Double layer semiconductor

Fig. 4.1 Structure of the electric double layer and electric potential distribution at (A) a metal-electrolyte solution interface, (B) a semiconductor-electrolyte solution interface and (C) an interface of two immiscible electrolyte solutions (ITIES) in the absence of specific adsorption. The region between the electrode and the outer Helmholtz plane (OHP, at the distance jc2 from the electrode) contains a layer of oriented solvent molecules while in the Verwey and Niessen model of ITIES (C) this layer is absent...

Electrical double layers are also characteristic of the semiconductor-electrolyte solution, solid electrolyte or insulator-electrolyte solution interface and for the interface between two immiscible electrolyte solutions (ITIES) (Section 4.5). 

The basic difference between metal-electrolyte and semiconductor-electrolyte interfaces lies primarily in the fact that the concentration of charge carriers is very low in semiconductors (see Section 2.4.1). For this reason and also because the permittivity of a semiconductor is limited, the semiconductor part of the electrical double layer at the semiconductor-electrolyte interface has a marked diffuse character with Debye lengths of the order of 10 4-10 6cm. This layer is termed the space charge region in solid-state physics. 

It should be noted that the study of the properties of an electrical double layer at semiconductor electrodes corresponds to study of the cell (in the simplest formulation)... 

The situation of the electric double layer at a semiconductor/electrolyte solution interface affected by light radiation will be dealt with in Section 5.10. 

Pleskov, Yu. V., Electric double layer on semiconductor electrode, CTE, 1, 291 (1980). 

For semiconductor electrodes and also for the interface between two immiscible electrolyte solutions (ITIES), the greatest part of the potential difference between the two phases is represented by the potentials of the diffuse electric layers in the two phases (see Eq. 4.5.18). The rate of the charge transfer across the compact part of the double layer then depends very little on the overall potential difference. The potential dependence of the charge transfer rate is connected with the change in concentration of the transferred species at the boundary resulting from the potentials in the diffuse layers (Eq. 4.3.5), which, of course, depend on the overall potential difference between the two phases. In the case of simple ion transfer across ITIES, the process is very rapid being, in fact, a sort of diffusion accompanied with a resolvation in the recipient phase. 

One possible solution is to obtain new experimental data, which is independent of co/pH curves. The zeta potential is of course a possibility, but it suffers from the intrinsic indeterminacy of the exact location in the double layer where it occurs. Another possibility is the surface potential, Vo, which will be defined below. Variations of Vo can be measured by using electrolyte/insulator/semiconductor structures. It has been shown by Bousse et al. (14) that the Vo/pH characteristics are determined mainly by the number of charged but uncomplexed surface sites, and are insensitive to complex-ation. This means that combined consideration of tro/pH and Vo/pH characteristics should lead to a more complete and reliable determination of model parameters. 

Although a family of OgS - Jig8 values are allowed under Equation 7 the actual equilibrium state of the oxide/solution interface will be determined by the dissociation of the surface groups and the properties of the electrolyte or the diffuse double layer near the surface. For surfaces that develop surface charges by different mechanisms such as for semiconductor, there will be an equation of state or charge-potential relationship that is analogous to Equation 7 which characterizes the electrical response of the surface. 

B , while for an n-type semiconductor the reverse is true. An analog to the SCR in the semiconductor is an extended layer of ions in the bulk of the electrolyte, which is present especially in the case of electrolytes of low concentration (typically below 0.1 rnolh1). This diffuse double layer is described by the Gouy-Chap-man model. The Stern model, a combination of the Helmholtz and the Gouy-Chapman models, was developed in order to find a realistic description of the electrolytic interface layer. 

Since the metal can be treated as a nearly perfect conductor, C is high compared with C, and cannot influence the value of the measured doublelayer capacitance. The role of the metal in the double layer structure was discussed by Rice, who suggested that the distribution of electrons inside the metal decides the properties of the double-layer. This concept was later used to describe double-layer properties at the semiconductor/electrolyte interface. As shown later, the electron density on the metal side of the interface can be changed under the influence of charged solution species (dipoles, ions). ... 

Fig. 6-99. An interfacial electric double layer on semiconductor electrodes a = charge of surface states 0.1 = interfadal charge of adsorbed ions IHP = inner Helmholtz plane.

Figure 5-41 illustrates the profile of electron level across the interfadal double layer of a semiconductor electrode (A) in the state of band edge level pinning and (B) in the state of Fermi level pinning. In Fig. 5-41 the cathodic polarization... 

Fig. 6-53. Interfadal charges, electron levels and electrostatic potential profile across an electric double layer with contact adsorption of dehydrated ions on semiconductor electrodes ogc = space charge o = charge of surface states = ionic charge due to contact adsorption dsc = thickness of space charge layer da = thickness of compact la3rer.

