Quantitative electric field mapping between electrically biased needles by scanning transmission electron microscopy and electron holography

Stray electric fields in free space generated by two biased gold needles have been quantified in comprehensive finite-element (FE) simulations, accompanied by first moment (FM) scanning TEM (STEM) and electron holography (EH) experiments. The projected electrostatic potential and electric field have been derived numerically under geometrical variations of the needle setup. In contrast to the FE simulation, application of an analytical model based on line charges yields a qualitative understanding. By experimentally probing the electric field employing FM STEM and EH under alike conditions, a discrepancy of about 60% became apparent initially. However, the EH setup suggests the reconstructed phase to be significantly affected by the perturbed reference wave effect, opposite to STEM where the field-free reference was recorded subsequently with unbiased needles in which possibly remaining electrostatic influences are regarded as being minor. In that respect, the observed discrepancy between FM imaging and EH is resolved after including the long-range potential landscape from FE simulations into the phase of the reference wave in EH.