Deep depletion layer

Fig. 5-44. Space charge layers of n-type semiconductor electrodes (c) an inversion layer, (d) a deep depletion layer.

Fig. 6-48. Differential capacity of a space charge layer of an n-type semiconductor electrode as a function of electrode potential solid cunre = electronic equilibrium established in the semiconductor electrode dashed curve = electronic equilibrium prevented to be established in the semiconductor electrode AL = accumulation layer DL = depletion layer IL = inversion layer, DDL - deep depletion layer.

The thickness of depletion and deep depletion layers may be approximated by the effective Debye length, Lo, ff, given in Eqn. 5-70 Ld, is inversely proportional to the square root of the impiuity concentration, In ordinary semiconductors... 

The energy levels in the solution are kept constant, and the applied voltage shifts the bands in the oxide and the silicon. The Gaussian curves in Figure 4b represent the ferrocyanide/ferricyanide redox couple with an excess of ferrocyanide. E° is the standard redox potential of iron cyanide. With this, one can construct (a) to represent conditions with an accumulation layers, (b) with flatbands, where for illustration, we assume no charge in interface states, and (c) with an inversion or deep depletion layer (high anodic... 

A fifth type of space charge layer, the deep depletion layer, may be formed under non-equilibrium conditions at the semiconductor surface when a high voltage is applied such that an inversion layer should form, but either (a) minority carriers are not available to accumulate at the surface in the time allotted or (b) the minority carriers are consumed in an electrochemical reaction as soon as they reach the surface. Such a space charge layer is unlikely to form within semiconductor electrodes at open circuit and is included here solely for completeness. 

Because of the very short time scale until the scheduled latmch (1997/98) and due to the tight financial boimderies, only already well known and proven technologies and components will be used. As the focal instrument, the CCD camera MAXI developed at MPE Garching and AIT for XMM EPIC (Brauninger et al. 1993) will be used. It containes a pn-CCD with a deep depletion layer, 64 X 120 pixels of 150 X each, and an efficiency... 

Fig. 2.14 Different types of space charges in n- and p-type semiconductors. A normal depletion layer contains only ionized donors or acceptors. An inversion layer is formed when the Fermi level crosses the midgap energy, and the minority carriers outnumber the majority carriers in a thin layer at the surface. When these minority carriers are consumed faster than they are generated, a deep depletion layer forms under these conditions the surface is not in thermal equilibrium and the Fermi level is not well defined in this region. In an accumulation layer, the adsorbed surface charges are compensated by majority charge carriers that accumulate at the surface...

The redox system in Figure 2.24b has a much more positive redox potential, and the balance of the Fermi eneigies causes a deep depletion layer at the semiconductor. Since Ep is closer to E electron exchange with the valence band becomes possible, which corresponds with hole exchange. The holes accumulate at the surface because the depletion barrier prevents their movement into the bulk and their recombination with electrons. The result is an inversion layer where electrons in the bulk are separated from holes at the surface. 

Thus, for deep levels it is possible that the region x2 — X in which they are effective as traps is substantially less than the total depletion layer thickness W. For the case of a current transient the effect of the edge region is to change the expression given by Eq. (18) to (Grimmeiss, 1977)... 

While experiments involving solution-phase reactants have provided deep insights into the dynamics of heterogeneous electron transfer, the magnitude of the diffusion-controlled currents over short timescales ultimately limits the maximum rate constant that can be measured. For diffusive species, the thickness of the diffusion layer, S, is defined as S = (nDt)1/2, where D is the solution-phase diffusion coefficient and t is the polarization time. Therefore, the depletion layer thickness is proportional to the square root of the polarization time. One can estimate that the diffusion layer thickness is approximately 50 A if the diffusion coefficient is 1 x 10-5 cm2 s-1 and the polarization time is 10 ns. Given a typical bulk concentration of the electroactive species of 1 mM, this analysis reveals that only 10 000 molecules or so would be oxidized or reduced at a 1 pm radius microdisk under these conditions The average current for this experiment is only 170 nA, which is too small to be detected with high temporal resolution. 

If the potential on the semiconductor has imposed on it an a.c. component, then the effect is to change the accumulated charge in the depletion layer according to eqn. (38). Assuming that no faradaic current is passing, i.e. the semiconductor is deep in depletion, the capacitive response of the semiconductor layer may be approximated as... 

The complexity afforded by these traps arises from the fact that the frequency range normally used in a.c. studies, 1-105 Hz, is likely to contain the relaxation frequency appropriate to such trap sites. To explore this concept, we may consider Fig. 32 [76]. We identify a deep trap level of energy E0 relative to the conduction band, lying below the Fermi level in the bulk of the semicondutor and therefore ionised only up to a distance l into the depletion layer. For x > l, only the shallow traps are ionised at equilibrium. Within the spirit of the Mott-Schottky approximation, we obtain (provided V 3= V0)... 

Evidently, as the depletion layer potential increases, so will the time constant for the reverse transient as long as the state is sufficiently deep for ft 1 at large band-bending, the transient apparently vanishes since ft -> 0. If, on the other hand, ft is not negligible compared with /, that is nakr P k(F (p0ft°, then fta — ft° (ft0)2kiF (j)0lkrns and the current is... 

Once a steady state is re-established, all the deep-lying levels within the depletion layer have been ionised if initially full or filled if initially empty. 

In summary we have reviewed the progress in the characterization of electrical properties of ZnO. Improved ohmic and Schottky contacts have been fabricated, the latter suitable for depletion layer spectroscopy. The shallow and deep donor levels have been identified for ZnO from various sources. Further control of deep donors seems necessary for achieving p-conductivity. 

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. ... 

The trend observed in the experimental data is in line with the theoretical modelling presented in Section 2.3.2. The conduction moves from a mechanism controlled by the presence of the depletion layer (theoretical value 1 experimental value 1.0 0.1) to one controlled by transport through the accumulation layer where the Boltzmann statistics are still valid (theoretical value 2 experimental value 2.35 0.12) to the extreme case in which the Fermi level extends deep into the conduction band on the surface. It could be demonstrated in the theory (BSrsan et al, 2011) that, in this area, the value should increase above 2, reflecting that the influence of the surface band bending on the resistance decreases. This decrease is also supported by the experimental/phenomenological parameter showing a value of 3.80 0.05. 

Here, P (y), the deepness of the depletion layer, in the presence of a redncing gas has the value jila. 

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