Determination of 3D electrostatic field at an electron nano-emitter

Differential phase contrast in scanning transmission electron microscopy has been applied to image nanoscale electrostatic fields of a sharp tungsten electron emitter with an apex radius of about 20 nm and under field emission conditions. Assuming axial symmetry of the nano-emitter, we derived a method based on the inverse Abel transform to quantitatively reconstruct an axial slice of the 3D electrostatic field from a single projection measurement. The highest field strength of 2.92 V/nm is measured at the nano-emitter apex under the condition of a bias voltage of −140 V with respect to the grounded counter electrode located at about 650 nm from the apex, resulting in an emission current of more than 2 μA. The experimental results are compared with simulations based on a finite element numerical Maxwell equation solver. Quantitative agreement between experiment and simulation has been achieved.