Fowler and Nordheim

While field ion microscopy has provided an effective means to visualize surface atoms and adsorbates, field emission is the preferred technique for measurement of the energetic properties of the surface. The effect of an applied field on the rate of electron emission was described by Fowler and Nordheim [65] and is shown schematically in Fig. Vlll 5. In the absence of a field, a barrier corresponding to the thermionic work function, prevents electrons from escaping from the Fermi level. An applied field, reduces this barrier to 4> - F, where the potential V decreases linearly with distance according to V = xF. Quantum-mechanical tunneling is now possible through this finite barrier, and the solufion for an electron in a finite potential box gives... 

Eq. (1.34) is the simplified version of the Fowler-Nordheim equation. In the original Fowler-Nordheim equation, there is an algebraic prefactor to the exponential factor. Experimentally, the exponential factor always dominates the functional dependence, leaving the existence and the specific form of the algebraic factor hardly distinguishable (see Fowler and Nordheim, 1928 Good and Muller, 1956). In practical units (work function cj> in eV, and the field intensity F in V/A), Eq. (1.34) becomes... 

The phenomenon of electron emission under the action of a strong external electric field on a metal has been known since the end of the 19th century. By the early 1920s this phenomenon had been comparatively well studied experimentally. The main features of cold emission have been theoretically explained by Fowler and Nordheim [31] on the basis of the ideas of electron tunneling. 

A second injection process is the tunnel effect at the Fermi energy of the metal (Fig. 8.24). It is also termed the field effect. For a triangular barrier <1> , the tunnel current density has been calculated by Fowler and Nordheim [32] ... 

Eield emission (EE) (also known as field electron emission or electron field emission) is the emission of electrons from a solid surface into vacuum induced by an electrostatic field. FE was first explained by quantum tunneling of electrons in the late 1920s [1], and the theory of FE from bulk metals was proposed by Fowler and Nordheim [2]. A family of approximate equations, called Fowler-Nordheim equations (F-N equations), are named in their honor and have been shown in terms of experimentally measured quantities as... 

Fowler and Nordheim showed that if the applied field is high enough, the work function is decreased even more and the potential barrier becomes so narrow that quantum mechanical tunneling can occur. The current-field dependence is represented by the relation... 

RH Fowler and L Nordheim, Electron emission in intense electric fields, Proc. R. Soc. Lond., 119 173-181, 1928. 

Th.e refinements of the theory, which have been worked out in particular by Houston, Bloch, Peierls, Nordheim, Fowler and Brillouin, have two main objects. In the first place, the picture of perfectly free electrons at a constant potential is certainly far too rough. There will be binding forces between the residual ions and the conduction electrons we must elaborate the theory sufficiently to make it possible to deduce the number of electrons taking part in the process of conduction, and the change in this number with temperature, from the properties of the atoms of the substance. In principle this involves a very complicated problem in quantum mechanics, since an electron is not in this case bound to a definite atom, but to the totality of the atomic residues, which form a regular crystal lattice. The potential of these residues is a space-periodic function (fig. 10), and the problem comes to this— to solve Schrodinger s wave equation for a periodic poten-tial field of this kind. That can be done by various approximate methods. One thing is clear if an electron... 

Fowler RH, Nordheim L, Electron emission in intense electric fields. Proceedings of the Royal Society A Mathematical, Physical and Engineering Sciences, 1928.119(781) 173-181. 

For the same the single layer devices based on Alq3, Peyghambarian et al. [83] found that the 1/V characteristics can also be described by an SCL current flow in the low cu ire lit regime. However, in the low current regime the 1/V characteristics can be qualitatively modeled by the Fowler-Nordheim equation (even if, quantitatively, the real device current differs from the calculated by seven orders of magnitude) [83] and thermionic emission ]78]. 

---