Strained Interfaces in TEM—Unlocking Material Information Through Dynamic Diffraction Analysis

The precise characterization of strained interfaces is essential for the continuous advancement of semiconductor nanodevices. Recent innovations, such as strain-induced polarization fields in gallium nitride (GaN), have yielded devices with higher carrier mobilities improving the performance of applications like fast-charging electronics. Transmission electron microscopy (TEM) is a powerful tool for investigating such nanoscale interfaces, as it offers sub-nanometer resolution, and it provides valuable information for measuring strain distribution.
When preparing a thin TEM lamella via focused ion beam (FIB), strain in the material, caused by lattice mismatch, inevitably partially relaxes at the free surfaces. This relaxation occurs because the removal of atoms relieves the mechanical stress, leading to localized lattice deformation both in the plane of the lamella and along the electron beam direction. These distortions significantly influence artifacts of multiple times elastic electron scattering, known as dynamic diffraction, which manifest as patterns within diffraction discs. Strain is normally measured as shift of diffraction disks relative to the zero beam in 4D-STEM by a method known as Center-of-Mass (COM). These patterns, however, hinder the precise evaluation of strain, particularly close to interfaces, by complicating precise detection of the diffraction discs center positions by COM. Since these patterns change continuously across the interface, conventional approaches often attempt to minimize the effects of dynamic diffraction, for example, by reducing the electron beam’s convergence angle (at the cost of spatial resolution) or by using precession electron diffraction to average over multiple beam tilts. However, these methods discard valuable phase information of the electron wave encoded in these patterns due to dynamic diffraction, especially along the beam direction.
Rather than mitigating dynamic diffraction effects, we take a different approach of utilizing them to directly reconstruct the displacement caused by strain relaxation. The first step in this process is to model the real sample accurately, going beyond idealized structures. This is achieved by solving the elasticity problem for a 84 nm thick Al_xGa_1-xN layer in GaN using finite-element method (FEM) calculations. The output from these simulations is then used as input for Bloch-wave based beam propagation simulations. Notably, since firstly the strain relaxation is dependent on the initial stress at the interface and secondly dynamic diffraction proved to be sufficiently sensitive to small variations in displacement, comparing these simulations with experimental data for a wide range of starting conditions allows us to infer material properties, such as the alloy composition x within the layer. To further support this effort, we are using a complimentary measurement of the local displacement, namely dark-field electron holography, as an interferometric measurement of the electron beam phase relative to that passing through a substrate region as reference. By comparing phase information from both 4D-STEM and holography with our calculations, we discuss the validity of the approximations and assumptions used in the simulations.