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Photoelectron diffraction in the layer-resolved mode brings more detailed information about local atomic arrangement than is obtained in the standard mode. This is demonstrated in crystals with diamond and zinc-blende structures, both for unpolarized photon excitation as well as for circularly polarized excitation. The full angular distributions of photoemission intensities are evaluated for large atomic clusters representing ideally truncated surfaces of Si(0 0 1) and GaAs(0 0 1). Highly structured layer-resolved patterns enable a more detailed understanding of the standard mode outcomes. Photoelectron intensities from atomic layers placed at different depths under the crystal surface provide direct evidence about electron attenuation and its anisotropy in crystals.

Photoelectron diffraction was used to get polar plots of the low-energy photoemission intensities from AlAs monolayer buried 2, 3 and 4 GaAs monolayers below the GaAs(0 0 1)- c (4×4) reconstructed surface. Unexpected differences in polar plots of the layer-resolved, synchrotron radiation excited photoelectron emission from even and odd AlAs monolayers were observed experimentally and obtained theoretically. This 26 eV kinetic energy photoelectron emission is accompanied by electron attenuation anisotropy and a non-exponential intensity decay in the near-surface region. The importance of the top surface layer and its reconstruction is demonstrated by theoretical simulations. Enhanced contributions of photoelectrons from individual subsurface layers in specific directions offer a way to investigate the desired subsurface atomic layers.

We calculated photoemission spectra within the one-step model for the (001) surface of the (AlAs) 2 (GaAs) 2 superlattice structure. The purpose is to discriminate between spectral features which are caused by the surface, and those which are characteristic properties of the superlattice. Direct transitions indicate the opening of band gaps at the Brillouin zone edge, which are characteristic for the modified periodicity of the superlattice. Furthermore, the layer resolved photocurrent shows that one can also identify excitations from AlAs which are hidden below the first two GaAs layers and from As atoms at the boundary between the different semiconductors. Furthermore, emissions from surface states and resonances are also recognized.

Attenuation of the electron current determines surface sensitivity of electron spectroscopies. Pronounced energy and directional dependencies of the electron attenuation in crystals differ strongly from those commonly used for amorphous solids. Quantum descriptions of the electron attenuation can be obtained from the complex band structure of crystal surfaces at energies above the vacuum level. Contributions, specific for concrete processes, are obtained from theoretical description of photoelectron spectroscopy and of electron diffraction.

Electron spectroscopy at low kinetic energies, e.g., valence band photoemission with vacuum ultraviolet light, is sensitive to the fine structure of the electron damping, i.e., to the magnitude and energy dependence of the optical potential. The basis of this quantity is usually given by a semiquantitative analytical derivation together with empirical findings from the escape depth. Only recently the optical potential has been determined ab-initio via calculating the self-energy. Here, this approach is used to calculate the self-energy and from this the wave functions in the conduction band regime with scattering boundary conditions for the surface system. For the former, the GW approximation is applied. For the latter, algebraic solvers in the Laue representation have been used to solve the Schrodinger equation for arbitrary potentials. The wave function is investigated to extract physical quantities, like the angle and energy dependent escape depth, which are significant in discussing electron scattering.