Thermionic-Field Emission

Thermionic field emission in classical treatments is assumed to be associated with the intermediate temperature range and where the electrons tunnel from the semiconductor to the metal at an energy above the conduction band edge. The component of the current for the TFE process from the semiconductor to the metal for this form of current transport has been expressed by Stratton [13] and Padovani and Stratton [14] as 

The constants b, Cm. and are the Taylor expansion coefficients for the exponent of the transparency of the barrier around an energy The energy Em is chosen to satisfy CmkT=l (This would make term in Equation 8.15 /k7). 

If the ortension of the Fermi level into the conduction band q V is taken as positive, mt Pm and jin constants are defined as 

In the case of nondegenerate semiconductors, the sign of the qVn term would be reversed. The energy Em at which the electron emission takes place can be found using CmKT = 1 and Equation 8.17 and is given by 

An inspection of Equation 8.15 together with Equations 8.16-8.18 leads to the recognition that the current-voltage characteristics are dominated by the exponential factor, and neglecting the error function term in Equation 8.15, the forward current density due to TFE can be expressed as 

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The change in work function which accompanies adsorption on a metal surface may be determined directly by thermionic, field-emission, and photoelectric methods. Indirect methods rely on the measurement of a C.P.D. between a reference electrode and the original and covered surfaces, respectively. 

This decrease of work function W is relatively small at reasonable values of electric field E. The Schottky effect can result, however, in essential change of the thermionic current because of its strong exponential dependence on the work function in accordance with the Sommerfeld formula (2-100). Dependence of the Schottky W decrease and thermionic emission current density on electric field are illustrated in Table 2-12 together with corresponding data on field and thermionic field emission (Raizer, 1997). The 4x change of electric field results in 800 x increase of the thermionic current density. 

Fowler-Nordheim Formula and Thermionic Field Emission... 

Table 2-12. Current Densities of Thermionic, Field, and Thermionic Field Emissions at Different Eleetric Fields E...

Electric field, 10 V/cm Schottky decrease of ff, V Thermionic emission, j, A/cm Field emission j, A/cm Thermionic field emission, y, A/cm ... 

Because thermionic emission is based on the synergistic effect of temperature and electric field, these two key parameters of electron emission can be just reasonably high enough to provide a significant emission current. Results of calculations of the thermionic field emission are also presented in Table 2-12. The thermionic field emission dominates over other mechanisms at T = 3000 K and > 8 10 V/cm. We should note that at high temperatures but lower electric fields < 5- 10 V/cm, electrons of the third group usually dominate the emission. The Sommerfeld relation in this case includes the work function diminished by the Schottky effect. 

Arcs with hot cathode spots. If the cathode is made from lower-melting-point metals like copper, iron, silver, or mercury, the high temperatme required for emission caimot be sustained permanently. Electric current flows in this case through hot spots that appear, move fast, and disappear on the cathode surface. Current density in the spots is extremely high (10" -10 A/cm ), which leads to intensive but local and short heating and evaporation of the cathode material while the rest of the cathode actually stays cold. The mechanism of electron emission from the hot spots is thermionic field emission. Cathode spots appear not only on the low-melting-point cathodes but also on refractory metals at low currents and low pressures. 

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. 

Thermionic emission over the barrier and field emission, that is the tunnel effect through the barrier, are limiting cases. AU injection processes of electrons of energy between Ep and Ep-i- are termed thermionic field emission. These processes... 

Field emission and thermionic field emission tunneling through a Schottky barrier on an n-type semiconductor (a) forward bias and (b) reverse bias. 

Padovani, F. and Stratton, R., Field and thermionic-field emission in Schottky barriers . Solid State Electron, 1966,9,695-707. 

Crowell, C. and Rideout, V., Normalized thermionic-field emission in metal-semiconductor barriers . Solid State Electron, 1969,12,89-105. 

As in the case of forward bias, considering the electron emission from the semiconductor to the metal, the reverse current-voltage characteristics for the thermionic field emission can be expressed in terms of more familiar parameters as... 

In addition to thermionic emission, thermionic field emission, and field emission (tunneling) currents, other currents such as defect-assisted turmeling, which may have a quasiohmic nature, can be lumped into what is called the leakage current of more or less unknown origin that can be expressed as... 

J t is considered to be a fitting parameter that represents defects and inhomogeneities at the metal-semiconductor interface and is the semiconductor resistance introduced in Equation 8.9. In semiconductors with less than ideal interfaces, a tunneling barrier Eg may not be predicted, in which case it should be considered as another fitting parameter. In practice, the terms iteo and hfeo are also considered to be fitting parameters that represent the magnitude of the contributions to the current from thermionic emission and thermionic field emission, respectively. 

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