Local Electronic Structure of Defects in GaN From Spatially Resolved Electron Energy-Loss Spectroscopy
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SPATIAL RESOLUTION IN EELS ON STEM The measurements in this paper were performed on a VG STEM HB501, a dedicated STEM with a cold field emission gun, operated at 100 kV. Several instrumental parameters determine the success of a spatially resolved EELS experiment on this microscope. These are most importantly the spatial resolution attainable and the energy resolution of the electron gun, the spectrometer and the detector. The attainable energy resolution is mainly limited by the gun and is close to 0.4 eV over the time of a typical experiment. The most obvious limit to the spatial resolution in an EELS experiment derives from the limited probe size attainable in a particular electron optical configuration. The competing effects of spherical aberration on one hand and diffraction and the initial virtual source size on the other must be balanced by finding those conditions which provide the optimum convergence angle to obtain the minimum probe size. The convergence angle is a function of the virtual objective aperture and the condenser excitation. The geometric broadening of the beam in the specimen in EELS is determined by the solid angle subtended by the collector aperture and is linear with specimen thickness. The resulting limit to the spatial resolution is then their product. In addition to theses effects, inelastic scattering is delocalised by a distance defined by the impact parameter. Even though more detailed calculations are available [1], a simple approximation [2] is sufficient for the present purpose. Fig. 1 shows the delocalisation expected in the present experiment. The electron beam was scanned across the edge of a GaN specimen into vacuum and energy-loss spectra were acquired during this process at regular intervals. The zero-loss peak was removed from the spectra and the energy-loss at which the inelastic intensity disappears for a given distance recorded. The value of the distance was adjusted for the probe size measured under the same experimental conditions by observing the change in the annular dark field signal while scanning across the edge of a carefully oriented MgO smoke cube. Assuming the contributions to the spatial resolution are gaussian it is possible to add the electron optical resolution, the aperture function and the impact parameter in quadrature. The resulting spatial resolution in the experimental configuration used here as a function of the STEM C, condenser current is given in Fig. 2 for two energy losses, in the low-loss region at the GaN band gap of 3.4 eV and for higher losses at the nitrogen K-edge at about 400 eV. The spatial resolution at low energy losses can be improved by collecting the EELS signal at a high momentum transfer [1]. This approach is not useful here since we are only interested in vertical interband transitions. 7
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