Flat-band condition

Zero bias Flat-band condition Bias > 1.8 V... 

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... 

If VEB is increased, IEB increases and the current density at the electrode eventually becomes equal to JPS. It has been speculated that this first anodic current peak is associated with flat-band condition of the emitter-base junction. However, data of flat-band potential of a silicon electrode determined from Mott-Schottky plots show significant scatter, as shown in Fig. 10.3. However, from C-V measurement it can be concluded that all PS formation occurs under depletion conditions independent of type and density of doping of the Si electrode [Otl]. 

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. 

Scheme I Interface energetics for an n-type Si photoanode at the flat-band condition showing the formal potential for a surface-confined ferricenium/ferrocene reagent relative to the position of the top of the valence band, E ,and the bottom of the conduction band,E , at the interface between the Si substrate and the redox/electrolyte system. Interface energetics apply to an EtOH/0.1 M [n-Bu N]C10 electrolyte system.

In the former case, the positions of the conduction and valence band edges at the interface (E and E ) are fixed with respect to the electrolyte redox levels, while in the latter case the positions of E and E with respect to the electrolyte redox levels vary with electrode potential. Thus, with unpinned band edges, redox couples lying outside the band gap under flat band conditions can lie within the band gap under band bending conditions or under illumination. 

When the device is biased forward, the voltage drop across the polymer is compensated. In the case when the applied voltage equals the difference in the work functions of the two metals, the so called flat band condition is obtained (see Fig. 5.2b). When the applied voltage exceeds this value, the width of the potential barrier for charge injection decreases and, at some critical field, charge injection into the polymer becomes possible. 

Fig. 5.2 Schematic band structure of the polymer LED as a function of the applied voltage (a) zero bias, (b) flat band condition, (c) conducting state.

In operation a negative bias is placed on the detector gate to provide a depletion area thereunder. The combined transfer and field gate is biased to provide a flat band condition in the substrate under the lower portion and to provide an n-channel 21 beneath the higher portion. When the bias on the detector gate is made sufficient negative, the electrons trapped in the depletion area move out and proceed through the n-channel and are collected in the diode 3. 

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. 3.35. Experimental J—V characteristics of an ITO/PEDOT PSS/PCBM/Au injection limited electron current (triangles) and calculated space charge limited hole current in OC4C10-PPV (circles) for a thickness of L = 170 nm and temperature T = 290 K. The inserted figure represents die device band diagram under the flat band condition of a bulk heterojunction solar cell using Au as a top electrode [65]. 

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. 

Flat band condition The onset voltage tor tunneling to occur... 

Fig. 6 Principles of device function for organic semiconducting layers sandwiched between two metallic electrodes a short circuit condition, b flat band condition, c reverse bias, and d forward bias. Band bending effects at the ohmic contacts are neglected...

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... 

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