  Three-dimensional (3D) electronic band structure is fundamental for
understanding a vast diversity of physical phenomena in solid-state systems,
including topological phases, interlayer interactions in van der Waals
materials, dimensionality-driven phase transitions, etc. Interpretation of
ARPES data in terms of 3D electron dispersions is commonly based on the
free-electron approximation for the photoemission final states. Our soft-X-ray
ARPES data on Ag metal reveals, however, that even at high excitation energies
the final states can be a way more complex, incorporating several Bloch waves
with different out-of-plane momenta. Such multiband final states manifest
themselves as a complex structure and excessive broadening of the spectral
peaks from 3D electron states. We analyse the origins of this phenomenon, and
trace it to other materials such as Si and GaN. Our findings are essential for
accurate determination of the 3D band structure over a wide range of materials
and excitation energies in the ARPES experiment.
