Equation Fowler-Nordheim

The field-induced tunneling across a potential barrier can be described using the Fowler-Nordheim equation [79] ... 

However, the values for the current, which are obtained using the Fowler-Nordheim equation with the actual device parameters, are several orders of magnitude [81, 82) higher than the values for the measured current in real devices. 

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]. 

Field emission is the emission of electrons from a solid under an intense electric field, usually at ambient temperatures. It occurs by the quantum mechanical tunneling of electrons through a potential barrier (Fig. 13.1). This leads to an exponential dependence of emission current density J on the local electric field, as given by the Fowler Nordheim equation,... 

CO adsorbed Pd/Al Oj, 37 69-70 diffuse reflectance spectroscopy, 34 14 Fowler-Nordheim equation, 21 72 Fraction exposed, of total metal atoms definition, 36 72-73... 

Fig. 1.38. The Fowler Nordheim equation for field emission. The relevant dimensions are much smaller than the tip radius. Therefore, a one-dimensional model is adequate. Neglecting the image-force effect, the potential U(z) outside the metal surface is linear with respect to distance z- The relevant parameters are work function of the material, tj), and the field intensity near the surface, F.

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... 

According to the Fowler-Nordheim equation, Eq. (1.34), the field-emission current from electrons at energy j E below the vacuum level is proportional to... 

Differences in work function occur not only on different faces of a clean metal crystal, but result also from the presence of adsorbed films, or monolayers of gases. Since the work function appears to the (l -power in the exponent of the Fowler-Nordheim equation (Equation 4), changes in X of a few hundredths of an electron volt produce marked changes in emission. 

It should be pointed out here that large decreases in the pre-exponential term of the Fowler-Nordheim equation occur on oxygen adsorption, so that the slope of a log Z/F vs. 1/V plot should be used for determination of X- These decreases were also found by Muller (1) for oxygen and by the writer for hydrogen on tungsten. They may correspond, at least in part, to a decrease in effective emitting area, both micro- and macroscopically. 

The reasoning which led to these conclusions was as follows. From the photographs we deduce whiesh fraction of the total current comes from particular areas, such as the 111 plane, the 100 plane, the 100 region, and the 110 region. We then compute current densities for these areas for each photograph. These current densities are converted to electron work functions ip by means of the well-established Fowler-Nordheim equation. ... 

The current density-voltage relationship of a contact in which a thin layer of insulating oxide covers the metal and the selective layer is electronically conducting follows the Fowler-Nordheim equation, which describes the tunneling current at metal-insulator-metal junctions. 

Field emission results from tunneling of electrons from a metal into a vacuum under application of a strong electric field. The tunneling mechanism is described in the WKB approximation for emission from metal surfaces which leads to the well known Fowler-Nordheim equation ... 

The electron omission from the tip is described approximately by the Fowler-Nordheim equation s, which can be expressed in the form... 

The field emission current density jF is described by the Fowler-Nordheim equation [93,95] ... 

The Fowler-Nordheim equation describing the electron flux in terms of the electric field and the work function of the surface can be applied in two ways to the problem of determining the emission properties of the gas covered surface ... 

When a potential V is applied between a metal tip and a plate, a large electrical field E can be generated at the tip because of its small curvature E = V/r). Thus, for V = 10 volt and r = 10" cm (10 m), an electrical field of 10 volt/cm ( 10 V/m) can be obtained, large enough to cause field electron emission [13, 14, 19, 21, 30, 40-42]. The applied potential reduces the barrier height, which is represented by the work function in the absence of the electrical field, according to the Fowler-Nordheim equation... 

Based on Fowler-Nordheim equation which was later noted to break down for Xe/W(l 10) [80W2]. 

This drawback has led to a focus on cold-cathode sources, which operate by tuneling from a surface in the presence of a strong electric field. The current density obtained is given in this case by the Fowler-Nordheim equation ... 

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... 

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