Potential distribution, at semiconductor

K. Uosaki and H. Kita, Effects of the helmholtz layer capacitance on the potential distribution at semiconductor/electrolyte interface and the linearity of the Mott-Schottky plot, J. Electrochem. Soc. 130, 895, 1983. 

Figure 2. Potential distribution at semiconductor-electrolyte interface (a) at equilibrium and (b) at polarization.

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...

Memming R, Schwandt (1967) Potential and charge distribution at semiconductor electrolyte interface. Angew chem. Int Ed 6 851-861... 

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,... 

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)... 

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. 

Fig. 8. Potential distribution at the semiconductor-electrolyte interface for (a) a negative charge density at the surface and (b) a positive charge density at the surface.

In this section, we first consider a general model of the faradaic processes occurring at the semiconductor-electrolyte interface due to Gerischer [11]. From Gerischer s model, using the potential distribution at the interface, we may derive a Tafel-type description of the variation of electron transfer with potential and we will then consider the transport limitations discussed above. We then turn to the case of intermediate interactions, in which the electron transfer process is mediated by surface states on the semiconductor and, finally, we consider situations in which the simple Gerischer model breaks down. 

The potential distribution at the surface of the semiconductor is such that the bulk of the potential change is accommodated within the depletion layer. It follows, as discussed in Sect. 4, that ns will be a strong function of the applied potential. However, the corollary of this is that the matrix element V and the thermal distribution parameters ox(Ec) and Qrei(Ec) will be much weaker functions of potential. Although, therefore, we would expect to find an exponential or Tafel-like variation of current with potential for a faradaic reaction on a semiconductor, the underlying situation is quite different from that of a metal. In the latter case, the exponential behaviour arises from the nature of the thermal distribution function Q and the concentration of carriers at the surface of the metal varies little with potential. To see this more clearly, we may expand eqn. (179) assuming that the reverse process of electron injection into the CB can be neglected eqn. (179) then reduces to... 

If c = 0, then VJ,h gives a measure of the flat-band potential provided r/re(i()x is known. In fact, this formula is very rarely obeyed in practice and deviations are both common and complex. Detailed theories of the potential distribution at the semiconductor-electrolyte interface have been presented, based on photovoltage measurements, but immense care needs to be taken in the interpretation of the photovoltage since kinetic effects apparently play a major role. This is especially true if surface recombination plays an important role [172]. 

Cao et al. reported an alternative Fermi-level pinning model to rationalize the potential distribution at negative applied potentials [147]. They suggested that the reduction of Ti surface states to TF , observed by low-temperature EPR spectroscopy, pins the Fermi level and, as the potential is raised further, the potential drops across the solution-semiconductor interface. 

Figure 2.14 (a) Potential distribution at the semiconductor-liquid interface (ref level of reference... 

During the 30 years from 1970, the potential distribution at many semiconductor electrodes has been studied. In the early stage of semiconductor electrochemistry primarily germanium and silicon electrodes were investigated because well-defined single crystals were available. It turned out much later that very important basic information had been obtained, especially with intrinsic germanium electrodes (ng = po), as will be shown below. In the following, Ge, Si and compound electrodes will be treated separately. 

The potential distribution at the interface has been studied for many compound semiconductors. Usually a straight line has been obtained when plotting 1/Csc vs. according to Eq. (5.27), as shown, for example, in Fig. 5.15 for an n-type CdS electrode in an aqueous electrolyte [28]. In addition, the flatband potential = 0), has... 

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