Thermal emission, Schottky

When we apply 10 V to a typical 100-nm-thick organic layer, we need to watch for an unexpected high electric field (106 V/cm2), which enables us to induce carrier injection and SCLC. First, we turn our attention to the behavior of current injection from electrodes. We have two possible mechanisms to inject charge carriers Schottky thermal emission and the tunneling injection processes, both of which are based on the theory of inorganic semiconductors. The Schottky emission process is described by41... 

It is difficult to measure metal/polymer Schottky energy barriers smaller than about 0.5 eV using internal pholoemission. Small Schotiky energy barriers lead to thermal emission currents produced by the absorption of light in the metal which are difficult to separate from true photocurrents 134]. If the structure is cooled to try to improve this contrast, it is often found that the significant decrease in the electrical transport properties of the polymer [27 [ makes it difficult to measure the internal photoemission current. To overcome this limitation, internal photoemission and built-in potential measurements are combined to measure small Schottky energy barriers, as described below. 

Fig. 10. DLTS spectrum for a Schottky-barrier diode on n-type ( 7 x 1015 P/cm3) silicon after hydrogenation (150°C, 50 min). The emission rate window e0 corresponds to delay times of 0.5 and 2.5 ms. Each peak is labeled with the measured activation energy for thermal emission of electrons (Johnson et al., 1987a).

In the absence of a gate voltage, the hole carrier injection through the Schottky barrier formed at the interface between metallic electrodes and semiconducting SWCNTs is dominated by thermal emission at room temperature. Considering this effect, the vs characteristics are described by the analytical Equation [10.5] ... 

Schottky (1914) emission is governed by the Richardson-Schottky equation of thermal emission over the image-force barrier... 

Similarly, the field emitter can be adapted by reducing the work function. The practical device is called the Schottky field emission gun, but it is really a field-enhanced thermionic emitter. The sharp tip is coated with zirconium oxide. The field is reduced by flattening the tip and acts to reduce the potential barrier, but the electrons are thermally excited over the low barrier, not sucked through it. 

One of the techniques for measuring the work function of surfaces uses the thermal emission of electrons from the heated surface under study [4]. According to the Richardson-Schottky equation, the electron current density, I, depends on the surface temperature, T, and the work function, / ... 

Field emission is characterized by its temperature independence. Here meff is the effective mass of the carrier in the dielectric. The essential assumption of the Schottky model is that a carrier can gain sufficient thermal energy to cross the barrier that results from superposition of the external field and image charge potential. Neither tunnelling nor inelastic carrier scattering is taken into account. The following current characteristic is predicted for the Schottky junction ... 

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... 

However, experimental ]V curves often deviate from the ideal /scl- In these cases, the measured current /inj is injection limited caused by a nonohmic contact or poor surface morphology. When the MO interface is nonohmic, carrier injection can be described by the Richardson-Schottky model of thermionic emission the carriers are injected into organic solid only when they acquire sufficient thermal energy to overcome the Schottky barrier ((()), which is related to the organic ionization potential (/p), the electron affinity (AJ, the metal work function (O, ), and the vacuum level shift (A) [34,35]. Thus, the carrier injection efficiency (rj) can be calculated by the following equation ... 

Schottky barrier thermionic emission theory [48], contained in the term ns, solution parameters are dominating Eq. 6. The potential dependence, however, results from the thermal population increase of the surface electron concentration due to the upward shift of the Fermi level upon forward biasing. 

Known models describing emission-limited discharge differ in mechanisms responsible for the charge transfer from the surface into the bulk. Most often these mechanisms include Schottky emission, tunneling, and thermal activation fiom discrete traps (Abkowitz et al. 1995 Kressman et al. 1999 Sessler 1999). Publications that allow for the continuous spectrum of surface traps are relatively few in number (Watson 1990 Watson et al. 1991), although the need for such an approach is obvious due to the highly disordered nature of the polymer surface. 

We now turn attention to conditions at the electrodes. These play vital roles in establishing the pre-breakdown conditions in the liquid under high electric stress and in triggering the breakdown itself. It has been natural to invoke electron injection at the cathode as an important component since high fields will lower the potential barrier to electron transfer across the interface whether it occurs by a thermally activated or tunnelling process. However, employment of the Schottky formula for field-assisted thermionic emission or the Fowler-Nordheim one for tunnel emission which are appropriately applicable only for electron transfer to a vacuum is a much too simplified solution to the problem. 

---