  Characterizing long-range electric fields and built-in potentials in
functional materials at nano- to micrometer scales is of supreme importance for
optimizing devices. E.g., the functionality of semiconductor heterostructures
or battery materials is determined by the electric fields established at
interfaces which can also vary spatially. In this study, we propose
momentum-resolved four-dimensional scanning transmission electron microscopy
(4D-STEM) for the quantification of these potentials and show the optimization
steps required to reach quantitative agreement with simulations for the GaAs /
AlAs hetero-junction model system. Using STEM the differences in the mean inner
potentials (DELTA MIP) of two materials forming an interface and resulting
dynamic diffraction effects have to be considered. We show that the measurement
quality is significantly improved by precession, energy filtering and a
non-zone-axis alignment of the specimen. Complementary simulations yielding a
DELTA MIP of 1.3 V confirm that the potential drop due to charge transfer at
the intrinsic interface is about 0.1 V, in agreement with experimental and
theoretical values found in literture. These results show the feasibility of
accurately measuring built-in potentials across hetero-interfaces of real
device structures and its promising application for more complex interfaces of
other polycrystalline materials on the nanometer scale.
