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.