Thermionic emission model

The forward current at a semiconductor-metal junction is mainly determined by a majority carrier transfer i.e. electrons for n-type, as illustrated in Fig. 1 d. In this majority carrier device the socalled thermionic emission model is applied according to which all electrons reaching the surface are transferred to the metal. In this case we have ... 

The temperature dependence of J, measured by extrapolation of the forward J-V data, is shown is Fig. 9.3. The saturation current density is given in the thermionic emission model by... 

Since the electron transfer from the conduction band into the surface state (Eq. 67) can be very fast and the corresponding rate may be determined by the thermal velocity of electrons toward the surface, it has to be assumed that the initial chemical etching reaction (66) is even faster. However, it is not clear whether this assumption is correct. Very recently it has been found that also the reduction of protons (H2-formation) at n-GaAs is a very fast reaction. The current potential dependence can actually be described by the thermionic emission model (see Eq. (65)) [142]. This result indicates that the electron transfer can occur at much higher rates if the electron acceptor is adsorbed on the surface. This assumption is supported by recent results reported by Nozik [143]. He repeated his fluorescence decay measurements by using nitrobenzene as an electron acceptor and found a much lower rate than for ferrocence. Nozik assumed that the high rate constant for ferrocence may also be due to adsorption. 

It is evident from Eq. (94) that the maximum photovoltage depends critically on the exchange current Jo- In the case of pn-junctions, jo is determined by the injection and recombination (minority carrier device). Whereas in Schottky-type of cells jo can be derived from the thermionic emission model (majority carrier device). The analysis of solid state systems has shown that jo is always smaller for minority carrier devices [20,21]. Using semiconductor-liquid junctions, both types of cells can be realized. If in both processes, oxidation and reduction, minority carrier devices are involved, then jo is given by Eq. (37a), similarly as... 

We recently received a report of a very interesting study of photon-induced thermionic emission by Campbell, Ulmer, and Hertel [26]. They observed delayed ionization when Ceo molecules absorbed two to four 308-nm (4.03 eV) photons, and fit the results to a thermionic emission model. Although the experiments are quite different, and somewhat difficult to compare quantitatively, their conclusions regarding the temperature (or internal energy) dependence of Cso thermionic emission appear to be very similar to ours. 

The mechanism most often used to describe the electron transfer across a semiconductor-metal Schottky junction, is the thermionic emission model. The theory, derived by Bethe [27], is based on the assumptions that (1) the barrier height is larger than kT. (2) thermal equilibrium exists at the plane which determines emission, and (3) the net current does not affect this equilibrium [16]. Accordingly, the current flow depends only on the barrier height. Considering an n-type semiconductor, the current density from the semiconductor to the metal is given by the concentration of... 

Fig. 2.6 Electron transfer at the semiconductor-metal interface according to the thermionic emission model...

Quite a large number of systems have been studied and most of the current-voltage curves follow the thermionic emission model [12,16]. Frequently, there is some difference in the slope for example, instead of a theoretical slope of 60 mV per decade in current, slopes of 70-75 mV were found. This deviation may either be due to an image-force-induced lowering of the barrier or to tunneling through the space charge layer, as has been quantitatively studied for Au/Si barriers [28]. These two effects have been treated in detail by Sze [16]. 

Eq. (2.31) is identical to Eq. (2.18) derived for a majority carrier device (thermionic emission model). Accordingly, the same type of current-voltage curve is expected as that given in Fig. 2.7. The characteristics of the models occur only in the preexponential factors, which indeed are different in both cases (compare Eqs. 2.17 and 2.30). As mentioned before the jo of the majority carrier device is only determined by the barrier height and some physical constants (Eq. 2.19), whereas the y o of the minority carriers depends on material-specific quantities such as carrier density, diffusion constant and diffusion length. 

Typical room temperature current-voltage (Z-V) characteristics of Ni/Au SDs are plotted in Figure 6.13. As we can see, the saturation current decreases monotonously with increasing SiN.r deposition time from 0 (the control sample) to 5 min which means that the effective Schottky barrier height increased owing to shallow defect reduction. Meanwhile, the series resistance and ideality factor also decreased when longer SiN deposition times were used. Based on the thermionic emission model, the forward current density at V > 3kT/q has the form [11] ... 

This behavior cannot be explained in the framework of the commonly used diffusion-limited thermionic emission model [110], which takes into account back-scattering into the metal due to the small mean-free path in the organic semiconductor and predicts the activation energy of the contact resistance to be larger than that of the mobility and larger than... 

The Schottky barrier height can be calculated if the thermionic emission model is regarded as valid ... 

Under reverse bias, the FN tunnelling mechanism did not apply. On the other hand, the current-density was found to follow Richardson-Schottky thermionic emission model, where tunnelling through the barrier is ignored and field-induced barrier lowering is taken into consideration. The current density at a temperature T is given by [13] ... 

We would expect here that the low carrier mobilities present in the disordered polyacetylene, estimated to be about 10 cm /Vsec, should put the Schottky barriers formed with it in the regime of the diffusion-limited current. We can reasonably take as a value for / the distance between hops estimated from the bipolaron hopping model, equation 11. This is estimated to be 3 nm, so that the inequality is only satisfied at values of Emax in excess of lO V/cm. We note that similar conclusions are made for the analysis of the behaviour of Schottky barriers formed with amorphous silicon/hydrogen alloys [56], though there are claims that the thermionic emission model is effective in this case, in spite of the low carrier mobilities [63]. 

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