Space depletion layer

To calculate the current-voltage characteristic of a MESFET, we assume that the conducting channel is at thermal equilibrium, and the space-chaige layer completely depleted. Eq. (14.28) becomes... 

Relation (18) for the potential-dependent PMC signal is a reasonably good approximation only for the depletion region, where the space charge layer is controlled by the presence of fixed electron donors (Afo). It would become even more complicated if bimolecular or even more complicated kinetic reaction steps were considered. 

The decrease of the PMC signal toward increasing depletion therefore reflects the increasing dynamics of minority carriers passing the space charge layer. No classical electrochemical technique has up to now permitted observation of this phenomenon with such clarity. 

For a sufficiently large potential increase, the charge in the interphase finally corresponds to the minority charge carriers (Fig. 4.12D). The greater the width of the forbidden band eg, the broader is the potential range A f in which the space charge region has the character of a depletion layer, i.e. is formed by ionized impurity atoms. 

When the semiconductor is highly doped, the space-charge region is thin, and electrons can tunnel through the barrier formed at a depletion layer. 

According to the macropore formation mechanisms, as discussed in Section 9.1, the pore wall thickness of PS films formed on p-type substrates is always less than twice the SCR width. The conductivity of such a macroporous silicon film is therefore sensitive to the width of the surface depletion layer, which itself depends on the type and density of the surface charges present. For n-type substrates the pore spacing may become much more than twice the SCR width. In the latter case and for macro PS films that have been heavily doped after electrochemical formation, the effect of the surface depletion layer becomes negligible and the conductivity is determined by the geometry of the sample only. The conductivity parallel to the pores is then the bulk conductivity of the substrate times 1 -p, where p is the porosity. 

Fig. 3 -13. (a) A ion levels at the surface and in the interior of ionic compound AB, and (b) concentration profile of lattice defects in a surface space charge layer since the energy scales of occupied and vacant ion levels are opposite to each other, ion vacancies accumulate and interstitial ions deplete in the space charge layer giving excess A ions on the surface. 

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

As the potential Ai )sc of an inversion layer increases and as the Fermi level at the electrode interface coincides with the band edge level, the electrode interface is in the state of degeneracy (Fermi level pinning) and both the capacity Csc and the potential A4>sc are maintained constant. Figure 5-48 shows schematically the capacity of a space charge layer as a function of electrode potential. As the electrode potential shifts in the anodic (positive) direction from a cathodic (negative) potential, an accumulation, a depletion, and an inversion layer are successively formed here, the capacity of the space charge layer first decreases to a minimum and then increases to a steady value. 

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 energy barrier of a depletion layer (the potential across a depletion layer I I) is called the Schottky barrier in semiconductor physics. Assuming that all the impurity donors or acceptors are ionized to form a fixed space charge in the depletion layer, we obtain the following approximate equation, Eqn. 5—75, for the thickness of depletion layer, dx, [Memming, 1983] ... 

We consider, now, an electron-depleted space charge layer that is gradually polarized in the anodic direction. As long as the Fermi level is located away from the surface state, the interfacial capacity is determined by the capacity of the depletion layer that obeys a Mott-Schottlsy relation as shown in Fig. 5-61. 

As anodic or cathodic polarization increases, the band level bending in a space charge layer (a depletion layer) becomes steeper, and the electron tunneling through the space charge layer is then ready to occur particularly in semiconductor electrodes of high concentrations of donors or acceptors where the space charge layer is thin. 

We examine an electron transfer of hydrated redox particles (outer-sphere electron transfer) on metal electrodes covered with a thick film, as shown in Fig. 8-41, with an electron-depleted space charge layer on the film side of the film/solution interface and an ohmic contact at the metal/film interface. It appears that no electron transfer may take place at electron levels in the band gap of the film, since the film is sufficiently thick. Instead, electron transfer takes place at electron levels in the conduction and valence bands of the film. 

When the cell circuit is closed in the dark, as shown in Fig. 10-25(b), the Fermi level is equilibrated between the metallic cathode and the n-lype semiconductor anode. As a result, a depletion layer of space charge (potential barrier, is formed in the semiconductor anode, thereby shifting the potential of the anode from the flat band potential to a more anodic (more positive) potential (= + ). In the dark, however, the anodic hole transfer... 

The space charge layer capacitance is inversely proportional to the width of the depletion layer w. As the width of the depletion layer approaches zero the capacitance approaches infinity, hence... 

Fig. 4.2 For an n-type bulk semiconductor in the presence of an electrolyte illustrated is (left) no space charge layer, (center) a space charge layer in a depletion region, (right) a space charge layer in an accumulation region.

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