Surface state capacity

As the Fermi level of the electrode approaches the surface state level of high state density, the surface state is charged or discharged as a capacitor. For convenience sake, we express the sum of a. and in Eqn. 5-86 as the surface state charge Qu and the capacity due to the surface state charge as the surface state capacity C.. Then, the interfadal capadty C is represented by the capadly of an equivalent drcuit shown in Fig. 5-60. 

The surface state capacity, Ch, is apparently zero in the range of potential where the Fermi level is located away from the surface state level (the state of band edge level pinning). As the Fermi level is pinned at the surface state, the capacity Ch increases to its maximum which is equivalent to the capacity Ch of the compact layer, because the surface state charging is equivalent to the compact layer charging in the state of Fermi level pinning. 

The surface state capacitance Css is different from the space charge layer capacitance Csc and the Helmholtz layer capacitance Ch in that there is in general no distance associated with the surface state capacity. 

Since the distance between the Fermi level E and the energy bands varies with (see Section 5.3) f is also changed. If Fp = Ft, the surface state is half-occupied (f = 0.5), as shown in Fig. 5.8. Since the charge depends on the potential across the space charge layer, a differential surface state capacity can be defined by... 

Fig. 5.8 Fermi function/and surface state capacity Qs vs. potential across the space charge layer A 0SC (theoretical curve)...

Electronic surface states may exist at the interface they give rise to an additional capacity, so that the band edges at the surface change their energies with respect to the solution. 

Fig. 5-60. Equivalent circuit for an interfacial electric double layer comprising a space charge layer, a surface state and a compact la3 er at semiconductor electrodes Csc = capacity of a space charge layer C = capacity of a surface state Ch = capacity of a compact layer An = resistance of charging and discharging the surface state.

We consider, now, an electron-depleted space charge layer that is gradually polarized in the anodic direction. As long as the Fermi level is located away from the surface state, the interfacial capacity is determined by the capacity of the depletion layer that obeys a Mott-Schottlsy relation as shown in Fig. 5-61. 

Fig. 5-61. Mott-Schottky plot of an n-type semiconductor electrode in presence of a surface state ib = flat band potential with the surface state fully vacant of positive charge Eft, - flat band potential with the surface state fully occupied by positive charge Q = maximum charge of the surface state e, = surface state level, s capacity of the surface state ( Ch ).

As the Fermi level reaches the surface state level, the interfacial capacity is determined by the capacity of the compact layer (the maximum capacity of the surface state) and remains constant in a range of potential where the Fermi level is pinned. A further increase in anodic polarization leads again to the capacity of the depletion layer in accordance with another Mott-Schottky plot parallel to the former plot as shown in Fig. 5-61. The flat band potential, which is obtained from the Mott-Schottlo plot, shifts in the anodic direction as a result of anodic charging of the siuface state. This shift of the flat band potential equals a change of potential of the compact layer, (Q /C = Q./Ch), due to the anodic charging of the surface state. 

At a semiconductor/solution interface, an n-type semiconductor (carrier density of 10 electrons cm A is in contact with a nonaqueous system using a redox system, i.e., no surface states. The capacity of this interface is 4 pF cm-2. Evaluate the potential differences within the semiconductor. (Bockris)... 

For the more accurate description of the Mott-Schottky dependences of semiconductor electrodes modified with small metal particles, it is reasonable to take into account the contribution of the capacity of electronic surface states (C ) induced by the... 

In all of this work there was little suggestion that the surface states of the palladium might behave differently from bulk states. Selwood (17) indicated that, from some sorption-magnetic susceptibility data for hydrogen sorbed on palladium which was finely dispersed on alumina gel, the ultimate sorption capacity was approximately at the ratio 2H/Pd. Trzebiatowsky and coworkers (25) deposited palladium on alumina gel in amounts ranging from 0.46 to 9.1% of gel weight. They found the palladium to be present in a normal crystal lattice structure, but its susceptibility was less than for the bulk metal. This suggested to the present authors that the first layer of palladium atoms laid down on the alumina gel underwent an interaction with the alumina, which has some of the properties of a semiconductor. Such behavior was definitely shown in this laboratory (22) in the studies on the sorption of NO by alumina gel. Much of this... 

On the basis of electrode kinetic data obtained in 1M NaOH for oxides in the range 0.1 < x < 0.5, van Buren et al. [77] concluded that the solid state electronic properties of these mixed oxies have no observable effect on the electron transfer kinetics and the oxides can be considered as pseudo-metallic from an electrochemical point of view. There are, however, several observations that make this conclusion questionable (a) Characterization data for the oxide electrode surfaces were not presented. In particular, the electrochemical real surface area (capacity, or BET) of the electrodes, and therefore comparison of apparent rate coefficients, are uncertain, (b) The... 

