Photoemission response of 2D electron states

Highlights: • A Fourier-analysis based description to the photoemission process is presented. • Photon-energy dependent photoemission response of 2D electron states reflects Fourier composition and confinement of their wavefunctions. • Previous photoemission results on surface, quantum well and molecular orbital states are revisited in terms of wavefunction analysis. - Abstract: A lucid Fourier analysis based description of the photoemission process is presented that directly relates photon energy (hv) dependent ARPES response of two-dimensional (2D) electron states to their wavefunctions. The states formed by quantum confinement of bulk Bloch waves (including Shockley-Tamm type surface or interface states, and quantum well states) show periodic peaks of ARPES intensity as a function of hv. Amplitudes of these peaks reflect Fourier series of the oscillating Bloch-wave component of the wavefunction, and their broadening the spatial confinement of its envelope function. In contrast, the 2D states formed by local orbitals (dangling bonds and defects at the surface or interface) show aperiodic hv-dependence, where the rate of decay reflects localization of these states in the out-of-plane direction. This formalism sets up a straightforward methodology to access fundamental properties of different 2D states, as illustrated by analysis of previous photoemission experimental data including the paradigm Al(100) surface state, quantum-well states in multilayer graphene and at the buried GaAlN/GaN interface, and molecular orbitals.