Schottky-barrier model

The same term is sometimes used to describe the potential-distance relations in semiconductors with a low concentration of surface states (hence the term Schottky barrier model ). However, as can be understood by a reconsideration of the mechanism there (see Figs. 10.6 and 10.7), the so-called barrier is either used for the acceleration of electrons in p-type cathodes or the electrodiffusion of holes to the surface in n-type anodes. Nevertheless, the term barrier is still applied. 

The first step was the evolution away from the Schottky barrier model of photoelectrochemistry caused by the evidence from the late 1970s onward that the rate of photoelectrochemical reactions was heavily dependent on surface effects (Uosaki, 1981 Szklarczyk, 1983). This was followed by the use of both a photocathode and a photoanode in the same cell (Ohashi, 1977). Then the use of nonactive thin protective passive layers of oxides and sulfides allowed photoanodes to operate in potential regions in which they would otherwise have dissolved (Bockris and Uosaki, 1977). The final step was the introduction of electrocatalysis of both hydrogen and oxygen evolution by means of metal islets of appropriate catalytic power (Bockris and Szklarczyk, 1983). 

The overreliance on the Schottky barrier model for reactions involving adsorbed intermediates must be revised to take into account the high surface state concentration to which they often give rise. This position is emphasized in that the most obvious environmental use of photoelectrochemistry is in splitting water to produce clean hydrogen. 

Although the Schottky barrier model (negligible surface states) is applicable for some electrochemical reactions involving redox species and electrode reactions with no surface bonding of intermediate radicals, most practical, useful photoelectrochemical reactions involve significant numbers of surface states. Draw the potential-distance relations for the corresponding Helmholtz approximation (a) for a photocathode and (b) for a photoanode. (Bockris)... 

The most inaccurate assumption, especially at low band-bending, is undoubtedly the first. However, the mathematical derivation leading to eqns. (396) and (397) cannot be easily modified to take account of depletion-layer recombination owing to the way in which the depletion layer is considered. In order to develop the theory to take into account recombination in the depletion layer, it is necessary to solve explicitly the transport equation in the depletion layer as well as the bulk. If we persevere, for the moment, with the Schottky barrier model and we continue, for the moment, with the assumption that recombination does not occur in the depletion layer (x < VF) then the transport equations for x < VF, x > VF are... 

The hole transport equation in the depletion layer may, assuming a Schottky barrier model, be written... 

Diagrams of electron depletion for oxide grains and the resistance of contact between grains, (a) Space charge layer model, (b) double Schottky barrier model, (c) regional and volume depletion model, (d) surface conductive grains contact model. 

The double Schottky barrier model (Fig. 1.4(b)) also turned out to be completely misleading. It focused attention on the electron transport path running through the centers of contacting grains. In reality, however, there... 

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. 

Parker [55] studied the IN properties of MEH-PPV sandwiched between various low-and high work-function materials. He proposed a model for such photodiodes, where the charge carriers are transported in a rigid band model. Electrons and holes can tunnel into or leave the polymer when the applied field tilts the polymer bands so that the tunnel barriers can be overcome. It must be noted that a rigid band model is only appropriate for very low intrinsic carrier concentrations in MEH-PPV. Capacitance-voltage measurements for these devices indicated an upper limit for the dark carrier concentration of 1014 cm"3. Further measurements of the built in fields of MEH-PPV sandwiched between metal electrodes are in agreement with the results found by Parker. Electro absorption measurements [56, 57] showed that various metals did not introduce interface states in the single-particle gap of the polymer that pins the Schottky contact. Of course this does not imply that the metal and the polymer do not interact [58, 59] but these interactions do not pin the Schottky barrier. 

The R-X plot shows the most variation in the subthreshold region, while the G-B plot shows the most variation above threshold. One sees from the G-B plot that the high frequency response of the diode is independent of bias (>1 MHz). To fit the data, one models each material phase or interface as a parallel R-C combination. These combinations are then added in series, and an overall series resistance and series inductance are added. For the data in Figure 10.6, three R-C elements are used. One R-C element is associated with the Schottky barrier. Another is associated with the high frequency bias-independent arc, which we believe is associated with the capacitance of the alkoxy-PPV. The thinness of the film... 

If the space charge in the semiconductor arises from the ionization of impurities only, as in the model we have used, the surface barrier is termed a Schottky barrier. The barrier region near the surface of the crystal is sometimes called the exhaustion region, as the mobile electrons have been removed from this region (16). 

The promise of photoelectrochemical devices of both the photovoltaic and chemical producing variety has been discussed and reviewed extensively.Cl,, 3,4) The criteria that these cells must meet with respect to stability, band gap and flatband potential have been modeled effectively and in a systematic fashion. However, it is becomirg clear that though such models accurately describe the general features of the device, as in the case of solid state Schottky barrier solar cells, the detailed nature of the interfacial properties can play an overriding role in determining the device properties. Some of these interface properties and processes and their potential deleterious or beneficial effects on electrode performance will be discussed. 

In many PEC systems the chemical kinetics for the primary charge transfer process at the interface are not observed at the light intensities of interest for practical devices and the interface can be modeled as a Schottky barrier. This is true because the inherent overpotential, the energy difference between where minority carriers are trapped at the band edge and the location of the appropriate redox potential in the electrolyte, drives the reaction of interest. The Schottky barrier assumption breaks down near zero bias where the effects of interface states or surface recombination become more important.(13)... 

An important parameter is the ionization potential Ip. It is needed to model the energetics of p-doping, in which an electron is removed from the topmost valence levels (see Chapter 13), and also electrical contacts on CPs, in order to understand charge injection, and therefore Schottky barriers, field-effect transistors, and light-emitting diodes, which are studied in Section V. 

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