Field-electron emission tunneling

Figure 7 Principle of field electron emission spectroscopy, (a) Electrons in a free electron solid occupy states of surface density N(E) (i), tunnel through a triangular barrier (ii), to yield a TED spectrum (iii), and R(E) of unity (iv). (b) The enhanced density of occupied states lying AE below Fermi level Ef (i), produced by the broadened level of adatom A (ii), leads to change in the TED (iii), and a resultant peak in R(E) at AE below Ef (iv)...

Field Electron Emission Field Ionization Electron Tunneling... 

Tunneling is a ubiquitous phenomenon. It is observed in biological systems (1), and in electrochemical cells (2). Alpha particle disintegration (3), the Stark effect (4), superconductivity in thin films (5), field-electron emission (6), and field-ionization (7) are tunneling phenomena. Even the disappearance of a black hole (or the fate of a multi-dimensional universe) may depend on tunneling, but on a cosmological scale (S-9). 

The central problem in the study of ionic conduction is to discover the details of the atomic transport processes involved in the growth of films. This will be discussed in the first part of this review. The electronic conductivity is of considerable theoretical interest and is of great practical importance for microelectronic devices. We discuss the system in which a thin metal counterelectrode replaces the electrolyte solution in which the oxide was made. Thermionic and field assisted emission, tunneling processes, impurity band conduction, and space-charge limited currents, have to be considered. We shall draw on results for oxide films made by other processes, such as evaporation and thermally promoted reaction with oxygen. 

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... 

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... 

Specimens for field emission sources are of a very fine needle shape, usually in the form of tungsten wire with a tip radius of <0.1 pm (Figure 5.4). Application of a potential of lkV thus generates a field of 106V/m which lowers the work function barrier sufficiently for electrons to tunnel out of the tungsten. FEG electron microscopes usually employ a gun potential of 3-4 keV. 

In the absence of an external field, electrons in the metal are confronted by a semi-infinite potential barrier (upper solid line in Fig. la), so that escape is possible only over the barrier. The process of thermionic emission consists of boiling electrons out of the Fermi sea with kinetic energy > x + M- The presence of a field F volts/cm. at and near the surface modifies the barrier as shown. It follows from elementary electrostatics that the potential V will not be noticed by electrons sufficiently far in the interior of the metal. However, electrons approaching the surface are now confronted by a finite potential barrier, so that tunneling can occur for sufficiently low and thin barriers. 

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. 

When the applied biases exceed the tunneling barrier height Ob, then cold-electron emission through a trapezoidal barrier can also occur from the electrode with greater surface roughness (e.g., the top electrode). This "field" emission is described by the Fowler30 -Nordheim3 [18] equation ... 

Methods of work function measurement are of two types, electron emission methods and condenser methods. In the former method heating, irradiation with light of a suitable wavelength or application of sufficiently strong electrical fields is used to cause electrons to tunnel through the surface potential barrier. The latter method consists of measuring the contact potential difference between the surface under study and a reference electrode. 

Electric-field-induced electron emission or tunneling and ionization of atoms at sharp tips are used to image surface atoms. 

Several possible current transport mechanisms are illustrated in Fig. 3. The schematic represents a Schottky barrier on an undoped sample under forward bias. The three arrows for electron transport are drawn for comparison with crystalline semiconductors in which thermionic emission, tunneling via thermionic field emission, or field emission represent the usual mechanisms. 

A field emission source uses a needle-like tungsten or carbon tip as the cathode, shown in Fig. 14.28. The tip is only nanometers wide, resulting in a very high electric field at the tip. Electrons can tunnel out of the tip with no input of thermal energy, resulting in an extremely narrow beam of electrons. Electron beams from heated filaments have a focal (cross-over) diameter of about 50 p,m while a field emission source has a crossover diameter of only about 10 nm. Field emission sources can serve as probes of surfaces at the nanometer scale (an Auger nanoprobe). 

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