Momentum microscopy is a novel technique that was developed for detecting the k-distribution of an ensemble of charged particles in a parallel-imaging device. Fig. 2 illustrates the basic principle of such an instrument. Electrons emitted from the sample are accelerated by a strong electrostatic immersion field forming part of the cathode lens (the planar sample surface acting as cathode). The backfocal plane of the objective lens is the image plane for the reciprocal (or Fourier) image. The radial coordinate in this image is a linear measure for the transversal semagacestat momentum k∥ (parallel to the sample surface). Momentum microscopy aims at utmost resolution of this reciprocal image; recently, a resolution of 5×10−3Å−1 was demonstrated in an optimized momentum microscope . This value translates into the best angular resolution achieved by hemispherical analyzers. However, unlike for hemispherical analyzers, the momentum resolution stays practically constant with increasing start energy. This is a property of cathode lenses owing to the high extractor field strength.
Since k∥ is conserved when the electrons escape from the surface, the reciprocal image represents a map of the energy bands in momentum space in terms of the EB vs k∥ spectral function (EB binding energy). For 2D systems (surface states, adsorbate systems, layered materials) this yields the full k−k momentum information at fixed photon energy. For 3D bulk systems, the photon energy has to be scanned in order to obtain a full tomogram of the 3D bulk Brillouin zone. Characterized by ultimate k∥-resolution, simultaneous recording of a large momentum region and an energy resolution in the 10meV range, momentum microscopy establishes a new route towards angular-resolved PES (ARPES) with utmost detection efficiency.
For low start energies a momentum microscope detects the full half space above the sample surface simultaneously. The cutoff (“photoemission horizon”) is defined by =0.51(Ekin)1/2, with Ekin being the kinetic start energy (in eV) and the parallel momentum at the horizon (in Å−1). An exemplary discussion of the photoemission horizon can be found in . The existing low-energy instruments are designed for parallel imaging of a momentum range of diameter 6Å−1, comprising typically more than the first Brillouin zone. For higher start energies (up to several keV) the lens optics can be modified in order to accept a larger momentum range at the expense of momentum and energy resolution. The trajectories shown in Fig. 2 have been calculated for an optimized high-energy lens (indicated schematically) for a start energy of 5keV. The rays correspond to a 2D (k,k) momentum range of diameter 30Å−1, establishing an unprecedented detection efficiency in HAXPES.
Fig. 2 shows the cathode lens, i.e. the initial part of the electron-optical column which is the most crucial for the space–charge interaction. In a momentum microscope more lenses follow for zooming in, for electron-optical confinement of the desired source volume, for retardation and for switching between momentum- and real-space imaging (spectroscopic PEEM). Although being optimized for maximum k-resolution, these instruments have also a good performance in real-space imaging. In k-imaging mode the role of real-space and reciprocal images are reversed. The beam crossovers correspond to Gaussian images. For good k-resolution a small source area is selected by a variable field aperture, placed in an intermediate Gaussian image plane. The magnification in the first Gaussian image is about 14, hence the average electron density is two orders of magnitude lower than in the source volume at the sample surface. Thus the space–charge interaction is weaker in the crossovers as compared to the region just above the source volume at the sample. Hence we restrict our analysis to this most critical region.