Flat band state

Fig. 2-81. Surface degeneracy caused by Fermi level pinning at a surface state of high state density (a) in flat band state (Ep ep), G>) in electron equilibrium (cp = cp). cp = surface Fermi level = surface ccmduction band edge level.

Fig. 10-4. G neration of electron-hole pairs by photoexdtation and their recombination or separation in semiconductor (a) generation and recombination of photoexdted electron-hole pairs in a flat band state, (b) generation and separation of photoexdted electron-hole pairs in a space charge layer.

Although the conductivity change Aa [relation (8)] of microwave conductivity measurements and the Ac of electrochemical measurements [relation (1)] are typically not identical (owing to the theoretically accessible frequency dependence of the quantities involved), the analogy between relations (1) and (8) shows that similar parameters are addressed by (photo)electrochemical and photoinduced microwave conductivity measurements. This includes the dynamics of charge carriers and dipoles, photoeffects, flat band and capacitive behavior, and the effect of surface states. 

At the interface of the nitride (Ef, = 5.3 eV) and the a-Si H the conduction and valence band line up. This results in band offsets. These offsets have been determined experimentally the conduction band offset is 2.2 eV, and the valence band offset 1.2 eV [620]. At the interface a small electron accumulation layer is present under zero gate voltage, due to the presence of interface states. As a result, band bending occurs. The voltage at which the bands are flat (the flat-band voltage Vfb) is slightly negative. 

The position of the C-V curve along the voltage axis is influenced by several solid-state as well as electrochemical parameters which are gathered in the equation for the flat-band voltage V rb of the EIS structure [1, 54] ... 

Here, Ws is the work function of electrons in the semiconductor, q is the elementary charge (1.6 X 1CT19 C), Qt and Qss are charges located in the oxide and the surface and interface states, respectively, Ere is the potential of the reference electrode, and Xso is the surface-dipole potential of the solution. Because in expression (2) for the flat-band voltage of the EIS system all terms can be considered as constant except for tp (which is analyte concentration dependent), the response of the EIS structure with respect to the electrolyte composition depends on its flat-band voltage shift, which can be accurately determined from the C-V curves. 

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... 

Fig. S-41. Band edge levels and Fermi level of semiconductor electrode (A) band edge level pinning, (a) flat band electrode, (b) under cathodic polarization, (c) under anodic polarization (B) Fermi level pinning, (d) initial electrode, (e) under cathodic polarization, (f) imder anodic polarization, ep = Fermi level = conduction band edge level at an interface Ev = valence band edge level at an interface e = surface state level = potential across a compact layer.

For simple semiconductor electrodes on which the charge of surface states and the charge of adsorbed ions are zero or remain constant, the flat band potential is obtained from Eqn. 5-84 to give Eqn. 5-87 ... 

Fig. 5-61. Mott-Schottky plot of an n-type semiconductor electrode in presence of a surface state ib = flat band potential with the surface state fully vacant of positive charge Eft, - flat band potential with the surface state fully occupied by positive charge Q = maximum charge of the surface state e, = surface state level, s capacity of the surface state ( Ch ).

As the Fermi level reaches the surface state level, the interfacial capacity is determined by the capacity of the compact layer (the maximum capacity of the surface state) and remains constant in a range of potential where the Fermi level is pinned. A further increase in anodic polarization leads again to the capacity of the depletion layer in accordance with another Mott-Schottky plot parallel to the former plot as shown in Fig. 5-61. The flat band potential, which is obtained from the Mott-Schottlo plot, shifts in the anodic direction as a result of anodic charging of the siuface state. This shift of the flat band potential equals a change of potential of the compact layer, (Q /C = Q./Ch), due to the anodic charging of the surface state. 

Fig. 8-16. Electron state density in a semiconductor electrode and in hjrdrated redox partides, rate constant of electron tunneling, and exchange redox current in equilibrium with a redox electron transfer reaction for which the Fermi level is close to the conduction band edge eF(sc) = Fermi level of intrinsic semiconductor at the flat band potential 1. 0 (tp.o) = exchange reaction current of electrons (holes) (hvp)) - tunneling rate constant of electrons (holes).

The point at which the straight line of (tph) versus Eintersects the coordinate of electrode potential represents the flat band potential. Equation 10-15 holds when the reaction rate at the electrode interface is much greater than the rate of the formation of photoexcited electron-liole pairs here, the interfadal reaction is in the state of quasi-equilibrium and the interfadal overvoltage t)j, is dose to zero. 

The flat band potential of semiconductor electrodes is determined by the potential across the compact las r at the electrode interface and is characteristic of individual semiconductor electrodes. For semiconductor electrodes in the state of band edge level pinning, the potential across the compact layer remains constant and independent of the electrode potential. For some semiconductor electrodes, however, photon irradiation changes the potential across the compact layer and, hence, shifts the flat band potential of the electrode. 

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 ... 

A shift of the flat band potential due to photoexcitation of the type shown in Fig. 10-18 results from the capture of holes in the surface state level, e , on the electrode as shown in Fig. 10-19. We now consider a dissolution reaction involving the anodic transfer of ions of a simple elemental semiconductor electrode according to Eqns. 10-24 and 10-25 ... 

Pig. 10-18. (a) PolarizatioD curves of anodic dissolution and (b) Mott-Schottky plots of an n-type semiconductor electrode of molybdenum selenide in the dark and in a photo-excited state in an acidic solution C = electrode capacity (iph) = anodic dissolution current immediately after photoexdtation (dashed curve) ipb = anodic dissolution current in a photostationary state (solid curve) luph) = flat band potential in a photostationary state. [From McEv( -Etman-Memming, 1985.]... 

Similarly, the flat band potential also shifts itself at photoexdted n-type semiconductor electrodes on which a transfer reaction involving anodic redox holes occurs via the surface state level e , if the rate of hole capture at the surface state is greater than the rate of hole transfer across the compact layer, as shown in Fig. 10-20(a). 

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