Grain Schottky barrier

The surface between grains is usually a region of increased electrical potential compared to the bulk, so that a barrier to conductivity occurs across the boundary. These grain boundary potentials are often called Schottky barriers. The height and form of the barrier depends sensitively upon the materials in contact. 

Figure 3.35 Formation of a Schottky (potential) barrier (a) isolated semiconductor and metal, (b) on contact a Schottky barrier is formed at the interface, and (c) Schottky barriers can also form between semiconducting grains separated by insulating layers.

There have been several proposed mechanisms for the operation of these sensors (Gopel, 1985 Franke et al., 2006). They all seem to converge on the existence and modulation of the Schottky barrier heterojunctions formed between the grains of the polycrystalline layer. They are equivalent to a chain of resistive elements connected in series. The density of surface states affects the depth of the Schottky barrier and depends on the interaction with the adsorbate (Fig. 8.8). The size of the grains apparently plays a major role. As the diameter of the grains decreases to below 5 nm, the space charge is smeared and the relative response of the sensor increases (Fig. 8.9). 

It is evident that the double layers at the grain boundaries constitute Schottky barriers which are similar in some respects to those formed in VDR resistors. In accord with this it is found that the resistivity-temperature relation of PTC material is voltage sensitive. The low-temperature resistivity may be reduced by a factor of 4 by an increase in applied field from 1 to 80kVm-1, and the ratio of maximum to minimum resistivities, above and below Tc, may be reduced from five to three orders of magnitude. 

Mark and Gora [24], commenting on the results, considered a model in which initiation is associated with a critical interface field at the Schottky-barrier contact between the metal electrode and the azide. Interface fields depend on properties of the sample and on the work function of the electrode, and are larger than the applied voltage divided by sample thickness. The model predicted an effect for uniform samples which was qualitatively consistent with experiment, but whose magnitude was too small to observe. However, the experimental samples were pressed pellets composed of individual grains which are likely to be separated by potential barriers [25,26]. Taking this into account, the model was consistent with experiment if initiation occurs at a critical interface field of about 2 X 10 V/m. This is a plausible value, in that fields in excess of 10 -10 V/m applied to surfaces of wide band-gap semiconductors commonly result in destructive breakdown due to carrier emission into the bulk from interface states [27-29]. 

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... 

Diagram representing how surface reactions are transduced into a measurable signal (qV3 is the height of the back to back Schottky barriers formed between the grains, qV is the height of the barrier formed at the interface between the electrode and the oxide). 

The microstructure of a ZnO varistor is the key to its operation. Grains of about 15-20 pm in diameter are separated by a Bi-rich intergranular film (IGF) that varies in thickness from 1 nm to 1 pm, as illustrated in Figure 14.38. Varistor action is a result of a depletion region formed on either side of the IGF. To explain varistor behavior we use an approach very similar to that used to describe Schottky barriers in metal-semiconductor junctions. 

Under the influence of deep acceptor states on grain boundary, the double Schottky barrier is generated as shown in Figure 2.1.2. According to Poisson s equation, its barrier height is given by... 

FIGURE 2.1.2 Band model of double Schottky barrier at grain boundary. 

The ZnO grains are n-type semiconductors. The intergranular traps are formed in this grain boundary due to the presence of Bi203 or PriOs and transition metal oxides, which cause the double Schottky barrier. 

When a voltage V is applied across the double Schottky barrier, the barrier height (j) decreases with increase of the voltage. A small fraction of electrons can penetrate the depletion region. These electrons, which are accelerated in the depletion region, can excite the valence electrons to conduction band. Therefore, holes recombine with the trapped electrons at the grain boundary, and decrease the barrier height. 

Guo, X., and Maier, J. (2001). Grain boundary blocking effect in zirconia a Schottky barrier analysis./. Electrochem Soc. 148 E121-E126. 

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