Semiconductor-electrolyte contact

In electrochemistry the semiconductor (phase I) is connected to an electrolyte (phase II). In equilibrium the electrochemical potential for the electrons in both phases must be equal. The electrochemical potential of the electrons in the semiconductor is equal to the Fermi energy. 

Application of an external potential mainly changes the potential gradient in the space-charge layer while the surface potential and the band position at the surface remain nearly constant. This is called band pinning. The band bending changes with the potential. 

---

The current-voltage (I-V) characteristic of a semiconductor-electrolyte contact is determined by both the semiconducting nature of the electrode, as well as by the ionic and molecular species present in the electrolyte. The current density at the electrode for a certain potential is limited by the reaction kinetic at the interface, or by the charge supply from the electrode or the electrolyte. 

Gerischer H (1991) Electron transfer kinetics of redox reactions at semiconductor/electrolyte contact a new approach. J Phys Chem... 

The situation where the excess electric charge in the bulk of the semiconductor is zero has a particular importance because this can often be obtained experimentally. This state is called flat band situation and the respective electrode potential, flat band potential because in the absence of electric fields inside the semiconductor the position of the band edge energies runs flat from the interior to the surface 20>. This energy pattern at the semiconductor-electrolyte contact is shown in Fig. 10 for the flat band situation, i. e. an anodic and a cathodic... 

Tiit t/fb can be determined experimentally by measurements of the differential capacitance of the semiconductor/electrolyte contact. The spact charge, >s, per unit area is given by... 

Figure 1. Geometric parameters characterizing the semiconductor-electrolyte contact...

The electronic properties of semiconductors junctions are strongly dependent on their interfaces. This is especially true for semiconductor/electrolyte contacts as in photoelectrochemical solar cells, for which a variety of possible reactants must be considered. 

The semiconductor/electrolyte contact has been extensively investigated since the 1970s. A recent review [32] and text books [33, 34] furnish details of the theory and applications of semiconductor electrodes. Below are given only some elements necessary for the discussion. Phenomenologically the liquid junction behaves more or less like a solid-state Schottky diode, with the electrolyte playing the role of the metal layer. 

The properties of the semiconductor/electrolyte contact are illustrated in Fig. 2(a) for an n-type semiconductor. The space-charge region develops as the potential is made more positive than the flat-band potential and its width, W, is given by the expression... 

Figure 2.21 shows a schematic of the setup for simultaneous measurement of the stationary light-induced excess minority carrier microwave reflectivity and the photocurrent at the semiconductor-electrolyte contact. The sample is illuminated from the front side and photoelectrochemistry is performed using the standard... 

Figure 9.2 Potential gradient and band bending in the double layer of a semiconductor-electrolyte contact. (A) n-Semiconductor and (B) p-semiconductor.

Another characteristic electrochemical property of a semiconductor/electrolyte contact is the double-layer capacitance, which is an approximation of the space-charge capacitance (Chapter 4). The space-charge capacitance can be determined by impedance measurements. If no current flows in the depletion region, the impedance is given by the reciprocal value of the space-charge capacitance. For other conditions the capacitance can be calculated from the complex impedance measurements. How to measure the impedance and to evaluate the data was described in Chapter 4 as well as the influence of diffusion processes in Chapter 5. 

Under conditions of electron accumulation, the interfacial capacitance C of a semiconductor/electrolyte contact tends to that of the Helmholtz layer (see Sect. 2.1.3.1 with Csc > Ch)- The width of the interfacial double layer is reduced to about 0.5 nm hence, it follows the internal surface of a porous electrode. As a result, the overall interfacial capacitance of a nanoporous system can be huge, being determined by the product of the total internal surface area of the system and the Helmholtz-capacitance per unit geometric surface area [148,149]. 

Often, the exponential dependence of the dark current at semiconductor-electrolyte contacts is interpreted as Tafel behavior [49], since the Tafel approximation of the Butler-Volmer equation [50] also shows an exponential increase of the current with applied potential. One should, however, be aware of the fundamental differences of the situation at the metal-electrolyte versus the semiconductor-electrolyte contact. In the former, applied potentials result in an energetic change of the activated complex [51] that resides between the metal surface and the outer Helmholtz plane. The supply of electrons from the Fermi level of the metal is not the limiting factor rather, the exponential behavior results from the Arrhenius-type voltage dependence of the reaction rate that contains the Gibbs free energy in the expraient It is therefore somewhat misleading to refer to Tafel behavior at semiconductor-electrolyte contacts. 

In a model that considers the situation at the semiconductor-electrolyte contact, the charge transfer rate and the surface recombination velocity have to be included [59]. In such a model, the currents related to charge transfer and to surface recombination are expressed by the excess carrier concentration at the surface (x = 0) according to... 

Semiconductor-Liquid Junction From Fundamen- semiconductor-electrolyte contacts (a) stable material, tals to Solar Fuel Generating Structures, (b) instable, (c) cathodically stable, (d) anodically stable... 

Figure II.1 Charge and Potential distribution at metal/electrolyte and semiconductor/electrolyte contact.

III. THE SEMICONDUCTOR ELECTROLYTE CONTACT UNDER ILLUMINATION AND PHOTODECOMPOSITION REACTIONS... 

If the semiconductor is connected with a counter electrode, a photocurrent is generated and photoelectrolysis occurs without an external voltage. This situation is delineated in Fig. III.5 for an n-type and a p-type semiconductor. An exact calculation of the distribution of the charge carriers at such an illuminated semiconductor electrolyte contact is very difficult. Some approximations can... 

Figure III.7 Distribution of minority carrier concentration in illuminated semiconductor/electrolyte contact for different surface concentrations.

---