Semiconductor potential distribution

The two semiconductor potential distribution conditions most relevant to dye sensitization of planar n-type semiconductors are shown schematically in Figure 2. The flat band-condition applies to the case where the band edges are flat right up to the solution interface (Figure 2a). Under ideal conditions, a positive applied potential does not alter the energetic position of the bands at the semiconductor-... 

Figure 2. Three semiconductor potential distribution conditions for an n-type semiconductor a) flat band condition, b) depletion condition, and c) depletion condition with Fermi-level pining.

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...

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. 

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,...

A representative potential distribution across the interface is shown in Fig. 3.9(c), taking the potential of the bulk solution as zero. The potential difference across the space charge region (psd occurs over a larger distance than that of the Helmholtz layer (pn). For an n-type semiconductor, (psc results from the excess positive charge of ionized donors in the bulk of the space charge region within the... 

Figure 4.12 is an illustration of the potential distribution for n-type semiconductor particles at the semiconductor-electrolyte interface. There are two limiting cases of equation (4.8.11) for photo-induced electron transfer in semiconductors. For large particles the potential drop within the semiconductor is defined by ... 

The potential distribution ( ) in the space-charge region is described, with due account for Eq. (13), by the self-consistent Poisson-Boltzmann equation. Its first integral can be calculated analytically, so that the electric field at the semiconductor surface Ssc = — /dx is expressed as (Garrett and Brattain, 1955 see also Frankl, 1967)... 

Figure 3 Schematic of a nanoporous 2 film in the dark showing the movement of compensating positive ions (circles with + ) through the film that screens a negative potential (electrons shown as - ) applied to the Sn02 substrate electrode, (a) The electric field is screened close to the substrate when the potential is positive of the conduction band, but (b) extends further into the semiconductor for more negative potentials. The potential distribution also depends on the relative rates of interfacial versus interparticle charge transfer (Fig. 2).

The band bending at the semiconductor/liquid (electrolyte solution) interface can be understood by considering the potential distribution at this interface. In a case where the electrolyte solution contains a redox couple (R/Ox), which causes an electrochemical redox reaction,... 

The potential distribution in the space chaige layer can be obtained by solving the Poisson equation for a given charge distribution. For a semiconductor/elecirolyte interface such as that shown in Fig.4.2, the potential,0(x), at a distance, x, from the semiconductor surface is given as follows ... 

Fig. 4.2 Schematic illustrations of (a) the charge distribution, (b) the charge-density distribution, (c) the potential distribution, and (d) the band bending at the semiconductor/redox electrolyte interface, assuming that no surface charge nor surface dipole is present.

Study of the Potential Distribution at the Semiconductor-Electrolyte Interface in Regenerative Photoelectrochemical Solar Cells... 

We will illustrate the difficulties and the opportunities which are associated with two complementary measuring techniques Relaxation Spectrum Analysis and Electrolyte Electroreflectance. Both techniques provide information on the potential distribution at the junction of a "real" semiconductor. Due to the individual characteristics of each system, care must be taken before directly applying the results which were obtained on our samples to other, similarly prepared crystals. 

Electrolyte Electroreflectance (EER) is a sensitive optical technique in which an applied electric field at the surface of a semiconductor modulates the reflectivity, and the detected signals are analyzed using a lock-in amplifier. EER is a powerful method for studying the optical properties of semiconductors, and considerable experimental detail is available in the literature. ( H, J 2, H, 14 JL5) The EER spectrum is automatically normalized with respect to field-independent optical properties of surface films (for example, sulfides), electrolytes, and other experimental particulars. Significantly, the EER spectrum may contain features which are sensitive to both the AC and the DC applied electric fields, and can be used to monitor in situ the potential distribution at the liquid junction interface. (14, 15, 16, 17, 18)... 

In the dark, the junction between an extrinsic (doped) semiconductor and a redox electrolyte behaves as a diode because only one type of charge carrier (electrons for n-type and holes for p-type) is available to take part in electron transfer reactions. The potential distribution across the semiconductor/electrolyte interface differs substantially from that across... 

Fig. 8.2. (a) Potential distribution across the semiconductor/electrolyte junction under depletion conditions, (b) Band bending corresponding to (a). 

Under steady state conditions, the concentration of holes at the surface is determined by the rate of their arrival from the bulk and on the rate of their removal by electron transfer and surface recombination. It is usually assumed that the potential distribution across the semiconductor/electro-lyte junction is not affected by illumination under potentiostatic conditions,... 

The potential distribution, and hence the extent of the band bending, within the space charge layer of a planar macroscopic electrode may be obtained by solution of the one-dimensional Poisson-Boltzmann equation [95]. However, since the particles may be assumed to have spherical geometry, the Poisson-Boltzmann for a sphere must be solved. This has been done by Albery and Bartlett [131] in a treatment that was recently extended by Liver and Nitzan [125]. For an n-type semiconductor particle of radius r0, the Poisson-Boltzmann equation for the case of spherical symmetry takes the form ... 

Fig. 16.1 Potential distribution at the semiconductor-electrolyte interface [Copyright Wiley-VCH Verlag GmbH Co. KGaA. Reproduced with permission from Memming (2001)]...

Photoelectrochemistry — In principle, any process in which photon absorption is followed by some electrochemical process is termed photo electro chemical, but the term has come to have a rather restricted usage, partly to avoid confusion with photoemission (q.v.). The critical requirements for normal photo electro chemical activity is that the electrode itself should be a semiconductor that the electrolyte should have a concentration substantially exceeding the density of -> charge carriers in the semiconductor and that the semiconductor should be reverse biased with respect to the solution. To follow this in detail, the differences in potential distribution at the metal-electrolyte and semiconductor-electrolyte interfaces need to be understood, and these are shown in Fig. 1, which illustrates the situation for an n-type semiconductor under positive bias. 

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