The Space Charge Layer

The first feature results in the formation of a space charge layer of variable extension if excess charge is accumulated at the contact between a semiconductor and an electrolyte. Fig. II.1 gives a schematic comparison of the charge distribution and the course of potential at the contact between an electrolyte and a metal or a semiconductor. 

The local concentration of the electronic charge carriers is given in such pictures by the distance between the Fermi level and the band edges  

These properties can be checked experimentally by capacity measurements. The most important situation for a semiconductor in connection with energy conversion is the depletion layer, i.e. a positive excess charge on an n-type or a negative excess charge on a p-type semiconductor. In this case, the differential capacity, provided that there are no slow relaxation processes inside the semiconductor and the position of the band edges at the surface of the semiconduc- 

In this equation, e is the dielectric constant of the material, e the permittivity of the vacuum, e the elemental charge, N. the concentration of donors in n-type, of acceptors in p-type semiconductors, is +1 for donors, -1 for acceptors  

If the majority carriers of the semiconductor are accumulated at the interface, the electrode behavior approaches that one of a metal because now the excess charge remains very concentrated at the interface. Fig. II.3 gives a picture of the capacity behavior of an n-type semiconductor against the potential drop across the interface in a linear representation and also in a Mott-Schottky plot. 

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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.

Dispersing a dielectric substance such as A1203 in Lil [34] enhances the ionic conductivity of Lil about two orders of magnitude. The smaller the particle size of the dielectrics, the larger is the effect. This phenomenon is explained on the basis that the space-charge layer consists of or Li, generated at the interface between the ionic conductor (Lil) and the dielectric material (A1203) [35],... 

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. 

Relation (18) for the potential-dependent PMC signal is a reasonably good approximation only for the depletion region, where the space charge layer is controlled by the presence of fixed electron donors (Afo). It would become even more complicated if bimolecular or even more complicated kinetic reaction steps were considered. 

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... 

The decrease of the PMC signal toward increasing depletion therefore reflects the increasing dynamics of minority carriers passing the space charge layer. No classical electrochemical technique has up to now permitted observation of this phenomenon with such clarity. 

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)...

Lanz and Com [51] proposed a 20-nm thick space charge layer on the Ti02 surface. When the fourth-order response with our TMA-covered surface is generated in the space charge layer, the broad width of the 826-cm band is understood as a depth-dependent wavenumber of the lattice vibration. 

Fig. 5. Arrhenius analysis of the dissociation rate (l/Td)of PH complexes in the space-charge layer of hydrogenated n-type silicon Schottky diodes. The diodes were reverse biased at 4 V during the anneals (Zhu et al., 1990). 

Figure 8.7 Tunneling through the space-charge layer at equilibrium and for an anodic overpotential. Note that the band bending is stronger after the application of the overpotential. The arrows indicate electrons tunneling through the space-charge barrier.

Three concentrations of each redox couple that ranged over two orders of magnitude were examined as well as a solution containing only electrolyte. The details of these comprehensive experiments will be published elsewhere (22.) however, several pertinent features are described here. The kinetic currents were measured at constant potential. In order to eliminate mass transfer limitations to the current, a jet electrode configuration was utilized (42). The capacitance of the space charge layer (Csc) was measured at the same potentials simultaneously with the kinetic currents. 

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. 

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