their optical and electrical properties. A common optical-based approach to estimate bandgaps of direct-gap semiconductors is to employ absorption spectroscopy. In this approach, one captures absorption spectra of materials and obtains absorption thresholds from Tauc plots. [3] The Tauc analysis provides a consistent way to compare among materials. However, as mentioned by Green et al., [4] these thresholds represent optical bandgaps, not electronic bandgaps, as the Tauc analysis underestimates the presence of excitonic transitions and broadening factors such as temperatures, defect densities, and material disorders. [4,5] Alternatively, one can capture the so-called band-to-band luminescence spectra from materials, which are results of radiative recombination between free electrons and holes in the conduction and valence bands, respectively. The peak wavelengths (or energies) of the luminescence spectra have been reported to be close to the absorption thresholds at room temperature by numerous authors [6][7][8][9][10] (also see Figure S1, Supporting Information). Thus, the two optical methods can be used to estimate the material optical bandgap although they often underestimate the true electronic bandgap. However, both of these approaches measure the spatially average optical bandgap over a certain area. Therefore, capturing spatially resolved optical bandgaps of the entire sample area requires point-by-point mapping in both X and Y directions, and thus it is time consuming and impractical for large-area device imaging or high-throughput production-line environments.In PV research and manufacturing, luminescence imaging, including both electroluminescence (EL) and photoluminescence (PL), is a mainstream characterization tool for crystalline silicon solar cells. [11][12][13][14][15][16][17] This camera-based method can provide fast diagnostics of PV materials and devices with micrometerscale spatial resolution. Recently, luminescence imaging has increased in significance for perovskite device and material characterization. Many works have extracted various device parameters of PSCs such as correlations between luminescence intensities and open-circuit voltages, [18][19][20] spatial distributions of nonradiative recombination centers, [21,22] series resistances from EL images, [23] and lateral inhomogeneities on each subcell in monolithic perovskite-silicon tandem structures. [24] It is also a powerful tool for monitoring long-term performance and A fast, nondestructive, camera-based method to capture optical bandgap images of perovskite solar cells (PSCs) with micrometer-scale spatial resolution is developed. This imaging technique utilizes well-defined and relatively symmetrical band-to-band luminescence spectra emitted from perovskite materials, whose spectral peak locations coincide with absorption thresholds and thus represent their optical bandgaps. The technique is employed to capture relative variations in optical bandgaps across various PSCs, and to resolve optical bandgap inhomogeneity within the same d...

Atomic force microscopy (AFM) probe with different functions can be used to measure the bonding force between atoms or molecules. In order to have accurate results, AFM cantilevers must be calibrated precisely before use. The AFM cantilever's spring constant is usually provided by the manufacturer, and it is calculated from simple equations or some other calibration methods. The spring constant may have some uncertainty, which may cause large errors in force measurement. In this paper, finite element analysis was used to obtain the deformation behavior of the AFM cantilever and to calculate its spring constant. The influence of prestress, ignored by other methods, is discussed in this paper. The variations of Young's modulus, Poisson's ratio, cantilever geometries, tilt angle, and the influence of image tip mass were evaluated to find their effects on the cantilever's characteristics. The results were compared with those obtained from other methods.

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Polarization-dependent hard X-ray excited optical luminescence (XEOL) was used to study not only the optical properties but also the crystallographic orientations of a non-polar a-plane ZnO wafer. In addition to a positive-edge jump and extra oscillations in the near-band-edge (NBE) XEOL yield, we observed a blue shift of the NBE emission peak that follows the polarization-dependent X-ray absorption near-edge structure (XANES) as the X-ray energy is tuned across the Zn K-edge. This NBE blue shift is caused by the larger X-ray absorption, generating higher free carriers to reduce the exciton-LO phonon coupling, which causes a decrease in the exciton activation energy. The extra oscillations in XANES and XEOL as the polarization is set parallel to the c-axis is attributed to simultaneous excitations of the Zn 4p - O 2pπ -bond along the c-axis and the bilayer σ-bond, whereas only the σ-bond is excited when the polarization is perpendicular to the c-axis. The polarization-dependent XEOL spectra can be used to determine the crystallographic orientations.