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Abstract Measuring local polar ordering is key to understanding ferroelectricity in thin films, especially for systems with small domains or significant disorder. Scanning nanobeam electron diffraction (NBED) provides an effective local probe of lattice parameters, local fields, polarization directions, and charge densities, which can be analyzed using a relatively low beam dose over large fields of view. However, quantitatively extracting the magnitudes and directions of polarization vectors from NBED remains challenging. Here, we use a cepstral approach, similar to a pair distribution function, to determine local polar displacements that drive ferroelectricity from NBED patterns. Because polar distortions generate asymmetry in the diffraction pattern intensity, we can efficiently recover the underlying displacements from the imaginary part of the cepstrum transform. We investigate the limits of this technique using analytical and simulated data and give experimental examples, achieving the order of 1.1 pm precision and mapping of polar displacements with nanometer resolution.
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The polarization difference and band offset between Al(Ga)N and GaN induce two-dimensional (2D) free carriers in Al(Ga)N/GaN heterojunctions without any chemical doping. A high-density 2D electron gas (2DEG), analogous to the recently discovered 2D hole gas in a metal-polar structure, is predicted in a N-polar pseudomorphic GaN/Al(Ga)N heterostructure on unstrained AlN. We report the observation of such 2DEGs in N-polar undoped pseudomorphic GaN/AlGaN heterostructures on single-crystal AlN substrates by molecular beam epitaxy. With a high electron density of ∼4.3 ×1013/cm2 that maintains down to cryogenic temperatures and a room temperature electron mobility of ∼450 cm2/V s, a sheet resistance as low as ∼320 Ω/◻ is achieved in a structure with an 8 nm GaN layer. These results indicate significant potential of AlN platform for future high-power RF electronics based on N-polar III-nitride high electron mobility transistors.