Space charge layer semiconductor

Figure Bl.28.9. Energetic sitiration for an n-type semiconductor (a) before and (b) after contact with an electrolyte solution. The electrochemical potentials of the two systems reach equilibrium by electron exchange at the interface. Transfer of electrons from the semiconductor to the electrolyte leads to a positive space charge layer, W. is the potential drop in the 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 Gartner model simulates charge collection by a potential-dependent space charge layer and considers diffusion into the space charge layer of charge carriers generated deep inside the semiconductor. The well-known Gartner formula for the photocurrent /ph is... 

Figure 28. Semiconductor interfaces with increasing electric fields in the space charge layer (from top to bottom) compared with tubes of different diameters through which an equivalent amount of water is pressed per unit time (equivalent to limiting current).

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... 

Fig. 3.4 Schematic representation of the cauliflower structure, showing the space charge layer in relation to the electrolyte and the semiconductor, and the pinching of cauliflowers , which is believed to be responsible for the disorder-dominated impedance. (Reprinted with permission from [71], Copyright 2009, The Electrochemical Society)...

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

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. 

Semiconductor structures that develop space charge layers and contact potentials, like films of proper thickness, films with applied external bias, homo- and hetero-(nano)junctions, permit significant suppression of bulk recombination processes and, potentially, allow high quantum yields. Spatial separation of electron and holes also allows the separation of cathodic and anodic processes in a photoelec-trochemical cell (eventually at the micro and nano level), minimizing surface re-... 

Space charge layers and contact potential for efficient charge carrier separation can be achieved with proper semiconductor structure in several ways. When possible semiconductor structures are considered, the charge separation can be attained in an active mode, i.e., by the use of a potential bias in a photoelectrochem-ical cell, or in a passive mode, i.e., with the use of proper contact between different phases. 

Semiconductor - Metal Junctions Besides the semiconductor-liquid interface, electron-hole separation can be attained also when the couple is generated in the space charge layer of a homo/heterojunction or semiconductor-metal junction. The metal can also act as electrocatalyst (e.g., for reduction of 02, H+ or C02). The development of the proper structure, including arrays of multiple junctions in series to enhance photovoltages and efficiently harvest radiation [53] and/ or the inclusion of suitable electrocatalysts, is crucial. 

It also appears in Eqn. 3—17 that the ion level ag-tso of a semiconductor is to some extent dependent on the potential of the space charge layer. 

This same theoretical approach can also apply to the space charge layer formed in solid semiconductors. Instead of the concentration of ions in aqueous solution, however, the concentration of electrons or holes is used with the space charge layer in semiconductors. Then, the Debye length is given by Eqn. 5-7 ... 

The thickness of these layers is in the range of <2h = 0.4 to 0.6 nm for the compact layer, space charge layer, and c(d = 1 to 10 nm for the diffuse layer. The thickness of space charge layer, dac, and the thicknesses of diffuse layer, (fd, depend on the concentrations of mobile charge carries Tii in the semiconductor and in the aqueous solution, respectively. The Debye length, Ljy, may be used as a measure of the thickness of these two respective layers as shown in Eqn. 5-61 ... 

Further, the thicknesses of the diffuse and space charge layers depend on the potentials Ma and i sc across the respective layers for the space charge layer the thickness, dgc, is expressed, to a first approximation, by dsc = 2Lox (eA /kT)- [Memming, 1983]. The Debye length, Ld, is about 100 nm in usual semiconductors with impurity concentrations in the order of 10 cm and is about 10 nm in dilute 0.01 M ionic solutions. 

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. 

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