Searching for Nitrogen-Vacancy Centers in Diamond with Multislice Electron Ptychography

The advent of powerful quantum computers would bring about numerous advancements in quantum cryptography, artificial intelligence, and physics-based simulations. A limitation of quantum computers today is keeping states coherent across a large array of qubits. Nitrogen-vacancy centers (NV-centers) in diamond could be a solution to this problem because of their qubit properties and random formation within the diamond lattice [1]. Further development of devices based around NV-centers require the ability to precisely measure their location in three dimensions. Electron tomography already allows for 3D atomic resolution images; however, this technique requires multiple scans to be taken across a wide range of angles, which proves to be challenging experimentally and computationally [2]. Multislice electron ptychography allows for the possibility to acquire a 3D reconstruction of the sample with only one data set; thus, drastically reducing the experimental and computational complexity. The tradeoff is that the depth resolution of multislice ptychography is still on the order of a few nm [3]. Therefore, I will outline key experimental and algorithmic parameters to improve the depth resolution of multislice ptychographic reconstructions. For our model, we use density function theory to acquire the atomic coordinates of NV-centers within a diamond lattice (Figure 1.a.). This unit cell is sent through our multislice scattering software [4] to produce 4-dimensional–scanning transmission electron microscopy (4D-STEM) data sets. The analytical depth resolution, d, of these datasets are dependent on the electron wavelength, λ, and the convergence angle of the microscope, α, by the equation: d=λα2⁠. Larger beam energies—smaller λ—and convergence angles will both produce a sharper depth resolution. Thus, we ran multislice ptychographic reconstructions [3] while changing these parameters (Figure 1.c.). In addition to the microscope parameters, we also investigated the effect of varying the number of layers at fixed sample thickness in the multislice algorithm. Typically, the number of slices or layers that the multislice algorithm solves is chosen such that each slice is around 1 nm thick, which has led to the best reconstructions in the past. Since the number of pixels in our depth plots (Figure 1.d.) is directly correlated to the number of layers, we chose to use fifty 2.84 Å thick slices when adjusting the microscope parameters. For each set of parameters, we ran a ptychographic reconstruction and produced a depth plot as shown in Figure 2.a. We then calculated the full width half maximum (FWHM) of the peaks that appear along the columns of atoms in our depth profiles (Figure 2.b.) as a means of qualitatively finding the depth resolution; the smaller the FWHM, the more resolved a single layer of atoms would be within our sample. We observed the FWHM decreasing as we independently increased both the convergence angle and beam energies from 30 to 60 mrad and 200 to 300 keV, respectively. Thus, striving for the highest beam energy and convergence angle allowed by the experimental setup should result in the best depth resolution. Additionally, we found a decrease in the FWHM for reconstructions that used more layers in the reconstruction (Figure 2.d.). This is likely due to the fact that there are more pixels to capture the behavior. Moving forward, we will investigate other experimental parameters like the scan step size and defocus; as well as algorithmic parameters like the size of computing groups that are run in parallel and the regularization enforcement between layers. With a solid foundation on how these parameters affect the depth resolution in simulations, we will transition our focus to experimental data on NV-centers. Recent work in tilt-corrected electron ptychography achieved a resolution that is close to atomic scale with only 5 total tilt angles [5]. We also plan to test this technique on the NV-center diamond lattice and compare it to our single scan multislice algorithm. The ability to find dopants or vacancies in a 3D material would have important applications for other scientific work, such as superconductors and semi-conductors. a) Diamond lattice visualized using VESTA with locations of vacancies and nitrogen dopants specified. Nitrogen atoms and vacancies do not appear on every slice of the lattice. b) Simulated HAADF image from the 4D-STEM dataset acquired through py4dstem [6]. c) Multislice ptychographic reconstruction of the diamond dataset using fold-slice (parameters: 300 keV beam, 30 mrad convergence angle, and 50 layers). d) Depth plot located at the dashed dot line in figure 1.c.; plot units are angstroms for the x and y axis, and normalized phase for the color map. Scale bar = 4 Å a) Depth plot for diamond with convergence angle of 60 mrad. b) Line plot along the atoms’ columns represented by the white dashed dot line in figure 2.a. c) Plot for calculated values of the full width half maximum (FWHM) of the line plot in figure 2.b. for various parameters. d) FWHM values as a function of the number of layers in the ptychographic reconstruction.