Semiconductors flat band-condition

A Schottky diode is always operated under depletion conditions flat-band condition would involve giant currents. A Schottky diode, therefore, models the silicon electrolyte interface only accurately as long as the charge transfer is limited by the electrode. If the charge transfer becomes reaction-limited or diffusion-limited, the electrode may as well be under accumulation or inversion. The solid-state equivalent would now be a metal-insulator-semiconductor (MIS) structure. However, the I-V characteristic of a real silicon-electrolyte interface may exhibit features unlike any solid-state device, as... 

Spontaneous water-splitting upon illumination needs semiconductors with appropriate electron affinity and flat band conditions. The flat band positions shift with electrolyte pH. Hence, an external bias needs to be applied between the electrodes in most cases to effect water splitting. The external bias can be either electrical or chemical. This external bias contribution should be subtracted from (3.6.11) or (3.6.12) to get the overall photoconversion efficiency. In the case of an external electrical bias, the efficiency can be defined as ... 

The simple picture of the MOS capacitor presented in the last section is complicated by two factors, work function differences between the metal and semiconductor and excess charge in the oxide. The difference in work functions, the energies required to remove an electron from a metal or semiconductor, is 0ms = —25 meV for an aluminum metal plate over a 50-nm thermally grown oxide on -type silicon with n = 1016 cm-3. This work function difference leads to a misalignment of energy bands in the metal and semiconductor which has to be compensated by a variation of the energy band with distance. When there is no misalignment the flat-band condition results. 

Band gap photochemical excitation of a semiconductor particle promotes an electron from the valence band to the conduction band, thus forming an electron-hole pair. Under illumination, the bands shift from their dark equilibrium positions to ones closer to the flat band condition, Scheme 9. Here the chemical potential of the electrons becomes different from that of the holes and a photovoltage develops. The concentration of free carriers, and hence of the number of available redox equivalents, will depend linearly on the incident light intensity. The free energy of these charge carriers will be related to... 

Fig. 5.3. Formation of a bulk heterojunction and subsequent photoinduced electron transfer inside such a composite formed from the interpenetrating donor/acceptor network, plotted with the device structure for such a junction (a). The diagrams showing energy levels of an MDMO-PPV/PCBM system for flat band conditions (b) and under short-circuit conditions (c) do not take into account possible interfacial layers at the metal/semiconductor interface...

Fig. 1. Four possible states of an n-type semiconductor as the sign of the charge in the surface region changes from positive to negative (a) an n-type accumulation layer, (b) the flat band condition, (c) a depletion layer, (d) an inversion layer. Ec and Ev represent the edge of the conduction band and valence band respectively. Bp represents the Fermi energy or chemical potential of electrons in the solid. + represents ionized donor atoms, mobile electrons and mobile holes.

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.

It is surprising that Kamat, O Regan and co-workers found a decreased injection yield at potentials near the flat-band condition. In the standard Gerischer model for sensitized planar electrodes, the low photocurrent near the flat band results because the injected carriers rapidly recombine with the oxidized sensitizer owing to the lack of a substantial depletion layer. Gerischer theory would not predict a decreased injection yield near the flat band, but this behavior can clearly be realized at sensitized nanocrystalline semiconductor films. 

Since the Fermi level, peF, of a p-type semiconductor electrode is inevitably lower than the Fermi level, nsF, of an n-type electrode of the same semiconductor, the electrode potential of the p-type is always more positive than that of the n-type under the flat band condition. The difference in the flat band electrode potential between the p-type and the n-type electrode is nearly equivalent to the band gap of the semiconductor. It is an observed fact that the electrode potential of most... 

Energy-band diagram of the band bending interface in the presence of surface states for a metal/n-type semiconductor (a) under flat band condition and (b) after contact formation. 

Fig. 2 Energy diagram of T1O2 nanotube (n-type semiconductor) when Ef sc>Ef,redox-fa) Position before semiconductor-electrolyte in contact, (b) equilibrium position after semiconductor-electrolyte in contact, (c) anodic bias (-f AU) which leads to increase in band bending and space charge layer (W), (d) cathodic bias which leads to flat band conditions (U = Uft,). Reproduced with permission from Ref. 32.

Figure 13.43 Surface electronic states and induced band bending of an n-doped semiconductor. (a) Filled surface states (donor type) are found below the valence band maximum, empty surface states (acceptor type) above the conduction band minimum. In this case no charge transfer between surface and bulk states occurs, corresponding to flat-band condition (i.e. no band bending), (b)...

Figure 3.20 Shows schematically the band edge offsets in the flat band condition for the types of semiconductor heterojunctions.

Fig. 5. NMOS capacitance voltage characteristics where C is the oxide capacitance, A shows low frequency characteristics, and B shows high frequency characteristics. At low frequencies C approaches C for negative voltages (accumulation) and positive voltages (inversion). In the flat-band (FB) condition there is no voltage difference between the semiconductor s surface and bulk. The threshold voltage, Dp for channel formation is the point where the...

Primarily connected to corrosion concepts, Pourbaix diagrams may be used within the scope of prediction and understanding of the thermodynamic stability of materials under various conditions. Park and Barber [25] have shown this relevance in examining the thermodynamic stabilities of semiconductor binary compounds such as CdS, CdSe, CdTe, and GaP, in relation to their flat band potentials and under conditions related to photoelectrochemical cell performance with different redox couples in solution. 

An example of the effect of photon irradiation on the flat band potential is shown in Fig. 10-18 this figure compares a Mott-Schott plot with the anodic polarization curve of the dissolution reaction of a semiconductor anode of n-type molybdeniun selenide in an acidic solution in the dark and in the photoexcited conditions. In this example photoe dtation shifts the flat band potential from Em in the dark to pii) in the photoexcited state is about 0.75 V more positive than Em. This photo-shift of the flat band potential, Emi )-Em, corresponds to the change in the potential, of the compact layer due to photoexcitation as defined in Eqn. 10-23 ... 

For heavily doped n-type semiconductors, the flat band is nearly coincident with the conduction band, while for heavily doped p-type semiconductors the flat band lies very close to the valence band edge. A necessary thermodynamic condition for the photoproduction of hydrogen and oxygen is that the p-type conduction band must be at or above the H7H2 half cell potential, while n-type valence band must lie below the 02/0H half cell potential. 

Let us note that according to Eq. (73) the sign of plasma electroreflection is determined by the sign of sc. The quantity A R/R is positive if 0 (accumulation layer) and is negative if , < 0. In other words, the flat band potential of the semiconductor can be determined from the condition that the sign of A R/R changes. 

It is well known that non-degenerated wide-band semiconductors tend to have low electrocatalytic activity. In particular, in the dark conditions under the electrode potentials higher than the flat-band potential (Efb), Ti02 electrodes with ordinary doping (Na = 1017 -... 

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