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 V_bi 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 V_bi 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.