranteed as the average of the forward and backward scans satisfies the constraint and we use it as the initial candidate signal. For the filtering process, the value of each point on the line is replaced by the average value of its two nearest neighbors, subject to the constraint that it is bounded by F a and B a. The algorithm is outlined in Algorithm 1. Illustration of the rubber band method using simulated data. The red and green curves are simulated forward and backward scan signals, respectively.
C. Julian Chen
A rubber band black is inserted between the two curves and pulled tight, yielding the final approximation of the true image. The first three postprocessing steps described above on atomic resolution fast scan data yield images that clearly show surface lattice structure, as in Figure 4 a. However, this image, like most atomic resolution STM images, contains both the information of atomic positions and the topography of the surface. The latter tends to obstruct the visibility of atomic positions.
If the topography information is discarded, then one can obtain a higher quality image containing only atomic positions. In this section we will describe such an algorithm. The first part of this algorithm is to remove all large scale topography information while retaining the local height information that is needed to distinguish the atoms. Clearly, we have.
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The best value for n is the number of pixels that covers more than atomic distances. The ranking map obtained this way is a ragged image. We apply a 2D median filter [ 15 ] to obtain a smoothed image. The idea of using the ranking map for feature enhancement can be viewed as the reverse of ranking based smoothing techniques such as median filtering.
However the ranking map algorithm presented here is unique in that it does not merely use the ranking to help determine the image intensity as in the median filtering method. In the ranking map method, the final image intensity is the ranking itself, and the original image is discarded once the ranking map is constructed. Electrochemically etched tungsten tip was cleaned by in situ electron bombardment heating. As already discussed in previous sections, the original unprocessed topography data from a fast scan with a scan rate of 0.
We can see that both original forward scan and backward scan suffer from significant noise but the patterns of noise are different, making noise elimination possible through combining the two images. The effect of the image restoration algorithm on the experimental image is shown in Figure 8 for three selected rows of the data.
The final corrected image is compared to a set of STM scans with slow scan rate on the same surface in Figure 2. The aligned forward and backward data from the same line of scans: a row 46; b row 80; c row For the atomic resolution fast scan data, the raw image in Figures 1 c and 1 d is overwhelmed by noise and has no observable atomic structure. The final processed image Figure 4 b , however, displays clearly the surface lattice structure.
One can even see the significant lattice strain and disorder due to the proximity of a large defect.
We have demonstrated an algorithm that can greatly reduce the noise and error of STM images by combining forward and backward scan data in a line-by-line manner. This allows us to push the scan rate for a conventional STM setup to beyond its normal limit, up to 10 times faster. An order of magnitude increase in the scan rate will greatly reduce systematic errors such as the scan drift and environmental noise and will also improve research productivity. Furthermore, this increase represents a first step towards the goal of real-time observation of dynamic processes on surface by STM.
Using the ranking map as the atomic resolution image, as described in this work, is a general algorithm for postprocessing STM images beyond fast scans. Any images obstructed by significant surface topology variations can be treated by this algorithm to yield sharp, atomic resolution results. This algorithm is also useful as an alternative way to enhance image features and can be used as a general tool in image processing technology. National Center for Biotechnology Information , U.