Corrugation Comparison

Warning, these notes are still in development...

Quick Description: If we have two structures that we wish to compare, one method to use is to take a look at their corrugation. We can look both at the average height of each structure and how much that height varies (corrugation) for each structure. This gives us an idea of what they should appear as individually and relatively when we are using STM. Moreover, we can use the height information to set the tip-sample distances to be the same for between structures, comparing their STS measurements at various tip-sample distances. Keep in mind that an STS measurement at one height for one structure and at another height for the other structure is like "comparing apples and oranges" (as Prof. Bartels would say), so it's important to analyze in this manner that puts each structure in comparable states.

The Point: Comparing two structures using corrugation.

Prerequisites: Optimized jobs of each structures with WAVECAR files and completed STS calculations  generated for both.

Notes: Although I discuss several ways of obtaining a simulated STM image, in this section, I describe everything in terms of using Jon's code because it outputs the necessary values that I want.

1. We want to use the same scale for each job. Using Jon's ExampleSTM code, we can generate a simulated STM image for one structure. For example, here I have an image of a 2H MoS2 structure on Cu(111). At a certain tip-sample distance, this will output three relevant values for you: scale, lowest point, and highest point. You can think of the difference between the latter two values as your image corrugation.
   
2. Repeat the same process for your second structure, in my case 1T MoS2 on Cu(111). Using the same scale value you just acquired, use this value instead when running "DispSTM" on your second structure. (Both simulated STM images should be generated with the same scale value.) This will move the tip to a location where it experiences a similar current/charge value from your system.
   
3. If you take the average of the corrugation values from each system, you can obtain the average height of each system using the following equation.
   
4. So now you can compare the heights and corrugations of each system at different tip height settings. Additionally, you can compare the difference that this makes in STS measurements. With Jon's ExampleIV Code, we can set the z values ourselves. Disregarding the offset we use in the above equation, we set the z value to be the height of the tip in the STM simulation. This requires the following change in the code.
   
5. Now you can form a table for comparing tip height vs. structure vs. STS (bandgap).

Optional: You may consider using a "more realistic" STM tip by applying median and Gaussian filters to the isosurface data. This involves delving into the molXML code and editing idxTable. Also, you may find that your corrugation and height values become weird at a certain distance away from the surface. I'm still trying to work out what this means, but according to Profesor Bartels, "maybe at the point of inflection (where the first deriv changes sign) we run out of the accuracy of our method".

Simulated STM

Quick Description of STM: Scanning Tunneling Microscopy (STM) functions via quantum tunneling. When two conductive materials are brought very close to each other (within a few angstroms), applying a bias voltage between the two materials will allow electrons to tunnel through the vacuum space between them. This flow of electrons is referred to as tunneling current and is dependent on three factors: the vacuum distance, the applied voltage, and the local density of states (LDOS). Because tunneling current exhibits an exponential relationship with distance, the tunneling signal is dominated by the current between the two closest atoms between the materials and thus exhibits atomic-scale resolution. For reduced noise, it is thus ideal to have an atomically sharped tip that scans of the sample of interest. Depending on the bias (positive or negative), electrons will either tunnel from sample to tip or from tip to sample. Functionally, a feedback system is used such that tip-sample distance (measured as height along the z-axis)is readjusted during scanning (a raster over x- and y- axes) of the sample to produce a constant current. In this manner, the topography of the sample is measured, thus enabling atomic-scale imaging of the sample.

The Point: Simulated STM creates an atomic scale image based off of computer-based model system. Generally, we can use simulated STM as a test device for evaluating the accuracy of the model. Should the model reproduce characteristic features displayed in experimental images, we are provided with some level of confirmation for the understanding of our sample system.

Prerequisites: An optimized model with a PARCHG file.

Notes: Traditionally, our lab uses much of the Mathematica code developed by Jon. We can also use VESTA to simply open the PARCHG file. Finally, there is also a nice program called HIVE that I link to at the end.

Mathematica:

1. Use the function chgData = ReadPARGHG[<filepath>] to read out the charge values 
2. Display the simulated STM with iso = DispIsoSurf[chgData, .1, SphereScale -> .2]
• adjust parameters as necessary
3. Use additional options to make the image more viewable. e.g...
• maxCell = cell[[1]] + cell[[2]] + cell[[3]];
• Show[ iso, PlotRange -> {{0, maxCell[[1]]}, {0, maxCell[[2]]},(*z-range:*){Surf[atoms] + .25, Surf[atoms] + 4}}, ImageSize -> 800 ]

VESTA (notes provided by Mark Micklich):

1. Open CHGCAR
2. Utilities > 2D Data Display
3. Press the "Slice" button and confirm "OK"

HIVE and HIVE tutorial (email Danny Vanpoucke for the program and manual):

"The HIVE-STM program is a small piece of software ...to generate STM images based on ... DFT-calculations. Starting from ab-initio VASP calculations, it uses the resulting output to allow the simulation of an STM experiment on your simulated model."

Tips and Tricks: Calculations find that the STM tip must preferably lie ~0.92-2 A away from the surface to image small features such as point defects. According to my random survey of scientists, it's normally about 4-7 A away from the surface where you get the best visualization. And in a scrap on information (from HIVE developer Danny Vanpoucke), you generally want the tip to stay within 15 A of the system. For more information on scanning conditions, you might check out here.