Fig. 5-56. Capacity Csc of a space charge layer and capacity Ch of a compact layer calculated for an n-type semiconductor electrode as a function of electrode potential Ct = total capacity of an interfadal double layer (1/Ct = 1/ Csc+ 1/Ch). [From Gerisdier, 1990.]...

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.

As shown in Fig. 9-9, the interfacial double layer of semiconductor electrode consists of a space charge layer with the potential of in the semiconductor and a compact layer with the potential of at the electrode interface. The potential 4+sc across the space charge layer controls the process of ionization of smface atoms (Eqn. 9-24) whereas, the potential across the compact layer controls the process of transfer of surface ions (Eqn. 9-33). The overvoltage iiac across the space charge layer and the overvoltage t b across the compact layer are eiq)ressed, respectively, in Eqn. 9-34 ... 

In the active state, the dissolution of metals proceeds through the anodic transfer of metal ions across the compact electric double layer at the interface between the bare metal and the aqueous solution. In the passive state, the formation of a thin passive oxide film causes the interfadal structure to change from a simple metal/solution interface to a three-phase structure composed of the metal/fUm interface, a thin film layer, and the film/solution interface [Sato, 1976, 1990]. The rate of metal dissolution in the passive state, then, is controlled by the transfer rate of metal ions across the film/solution interface (the dissolution rate of a passive semiconductor oxide film) this rate is a function of the potential across the film/solution interface. Since the potential across the film/solution interface is constant in the stationary state of the passive oxide film (in the state of band edge level pinning), the rate of the film dissolution is independent of the electrode potential in the range of potential of the passive state. In the transpassive state, however, the potential across the film/solution interface becomes dependent on the electrode potential (in the state of Fermi level pinning), and the dissolution of the thin transpassive film depends on the electrode potential as described in Sec. 11.4.2. 

Electrochemistry at Electrodes is concerned with the structure of electrical double layers and the characteristic of charge transfer reactions across the electrode/electrolyte interface. The purpose of this text is to integrate modem electrochemistry with semiconductor physics this approach provides a quantitative basis for understanding electrochemistiy at metal and semiconductor electrodes. 

The lure of new physical phenomena and new patterns of chemical reactivity has driven a tremendous surge in the study of nanoscale materials. This activity spans many areas of chemistry. In the specific field of electrochemistry, much of the activity has focused on several areas (a) electrocatalysis with nanoparticles (NPs) of metals supported on various substrates, for example, fuel-cell catalysts comprising Pt or Ag NPs supported on carbon [1,2], (b) the fundamental electrochemical behavior of NPs of noble metals, for example, quantized double-layer charging of thiol-capped Au NPs [3-5], (c) the electrochemical and photoelectrochemical behavior of semiconductor NPs [4, 6-8], and (d) biosensor applications of nanoparticles [9, 10]. These topics have received much attention, and relatively recent reviews of these areas are cited. Considerably less has been reported on the fundamental electrochemical behavior of electroactive NPs that do not fall within these categories. In particular, work is only beginning in the area of the electrochemistry of discrete, electroactive NPs. That is the topic of this review, which discusses the synthesis, interfacial immobilization and electrochemical behavior of electroactive NPs. The review is not intended to be an exhaustive treatment of the area, but rather to give a flavor of the types of systems that have been examined and the types of phenomena that can influence the electrochemical behavior of electroactive NPs. 

Examples of electroactive NP materials discussed in the review include Ti02, Mn02, iron oxides, other metal oxides, hydroxides and oxyhydroxides and Prussian Blue. We use the term electroactive N Ps to refer to the faradaic electroactivity in such materials and to distinguish them from NPs comprised of metals (such as Au, Ag, Pt, Co, etc.) or semiconductors (such as CdS, CdSe, etc.). This distinction is based on the ability of many electroactive NPs to undergo faradaic oxidation or reduction of all of the metal (redox) centers in the NP. This is in contrast to the behavior of many metal and semiconductor NPs for which oxidation or reduction is fundamentally an interfacial, double-layer process. This deflnition is somewhat arbitrary, since the smallest metal and semiconductor NPs behave molecularly, blurring the distinction... 

We observe that the sign of A

additional potential jump on the surface of the semiconductor due to the electric double layer, which arises on the surface in adsorption and figures as one of the terms in the experimentally measured work fimction. Such an electric double layer may be the result of the polarization of the chemisorbed particles (when the dipole moments of the chemisorbed particles are directed normally to the surface). This can be the case, for example, in weak chemisorption (when the total charge of the surface remains unchanged). 

Fig. 6.3 Schematic picture of the electrochemical potential ( > as a function of distance x in an oxide semiconductor electrolyte system a) bulk semiconductor potential b) solid/solution interface potential c) space charge potential d) flat band potential e) potential in the double layer (White, 1990, with permission.

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