Impact of beam size and diffraction effects in the measurement of long-range electric fields in crystalline samples via 4DSTEM.

Measuring long-range electric fields by 4-dimensional scanning transmission electron microscopy (4DSTEM) is on the verge to becoming an established method, though quantifying and understanding all underlying processes remains a challenge. To gain further insight into these processes, experimental studies employing the center-of-mass (COM) method of the model system of a GaAs p-n junction are carried out in which three ranges of the semi-convergence angle α are identified, with an intermediate one where measuring the built-in potential Vbi is not feasible. STEM multislice simulations including both atomic and nm-scale fields prove that this intermediate range begins once diffraction disks start overlapping with the undiffracted beam. The range ends when the diffraction disks' intensities become so low that they do not affect the measurement significantly anymore and when high-intensity diffractions overlap the center disk completely. From simulations without influence of atoms it is concluded that measuring Vbi has advantages over measuring the electric-field strength, as the potential difference does neither show a significant dependence on the beam size, nor on the specimen thickness.

Measuring Spatially-Resolved Potential Drops at Semiconductor Hetero-Interfaces Using 4D-STEM.

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 hetero-structures or battery materials is determined by the electric fields established at interfaces which can also vary spatially. In this study, momentum-resolved four-dimensional scanning transmission electron microscopy (4D-STEM) is proposed for the quantification of these potentials and the optimization steps required to reach quantitative agreement with simulations for the GaAs/AlAs hetero-junction model system are shown. Using STEM the differences in the mean inner potentials (∆MIP) of two materials forming an interface and resulting dynamic diffraction effects have to be considered. This study shows that the measurement quality is significantly improved by precession, energy filtering and a off-zone-axis alignment of the specimen. Complementary simulations yielding a ∆MIP of 1.3 V confirm that the potential drop due to charge transfer at the intrinsic interface is ≈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.