Non-topographic current contrast in scanning field emission microscopy.

In scanning field emission microscopy (SFEM), a tip (the source) is approached to few (or a few tens of) nanometres distance from a surface (the collector) and biased to field-emit electrons. In a previous study (Zanin et al. 2016 Proc. R. Soc. A 472, 20160475. (doi:10.1098/rspa.2016.0475)), the field-emitted current was found to change by approximately 1% at a monatomic surface step (approx. 200 pm thick). Here we prepare surface domains of adjacent different materials that, in some instances, have a topographic contrast smaller than 15 pm. Nevertheless, we observe a contrast in the field-emitted current as high as 10%. This non-topographic collector material dependence is a yet unexplored degree of freedom calling for a new understanding of the quantum mechanical tunnelling barrier at the source site that takes into account the properties of the material at the collector site.

Exact eigenstates of a nanometric paraboloidal emitter and field emission quantities.

The progress in field emission theory from its initial Fowler-Nordheim form is centred on the transmission coefficient. For the supply (of electrons) function one still uses the constant value due to a supply of plane-waves states. However, for emitting tips of apex radius of 1-5 nm this is highly questionable. To address this issue, we have solved the Schrödinger equation in a sharp paraboloidally shaped quantum box. The Schrödinger equation is separable in the rotationally parabolic coordinate system and we hence obtain the exact eigenstates of the system. Significant differences from the usual Cartesian geometry are obtained. (1) Both the normally incident and parallel electron fluxes are functions of the angle to the emitter axis and affect the emission angle. (2) The WKB approximation fails for this system. (3) The eigenfunctions of the nanoemitter form a continuum only in one dimension while complete discretization occurs in the other two directions. (4) The parallel electron velocity vanishes at the apex which may explain the recent spot-size measurements in near-field scanning electron microscopy. (5) Competing effects are found as the tip radius decreases to 1 nm: The electric field increases but the total supply function decreases so that possibly an optimum radius exists.

Beam spot diameter of the near-field scanning electron microscopy.

We have examined the beam spot diameter at the anode of the scanning electron microscopy (SEM) in the near-field mode as a function of the anode-tip distance d. The detector lateral resolution of this type of microscopy is approximately equal to this spot diameter. For our calculations we have simulated the apex region of the tip with an ellipsoid of revolution of radii R1 and R2 with R1>R2 as suggested by TEM images of the realistic tips. We have then solved the Laplace equation to obtain the electrostatic potential and to this we have added a spherical image potential. The calculated electrostatic field is highly asymmetric, being strong along the tip-axis and weakening quickly towards the sides. When a 3-dimensional WKB approximation is used to calculate the electron paths corresponding to such a potential, the latter are shown to bend significantly towards the vertical (tip-axis) direction producing a beam narrowing effect very similar to the beam narrowing effect we discovered for the traditional SEM case. When the values of R1, R2 are chosen from fittings to the TEM images of the tips used in the experiments, the beam spot diameter W at the anode (d=25 nm) varies from 12.5 nm to 9 nm depending on the fitted R1, R2. These values of W are considerably smaller than previously predicted by calculating solid angles of emission from spherical surfaces (41 nm) but also much closer to the detector lateral resolution (6-7 nm) obtained from differentiating the experimental current step. This trend continued at all other d examined. Furthermore the beam width W was found to decrease quickly with increasing sharpness S=R1/R2 of the tip and then saturate. W is also decreasing with decreasing R1, R2 with S kept constant. We deduce that the sharpness of the tip is important not only for creating high extraction fields but also for guaranteeing a very small beam spot diameter.