edfas.org 5 ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 4 and diffraction pattern are then calculated. The modulus of the calculated diffraction pattern is then replaced with the square root of the experimentally measured data. An updated exit wave is back calculated and new values for O(r) and P(r) are determined using update functions. Each diffraction pattern is analyzed, and both the object and probe functions are updated at each step. A single cycle of the ePIE algorithm is complete once this process is conducted for all the diffraction patterns within the 4D dataset. This process is repeated until some convergence metric is satisfied. Upon convergence, the probe and object function are reconstructed. An example ptychographic result showing a reconstruction of the sample is shown in Fig. 2, Panel I, while examples of reconstructed probes can be viewed in references.[6,8] MEASURING THE PHASE SHIFT: PHASE CONTRAST IMAGING AND MORE The reconstructed transmission function quantifies the change in modulus and phase of the electron wave as it transmits through the sample. We will focus on the phase component of the reconstruction as it affords sev- eral benefits when compared to conventional STEM imaging modes. High angle annular dark field (HAADF) imaging is widely used because its incoherent character[14] makes image interpretation relatively straightforward and the signal intensity is sensitive to sample thickness and atomic number. However, HAADF-STEM lacks the necessary dynamic range to simultaneously image low and high atomic number elements, whereas ptychography can achieve this. For example, ptychography has been used to resolve both the anion and cation atomic columns in LaB6, [15] GaN,[16] and Li containing cathode materials.[17,18] This behavior is exemplified in Fig. 2, Panel I, where both the Ga and N atomic columns are observed in the phase image, while only the Ga atomic columns are observed in the HAADF image. Traditional phase contrast imaging modes (e.g., bright field) can also simultaneously resolve light and heavy atoms, but there can be ambiguities such as contrast reversals when interpreting the image, and Fig. 1 Panel I: A cartoon of a 2D array of probe positions where the area of illuminated specimen overlaps between each probe position. Panel II: A schematic of STEM with a thin sample using a defocused probe (a), a focused probe (b), on a thick sample (c), and the depiction of how a thick sample is modeled using the multislice algorithm. Panel III: A flowchart describing the iterative ePIE algorithm. Reproduced with permission from Maiden and Rodenburg.[8] (a) (b) (c)
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