Semiconductor electrode space-charge layer

Before constructing an electrode for microwave electrochemical studies, the question of microwave penetration in relation to the geometry of the sample has to be evaluated carefully. Typically only moderately doped semiconductors can be well investigated by microwave electrochemical techniques. On the other hand, if the microwaves are interacting with thin layers of materials or liquids also highly doped or even metallic films can be used, provided an appropriate geometry is selected to allow interaction of the microwaves with a thin oxide-, Helmholtz-, or space-charge layer of the materials. 

Another technique consists of MC measurements during potential modulation. In this case the MC change is measured synchronously with the potential change at an electrode/electrolyte interface and recorded. To a first approximation this information is equivalent to a first derivative of the just-explained MC-potential curve. However, the signals obtained will depend on the frequency of modulation, since it will influence the charge carrier profiles in the space charge layer of the semiconductor. 

The schemes in Figs. 44 and 45 may serve to summarize the main results on photoinduced microwave conductivity in a semiconductor electrode (an n-type material is used as an example). Before a limiting photocurrent at positive potentials is reached, minority carriers tend to accumulate in the space charge layer [Fig. 44(a)], producing a PMC peak [Fig. 45(a)], the shape and height of which are controlled by interfacial rate constants. Near the flatband potential, where surface recombination... 

A particular important property of silicon electrodes (semiconductors in general) is the sensitivity of the rate of electrochemical reactions to the radius of curvature of the surface. Since an electric field is present in the space charge layer near the surface of a semiconductor, the vector of the field varies with the radius of surface curvature. The surface concentration of charge carriers and the rate of carrier supply, which are determined by the field vector, are thus affected by surface curvature. The situation is different on a metal surface. There exists no such a field inside the metal near the surface and all sites on a metal surface, whether it is curved not, is identical in this aspect. 

The fundamental reason for the uneven distribution of reactions is that the rate of electrochemical reactions on a semiconductor is sensitive to the radius of curvature of the surface. This sensitivity can either be associated with the thickness of the space charge layer or the resistance of the substrate. Thus, when the rate of the dissolution reactions depends on the thickness of the space charge layer, formation of pores can in principle occur on a semiconductor electrode. The specific porous structures are determined by the spatial and temporal distributions of reactions and their rates which are affected by the geometric elements in the system. Because of the intricate relations among the kinetic factors and geometric elements, the detail features of PS morphology and the mechanisms for their formation are complex and greatly vary with experimental conditions. 

In Eqn. 5-65 it appears that most of the change of electrode potential occurs in the space charge layer with almost no change of potential both in the compact layer and in the diffuse layer. This pattern may be regarded as characteristic of semiconductor electrodes. 

Fig. 5-42. Potential across an interlace of semiconductor electrode distributed to the space charge layer, At>sc, and to the compact layer,. as a function of total potential,...

Fig. 6-43. Space charge layers of semiconductor electrodes (a) an accumulation...

Fig. 5-44. Space charge layers of n-type semiconductor electrodes (c) an inversion layer, (d) a deep depletion layer.

In the same way as described in Sec. 5.2 for a diifiise layer in aqueous solution, the differential electric capacity, Csc, of a space charge layer of semiconductors can be derived from the Poisson s equation and the Fermi distribution function (or approximated by the Boltzmann distribution) to obtain Eqn. 5-69 for intrinsic semiconductor electrodes [(Serischer, 1961 Myamlin-Pleskov, 1967 Memming, 1983] ... 

Further, the capadty of the space charge layer of n-type or p-fype semiconductor electrodes, in which all the donors or acceptors are ionized, has been derived as shown in Eqn. 5-70 [Gterischer, 1961] ... 

Fig. 5-46. Differential capacity estimated for an electrode of intrinsic semiconductor of germanium by calculation as a function of electrode potential C = electrode capacity solid curve = capacity of a space charge broken curve = capacity of a series connection of a space charge layer and a compact layer. [From Goischer, 1961.)...

Fig. 6-48. Differential capacity of a space charge layer of an n-type semiconductor electrode as a function of electrode potential solid cunre = electronic equilibrium established in the semiconductor electrode dashed curve = electronic equilibrium prevented to be established in the semiconductor electrode AL = accumulation layer DL = depletion layer IL = inversion layer, DDL - deep depletion layer.

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.

In contrast to metal electrodes in which the electrostatic potential is constant, in semiconductor electrodes a space charge layer exists that creates an electrostatic potential gradient. The band edge levels and in the interior of semiconductor electrodes, thereby, differ from the analogous and at the electrode interface hence, the difference between the band edge level and the Fermi level in the interior of semiconductor electrodes is not the same as that at the electrode interface as shown in Fig. 8-14 and expressed in Eqn. 8—47 ... 

When the total overvoltage ti is distributed not only in the space charge layer t)8c but also in the compact layer tih, the Tafel constants of a and a each becomes greater than zero and the Tafel constants of a and each becomes less than one. In such cases, Kiv) and ip(T ) do not remain constant but increase with increasing overvoltage. Further, if Fermi level pinning is established at the interface of semiconductor electrodes, the Tafel constant becomes dose to 0.5 for... 

When the transport current of electrons or holes in semiconductor electrodes more or less influences the interfacial electron transfer current, the overvoltage T) consists of an overvoltage of space charge layer iisc, an overvoltage of compact layer t]h, and a transport overvoltage tit in semiconductors as expressed in Eqn. 8-68 ... 

Fig. 8-28. Cathodic polarization curves for several redox reactions of hydrated redox particles at an n-type semiconductor electrode of zinc oxide in aqueous solutions (1) = 1x10- MCe at pH 1.5 (2) = 1x10 M Ag(NH3) atpH12 (3) = 1x10- M Fe(CN)6 at pH 3.8 (4)= 1x10- M Mn04- at pH 4.5 IE = thermal emission of electrons as a function of the potential barrier E-Et, of the space charge layer. [From Memming, 1987.]...

As anodic or cathodic polarization increases, the band level bending in a space charge layer (a depletion layer) becomes steeper, and the electron tunneling through the space charge layer is then ready to occur particularly in semiconductor electrodes of high concentrations of donors or acceptors where the space charge layer is thin. 

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 equilibriiun of interfacial redox reactions of the adsorbed protons and hydrogens, the Fermi level of semiconductor electrons at the electrode interface equals the Fermi level e p(h /h) of interfacial redox electrons in the adsorbed protons and hydrogens. The Fermi level e gc) th interface of semiconductor electrode depends on the potential /l< )sc of the space charge layer as shown in Eqn. 9-66 ... 

When a semiconductor electrode is at the flat band potential, photoexdted electrons and holes are soon annihilated by their recombination. In the presence of a space charge layer, however, the photoexdted electrons and holes are separated, vrith each moving in the opposite direction under an electric field in the space charge layer as shown in Fig. 10-4. 

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