Schottky barrier thermionic emission

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. 

The results of several studies were interpreted by the Poole-Erenkel mechanism of field-assisted release of electrons from traps in the bulk of the oxide. In other studies, the Schottky mechanism of electron flow controlled by a thermionic emission over a field-lowered barrier at the counter electrode oxide interface was used to explain the conduction process. Some results suggested a space charge-limited conduction mechanism operates. The general lack of agreement between the results of various studies has been summari2ed (57). 

A polymer layer al a contact can enhance current How by serving as a transport layer. The transport layer could have an increased carrier mobility or a reduced Schottky barrier. For example, consider an electron-only device made from the two-polymer-layer structure in the top panel of Figure 11-13 but using an electron contact on the left with a 0.5 eV injection barrier and a hole contact on the right with a 1.2 cV injection barrier. For this case the electron current is contact limited and thermionic emission is the dominant injection mechanism for a bias less than about 20 V. The electron density near the electron injecting contact is therefore given by... 

The recombination current density, Jr, can be treated effectively as a Schottky barrier diode current density. Including both thermionic emission and diffusion charge transport mechanisms (13) Jr can be written as... 

Because the spacing between pores is always less than the width of the depletion layer and PS has a very high resistivity, Beale et al. proposed that the material in the PS is depleted of carriers and the presence of a depletion layer is responsible for current localization at pore tips where the field is intensified. This intensification of field is attributed to the small radius of curvature at the pore tips. For lowly doped p-Si the charge transfer is by thermionic emission and the small radius of curvature reduces the height of the Schottky barrier and thus increases the current density at the pore tips. For heavily doped materials the current flow inside the semiconductor is by a tunneling process and depends on the width of the depletion layer. In this case the small radius of curvature results in a decrease of the width of the depletion layer and increases the current density at pore tips. The initiation was considered to be associated with the surface inhomogeneities, which provide the initial localized high current density at small surface depressions. 

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... 

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] ... 

FIGURE 2.4.2 (a) Simple band line-up diagram for a metal-organic semiconductor interface assuming that the Mott-Schottky rule holds and that the vacuum levels for the metal and semiconductor are aligned, (b) Application of a positive bias to the metal can result in hole injection into the semiconductor by thermionic emission over the barrier, (c) Band line-up diagram in the case where an interface dipole is present, causing a shift (A) in the vacuum levels across the junction. 

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

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. 

Fig. 5. Thermionic emission plot for an annealed Pd/a-Si H Schottky barrier. The slope gives an effective barrier height of 0.97 eV. [From Thompson et al. (1981).]...

At this stage the critical issues regarding a-Si H Schottky barriers are addressed. The first is whether the forward-bias transport of undoped diodes is limited by diffusion or thermionic emission. This point may prove crucial to interpreting other experiments such as DLTS or frequency-dependent C- V to obtain gap-state densities. It seems from the experiments described to date, that well-prepared, well-characterized interfaces for at least some metals yield transport characteristics consistent with the thermionic emission theory. 

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 ... 

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. 

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] ... 

In practice it has been found that intimate contacts formed between metal films and crystalline semiconductors exhibit poor photovoltaic response. This is caused by the fact that the thermionic emission dark current at the Schottky barrier leads to significantly higher dark currents than is normally encountered in a homojunction or heterojunction structure. This problem, however, can be got round while still preserving the potential advantages of the Schottky barrier by allowing a very thin oxide or insulating layer to be formed between the semiconductor and the metal contact. The introduction of this layer leads to the ccxnmon form of Metal-Insulator-Semiconductor Schottky Barrier Solar Cell (MIS SBSC) with hich we are primarily concerned here. 

The forward bias dark current of a Schottky barrier diode has already been demonstrated to be caused by the thermionic emission of majority carriers from the semiconductor to the metal. It can be represented by the equation... 

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. 

To determine barrier heights and ideality factors for the nanodiodes, we fit the current-voltage curves of our devices to the thermionic emission equation. For thermionic emission over the barrier, the current density of Schottky contacts as a function of applied voltage is given by [69]. 

Riess and coworkers at the University of Bayreuth proposed a Schottky barrier model for the operation of ITO/PPV/Al LEDs [70,71,94]. They argue that the current is predominantly carried by holes and that this hole current is limited by the Schottky barrier formed at the PPV/Al interface rather than by any barrier at the ITO/ PPV interface. They model the current-voltage characteristics using the equation for thermionic emission across a Schottky barrier from a semiconductor into a metal. It should be noted that the doping levels estimated for these devices are in the range 10 -10 cm, considerably higher than the values estimated by Marks et al. for their devices. 

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