High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography

Abstract

We present an efficient method of imaging 3D nanoscale lattice behavior and strain fields in crystalline materials with a new methodology -three dimensional Bragg projection ptychography (3DBPP). In this method, the 2D sample structure information encoded in a coherent high-angle Bragg peak measured at a fixed angle is combined with the real-space scanning probe positions to reconstruct the 3D sample structure. This work introduces an entirely new means of three dimensional structural imaging of nanoscale materials and eliminates the experimental complexities associated with rotating nanoscale samples. We present the framework for the method and demonstrate our approach with a numerical demonstration, an analytical derivation, and an experimental reconstruction of lattice distortions in a component of a nanoelectronic prototype device.Inversion methods provide a powerful alternative to traditional objective-lens-based microscopy. Techniques that numerically invert coherent diffraction patterns into real space images have provided substantial gains in resolution and sensitivity in certain optical, electron, and x-ray microscopy experiments, especially where image-forming lenses are inefficient or difficult to incorporate. The resulting images, formed by inverting reciprocal space diffraction patterns, contain quantitative information that encodes local physical parameters such as permittivity, density, and atomic displacement at sub-beam-size spatial resolutions.When implemented with hard x-rays, these coherent diffraction imaging (CDI) techniques have enhanced our understanding of the internal structure of nano-and meso-scale materials, especially in operating environments that are difficult to access with other probes. Furthermore, x-ray microscopy methods based on Bragg diffraction are of particular interest because the sensitivity of x-rays to crystalline distortions in materials can be leveraged to reveal the interplay between structure and properties without disturbing environmental boundary conditions. However, the routine application of inversion methods to coherent hard x-ray Bragg diffraction is still limited by stringent experimental requirements and long measurement times.Given the potential impact of non-destructive 3D structural microscopy and the limitations of current 3D Bragg coherent x-ray inversion methods, advances in Bragg phase retrieval methods that facilitate the rapid imaging of crystal lattice behavior in realistic environments are critically important. Here, we introduce a new coherent Bragg diffraction imaging approach, three dimensional Bragg projection ptychography (3DBPP), that provides such a capability. 3DBPP enables 3D image reconstruction from a series of 2D Bragg diffraction patterns measured at a single incident beam angle, thus forming a new mode of inversion-based 3D strain-sensitive imaging. As we discuss in this article, 3DBPP is a hybrid real / reciprocal space technique that takes advantage of the high angle of separation between the incident and diffracted beam in a Bra...

Using automatic differentiation as a general framework for ptychographic reconstruction

“…The detector records a set of two-dimensional (2D) coherent diffraction patterns at overlapping scan positions at one or more angles near the Bragg diffraction condition. The diffraction patterns are then used to reconstruct a three-dimensional (3D) strain-sensitive image of an extended crystalline sample [64]. An example experimental geometry with the exit beam at a 60 • angle to the incident beam direction is shown in fig.…”

“…To develop the maBPP forward model, we consider a 3D diffracting crystal volume O and an illumination volume P. The incident probe direction k i and the exit beam direction k f satisfy the Bragg diffraction condition when the scattering vector q = k f − k i coincides with some reciprocal lattice vector G hkl for the crystal. At the Bragg condition, if the probe volume interacts with the slice of the object indicated by the lateral shift operator S j , then the 2D exit wave ψ j is calculated as [64]…”

Nondestructive three-dimensional imaging of crystal strain and rotations in an extended bonded semiconductor heterostructure

“…In the future, it will be possible to take it fully into account with the use of the new formalism developed in Ref. [25].…”

Performance evaluation of Bragg coherent diffraction imaging

“…This unique capability to access displacement field in nanocrystals finds wide applications, especially in investigating morphology and displacement evolutions under varying external conditions, such as chemically derived stress [6][7][8], temperature introduced strain [9], dislocation propagation during crystal growth [10,11], laser pulse induced lattice dynamics [12,13], radiation damage on protein crystals [14,15], static pressure driven strain [16,17], lattice defects during battery charging [18][19][20], as well as ion-implantation-induced strains [21]. Bragg CDI has also been further developed to integrate with lateral scans for enlarged field of view [22][23][24][25][26][27][28].…”