Practical Electron Microscopy and Database

Geometrical Phase Analysis (GPA) has been a widely used technique for more than 15 years to analyze strain from high-resolution transmission electron microscopy (HRTEM) images. Originally designed for smaller specimens such as quantum dots, GPA relies on the precise sampling of atomic columns, which can be sensitive to specimen preparation issues like variations in thickness. However, the introduction of high-angle annular dark field scanning transmission electron microscopy (HAADF STEM) has made GPA more robust. HAADF STEM imaging is less affected by experimental conditions and preparation issues, offering a clearer view of atomic columns with improved stability.

The GPA technique involves taking a Fourier transform of the high-resolution image and selecting the relevant lattice planes, from which phase images are generated. From these phase images, deformation maps can be calculated for various strain components such as in-plane and out-of-plane deformations. By analyzing the Fourier transform of HAADF images, GPA algorithms can map strain with high precision over large fields of view, using both in-plane (e.g., ε_x) and out-of-plane (e.g., ε_z) deformation maps.

Unlike other methods, GPA provides easy access to both shear strain and rotation information from the same dataset, making it a versatile tool for strain analysis. The spatial resolution depends on the sampling of the atoms in the original image, with finer sampling providing higher accuracy in the resulting deformation maps. It is particularly useful for analyzing the strain in modern semiconductor devices, where precision and large-area analysis are required.

Despite its robustness, GPA is still sensitive to scan distortions and noise, particularly in large field-of-view scans or when using fast acquisition settings. However, recent improvements in electron microscope stability, HAADF detectors, and image processing have greatly enhanced the reliability and precision of GPA for semiconductor strain mapping.

The HAADF STEM image shown in Figure 0010 represents the spatial arrangement of atoms or periodic structures in the sample. The FFT (Fast Fourier Transform) map provides a frequency domain representation of the lattice. The FFT map reveals the periodicity and symmetry of the lattice by converting spatial information into frequency components. Peaks in the FFT map indicate dominant periodic features, and their positions and intensities reflect the underlying structural order and any distortions in the lattice. The Total GPA (Geometrical Phase Analysis) map combines phase gradients calculated in both the x- and y-directions to visualize the overall strain or deformation in the lattice. The GPA map quantifies local strain (or displacement gradients) in the lattice, making it a valuable tool for identifying strain fields, defects, or deformations in crystalline structures.

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