Space charge capacity

The total interfacial capacity C is a series combination of the space-charge capacities C c of the semiconductor and C oi of the solution side of the interface. However, generally Csoi Csc, and the contribution of... 

It will be seen that the values of the space-charge capacities are low (-0.01-1 fiF cm 2) compared with the capacities (-17 (J.F cm 2) of the region between the semiconductor surface and the OHP plane, the Helmholtz-Perrin parallel-plate region. That is why the space-charge capacities (the inverted parabolas) are noticed, for the observed capacity is given by two capacitors in series, the space charge, Csc, and Helmholtz-Perrin HP capacitors. Thus,... 

The Mott-Schottky plot obtained experimentally for the Ag-modified Ti02 electrode, which satisfy the above requirements, differs from that for the initial electrode by the slope value, with an insignificant shift of the point obtained after extrapolating the plot to the electrode potential axis (Fig. 6.15). Since for the realization of such electrode system we have used a semiconductor characterized by the high concentration of ionized donors, under consideration of Mott-Schottky dependence it is worthwhile to take account of the Helmholtz layer capacity (CH) placed in series with the space charge capacity [100] ... 

Fig. 10. Theoretical values of the space charge capacities as a function of the space charge potential V ...

Zviagin and Liutovich (11) found similar minimum values for p-type Si as we did for the Ge samples. The theoretical curve of the Russian authors is calculated on the assumption that the minority carriers are depleted. This is possible for a p-type semiconductor only in the case of cathodic polarization. Since the Russian authors did not take into account the possibility of enrichment of the minority carriers, they did not get a distinct minimum of the theoretical capacity-potential curve. We found the minimum for n-type Ge under reverse bias, i. e., under anodic current. This result is to be expected (in contrast to a common rectifier) as long as the resistance across the phase boundary (R ) is high compared to the recombination rate or the rate orformation of free carriers. It is to be expected, in other words, as long as the electrochemical potential of the free carriers remains nearly constant across the space charge up to the surface. The Russian authors point out that the measured capacity is not equal to the space charge capacity, but should be related to it. This relationship is indicated by the measured frequency dependence of the measured impedances. It is in agreement with our assumption that the... 

Since the space charge capacity is usually much smaller than the capacity Ch of the Helmholtz double layer, it can easily be determined experimentally. 

Fig. 8. Mott-Schottky plot of the space charge capacity vs electrode potential at n- and p-type GaP in O.I M H2SO4 [47]...

Changes in space-charge capacity can be used to observe the effect of charging and discharging of electronic states in a semiconductor subject to sub-bandgap illumination. Show that the change in observed capacity caused by illumination can be referenced to the unilluminated case by... 

Equation (1.24) is the much-used Mott-Schottky equation, which relates the space charge capacity to the surface barrier potential Vs. Two important parameters can be determined by plotting versus Vapp the flatband potential Vn, at = 0 (where Vs = 0) and the density of charge in the space charge layer, that is, the doping concentration N. ... 

FIGURE 1.8. Variation of the space charge capacity with a band bending of V, on an n-type semiconductor with an accumulation layer or an inversion layer. Mobile carriers are at the surface in the inversion so the capacity is high. If minority carriers do not accumulate at the surface at a large band bending, a deep depletion curve results. After Morrison. ... 

This is illustrated in Fig. 4.7. In the simplest case the solid-liquid interface can be described by a charge transfer resistance R and a capacity in parallel (Helmholtz capacity for metal electrodes, Ch, and a space charge capacity for semiconductor elec-... 

It should be emphasized that impedance measurements are mainly used for measuring space charge capacities. They are usually performed in a frequency range of 10 kHz up to nearly 1 MHz depending on the Faraday current. 

This equation shows clearly that the space charge capacity Qc depends strongly on the potential across the space charge layer, although in a rather complex way. Before analyzing this relation in more detail it is useful to introduce two further equations. In accordance with Eqs. (5.14) and (5.15) the electron and hole densities at the surface are given by... 

Fig. 5.5 Accumulation, depletion and inversion layer at thc semiconductor-electrolyte interface a) space charge capacity C e vs. potential across the space charge layer A

Fig. 5.6 Mott-Schottky plot of the space charge capacity vs. potential across the space charge layer vs. for an n type semiconductor electrode (theoretical curve).

It should be mentioned here, that the capacity of the space charge layer in an intrinsic semiconductor looks very similar to that of the diffuse Gouy layer in the electrolyte (compare with Eq. 5.8). This is very reasonable because the Gouy layer is also a kind of space charge layer with ions instead of electrons as mobile carriers. Q was actually derived by the same procedure as given here for Csc- Similarly as in the case of Cn and C(j, the space charge capacity Cjc and the Helmholtz capacity Ch can be treated as capacitors circuited in scries. We have then... 

Accordingly, the space charge capacity can only be measured for < Ch- This condition can usually fulfilled with semiconductors of a carrier density smaller than uq = 10 cm". In addition a thickness of the space charge layer, can be derived using the relation d = eeo/C (valid for a capacitor with fixed plates). Applying this to a depletion layer, one obtains from Eq. (5.27)... 

Fig. 5.12 a) Space charge capacity (right scale) of intrinsic Ge vs. electrode potential after anodic and cathodic prepolarization at pH2. b) Current-potential curve. Both measurements were performed at a scan rate of 0.35 V s" (After ref. [22])... 

Fig. 5.14 Space charge capacity vs. electrode potential for an n type silicon electrode (1 Q cm material) in 10 M HF open circles experimental values solid line theoretical curve, a) Linear plot of Csc b) Mott-Schottky type of plot. (After ref. [26])...

In the case of GaAs a change of the potential across the Helmholtz layer was observed upon anodic and cathodic prepolarization, which was interpreted in terms of hydroxyl and hydride surface layers, as for Ge (see Section 5.3.1) A linear Mott-Schottky dependence for an n-GaAs electrode was only found at sufficiently high scan rates after anodic or cathodic prepolarization as shown in Fig. 5.17 [40], It is worth mentioning that all reliable capacity measurements could be interpreted in terms of space charge capacities, i.e. additional capacities due to surface states were not found. 

Fig, 5.17 Mott-Schottky plot of thc space charge capacity vs. electrode potential for n-GaAs in aqueous solutions under stationary conditions and after different prcpolarizations scan rate 0.2 Vs-. (After ref. [40])... 

According to measurements of the space charge capacity dependent on the electrode potential (Mott-Schottky measurements, see Section 5.3), any variation of the electrode potential leads usually only to a corresponding change of the potential,... 

Electrode area Richardson constant Activity coefficient Differential Helmholtz capacity Differential space charge capacity Concentration of species j in solution... 

Quantitative measurements of the space charge capacity (Ch can be neglected, since Ch Csc in a series relationship) and a consecutive comparison with theoretical Csc values, performed at first with intrinsic germanium, has shown that an externally applied potential appears only across the space charge layer, whereas, in contradiction to the case of metal... 

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