Large lattice distortions and size-dependent bandgap modulation in epitaxial halide perovskite nanowires

Metal-halide perovskites have been shown to be remarkable and promising optoelectronic materials. However, despite ongoing research from multiple perspectives, some fundamental questions regarding their optoelectronic properties remain controversial. One reason is the high-variance of data collected from, often unstable, polycrystalline thin films. Here we use ordered arrays of stable, single-crystal cesium lead bromide (CsPbBr3) nanowires grown by surface-guided chemical vapor deposition to study fundamental properties of these semiconductors in a one-dimensional model system. Specifically, we uncover the origin of an unusually large size-dependent luminescence emission spectral blue-shift. Using multiple spatially resolved spectroscopy techniques, we establish that bandgap modulation causes the emission shift, and by correlation with state-of-the-art electron microscopy methods, we reveal its origin in substantial and uniform lattice rotations due to heteroepitaxial strain and lattice relaxation. Understanding strain and its effect on the optoelectronic properties of these dynamic materials, from the atomic scale up, is essential to evaluate their performance limits and fundamentals of charge carrier dynamics.

PL and PLE measurements were conducted in a homebuilt microscope based on an inverted Olympus IX71 body. A supercontinuum light source (SuperK Extreme, NKT photonics) was used to provide the excitation for all measurements. To obtain a wide-field excitation spot, a defocusing lens was introduced to focus the excitation onto the back aperture of the objective (Olympus LucPlanFL 40X, NA=0.6). Rather than a dichroic mirror, we employed a so-called "spotted" mirror where a small region of aluminum is coated onto a larger glass substrate (not drawn to scale). As such, the excitation can be focused onto a small region in the excitation path where the collected emission can largely pass to be detected. This allowed for a broad excitation range to be used. At the position where the image is formed, we placed a variable slit such that narrow part of the image is passed to the camera (Princeton ProEM CCD). The excitation light reflected off the back surface of the sample is filtered out with a long pass filter which we can vary according to the excitation wavelength. Prior to reaching the camera, the image is passed through a transmission grating such that the image that passes through the narrow slit is maintained in the zero order diffraction, while the 1st order diffracted light spreads out laterally on the detector with a distance from the zero order based on photon energy. This effectively yields the spectrum of the light emitted at any point along the slit. Placing the wire parallel to the slit opening and adjusting its width to match the width of the wire, we obtain a spectrum at every point of the wire with a spatial resolution of ~500 nm and a spectral resolution of 2.1 nm. For PL excitation (PLE) measurements, we set the long-pass filter to pass only the tail of the emission while scanning the excitation between 450 nm -520 nm in 2 nm increments.
The reason for only passing the tail is to resolve the absorption onset in the PLE spectrum.
For PL emission measurements we used excitation at 458 nm and the long-pass filter set to capture the entire emission peak. Simply changing the filter, we were capable of comparing both PL emission and PL excitation of the same points in the same wire.
Supplementary Figure 5. Emission trend of tapered nanowires on sapphire. Peak energy of emission versus the height of 3 tapered nanowires grown on sapphire (wire 1-3). The trend has 2 distinctive regimes, a linear regime above ~100 nm and an exponential regime below ~100 nm. Source data are provided as a Source Data file.  Figure 7. CL spectroscopy on a single tapered surface-guided epitaxial CsPbBr3 nanowire (A) CL map: Each 100 nm 2 pixel represents a full CL spectrum (450-520 nm) and the integrated intensity of the emission peak generates the gray-scale contrast of the image. (B) A typical Gaussian fit that is done at each pixel. The extracted wavelength of the emission peak is displayed using a color scale (480-520 nm) to generate the emission peak wavelength map (C). The selected diffraction spots, and generated (B) in-plane and (C) out-of-plane relative reciprocal-lattice spacing map and the in-plane and out-of-plane relative reciprocal-lattice rotation map for the CsPbBr3 selected planes. The selected diffraction spots, and generated (D) in-plane and (E) out-of-plane relative reciprocal-lattice spacing map and the in-plane and outof-plane relative reciprocal-lattice rotation map for the sapphire selected planes taken as reference.
Scanning electron diffraction maps for 4 nanowires with heights between 34 nm and 219 nm.
Supplementary Figure 9. Nanobeam scanning electron diffraction (SED, or 4D-STEM) analysis overview of surface guided CsPbBr3 nanowires with large and small heights. For every nanowire cross-section (A-D) the corresponding relative reciprocal-lattice spacing map for in-plane (a) and out-of-plane (b) planes, and the corresponding relative reciprocal-lattice rotation map for in plane (c) and out-of-plane (d) planes.
Scanning electron diffraction line profiles for 4 nanowires with heights between 34 nm and 219 nm.
Supplementary Figure 10. Line profiles of (A) the lattice parameter evolution from bottom to apex and (B) lattice rotation across the nanowires extracted from the SED maps in Supplementary Figure 9. Source data are provided as a Source Data file. Source data are provided as a Source Data file.