The position of energy bands at the surface of particles cannot be determined exactly, because capacity measurements are not possible. Their position can only be estimated by checking which reaction is possible. Frequently, methyl viologen (MV ) has been used as an electron acceptor which can accept an electron from the conduction bemd upon illumination, provided the conduction band is above the reduction potential of MV. The radical (MV formed in this reaction is usually spectroscopically [16] or electrochemically [180] analyzed. These methods, however, give a very rough estimate, because usually it is not known whether surface states are involved in the charge transfer process. 

FIGURE 1.10. An equivalent circuit for the electrical components at the semiconductor/electrolyte interface in the absence of an oxide. represents the resistance of the electrolyte Ch is the capacity of the Helmholtz double layer and Rf is the charge transfer resistance 0, and Ru are the capacitance and resistance associated with the space charge layer in the semiconductor C, and are the capacitance and resistance of the surface states. 

Concluding the above considerations we can state that the concept of global activity coefficients gives a simple method for assessing the adsorbent heterogeneity in the liquid - solid adsorption and can be useful for accepting the values of surface phase capacity. 

It should be mentioned that surface states were also formed on a =Ge-OH surface by dipping the electrode into a solution containing a small concentration (10 M) of Au, Ag or Cu ions, detected as an additional peak in the capacity curve or by surface recombination measurements [16, 24]. A density of surface states in the order of 10 cm" was determined. 

In the case of GaAs a change of the potential across the Helmholtz layer was observed upon anodic and cathodic prepolarization, which was interpreted in terms of hydroxyl and hydride surface layers, as for Ge (see Section 5.3.1) A linear Mott-Schottky dependence for an n-GaAs electrode was only found at sufficiently high scan rates after anodic or cathodic prepolarization as shown in Fig. 5.17 [40], It is worth mentioning that all reliable capacity measurements could be interpreted in terms of space charge capacities, i.e. additional capacities due to surface states were not found. 

If all surface states are occupied by electrons their density is given by A, = AQs/e (Eq. 5.35). Assuming a Helmholtz capacity of Ch 10F cm" one obtains /V, in the order of about lO cm 2 for a shift of ACfb = 0.2 V. It is interesting to note that the shift of the flatband potential occurs mostly at very low light intensities, and it saturates at higher light intensities because then all surface states are filled [45]. In Fig. 5.20 the shift of energy bands is indicated for some semiconductors. 

It is clear that the surface recombination velocity. sy can also be determined by photoluminescence decay measurements. One nice example (n-lnP) is given in Fig. 7.61. InP is a semiconductor which exhibits in contact with H2O a rather low surface recombination (i r < 500 cm s" , curve a). After the electrode had been dipped into a solution of CuSOy, Rosenwaks et al. found a considerably steeper decay (curves b-d) [83]. An excellent agreement between theoretical and experimental curves was obtained. Values of up to = 3.5 X 10 cm s were reported for the surface recombination velocity. The same authors showed by capacity measurements that an additional capacity due to surface states occurs simultaneously, as already discussed in Section 5.2.4. 

In order to estimate the effect of surface states on the potential distribution, we have to calculate their capacity Css =... 

The capacity measured is assumed to represent only the capacity of the space-charge region in the semiconductor and not to include, for example, the capacity of surface states, adsorption capacity, etc. In certain cases, this condition is satisfied, for example, on a zinc oxide electrode but more frequent is the situation where the contribution of the capacity of surface states is considerable. 

Finally, it should be noted that in many cases where < 0, is determined by the capacity method uncertainty arises, which is related to the frequency dependence of Mott-Schottky plots. (In particular, the frequency of the measuring current is increased in order to reduce the contribution of surface states to the capacity measured.) As the frequency varies, these plots, as well as the plots of the squared leakage resistance R vs. the potential (in the electrode equivalent circuit, R and C are connected in parallel), are deformed in either of two ways (see Figs. 6a and 6b). In most of the cases, only the slopes of these plots change but their intercepts on the potential axis remain unchanged and are the same for capacity and resistance plots (Fig. 6b). Sometimes, however, not only does the slope vary but the straight line shifts, as a whole, with respect to the potential axis, so that the intercept on this axis depends upon the frequency (Fig. 6a). 

Oxygen storage capacity is an internal parameter of three way catalysts, depending on the surface state both of the noble metals and of the ceria. For this reason, there is a close correlation between OSC of three way catalysts and their catalytic activity. However, the conversion vs OSC profiles depend on several factors... 

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