Invented by Erwin Wilhelm Muller in 1936, it became one of the first surface analysis techniques that approached near-atomic resolution. The microscope’s design is presented in Fig. 1. A Field Emission Microscope consists of a metallic sample in the form of a sharp tip and a conducting fluorescent screen enclosed in an ultrahigh vacuum. The sample is held at a large negative potential (1-10 keV) relative to the fluorescent screen. The tip curve radius is ~100 nm; thus, the electric field near the tip apex will have the strength of 10¹⁰ V/m, which is high enough for the field emission of electrons to take place. The electrons emitted from the tip travel along the field lines and produce bright and dark patches on the fluorescent screen, giving a one-to-one correspondence with the crystal planes of the hemispherical emitter. The emission current varies strongly with the local work function in accordance with the Fowler-Nordheim equation:



where — emission current density, F — electric field value, — work function, and b — parameters. Hence, the FEM image displays the projected work function map of the emitter surface. The closely packed faces ({110}, {211} and {100}) have higher work functions than atomically rough regions and thus they show up in the image as dark spots on the brighter background (see Fig. 2).

Linear magnifications of about 10⁵ to 10⁶ are attained. The spatial resolution of this technique is in the order of 2 nm and is limited by the momentum of the emitted electrons parallel to the tip surface, which is close to the maximum velocity (Fermi velocity) of the electron in metal.

Application of field emission microscopy is limited by the materials which can be fabricated in the shape of a sharp tip, can be treated in ultra-high vacuum environment, and can tolerate the high electrostatic fields.