Space charge function

Fig. 5.2-611 The space charge function Fs vs, b) for n-type semiconductors ( b > 0) plotted versus band bending Vsk T. The function for p-type semiconductors ( b < 0) may be obtained from the relation F ub, -Vs) = F -Ub, Vs) [2.47, p.25]...

Polaron kinetics is also unaffected by variations in the applied voltage, as shown in Figure 8-I4b. The inset of Figure 8- 14b shows CPG efficiency as a function of the applied electric field. Symmetry with respect to the LED bias voltage rules out space charge effects and cxeiton-carrier interactions. In addition, we note that (A7/T),vi, has a quadratic dependence on the electric field, similarly to... 

Blom et al. [85] stated that the l/V characteristics in LEDs based on ITO/di-alkoxy-PPVs/Ca are determined by the bulk conductivity and not by the charge carrier injection, which is attributed to the low barrier heights at the interface ITO/PPV and PPV/Ca. They observed that the current flow in so called hole-only devices [80], where the work function of electrodes are close to the valence band of the polymer, with 1TO and Au as the electrodes, depends quadratically on the voltage in a logl/logV plot and can be described with following equation, which is characteristic for a space-charge-limitcd current (SCL) flow (s. Fig. 9-26) ... 

To evaluate the contribution of the SHG active oriented cation complexes to the ISE potential, the SHG responses were analyzed on the basis of a space-charge model [30,31]. This model, which was proposed to explain the permselectivity behavior of electrically neutral ionophore-based liquid membranes, assumes that a space charge region exists at the membrane boundary the primary function of lipophilic ionophores is to solubilize cations in the boundary region of the membrane, whereas hydrophilic counteranions are excluded from the membrane phase. Theoretical treatments of this model reported so far were essentially based on the assumption of a double-diffuse layer at the organic-aqueous solution interface and used a description of the diffuse double layer based on the classical Gouy-Chapman theory [31,34]. 

FIGURE 7.3 Simplified equivalent circuit of an original (unmodified) EIS structure (a) and EIS biosensor functionalized with charged macromolecules (b). Cj, Cx and CML are capacitances of the gate insulator, the space-charge region in the semiconductor, and the molecular layer, respectively / u is the resistance of... 

The potential i sc of the space charge layer can also be derived as a fixnction of the surface state charge Ou (the surface state density multiplied by the Fermi function). The relationship between of a. and M>sc thus derived can be compared with the relationship between and R (Eqn. 5-67) to obtain, to a first approximation, Eqn. 5-68 for the distribution of the electrode potential in the space charge layer and in the compact layer [Myamlin-Pleskov, 1967 Sato, 1993] ... 

Fig. 6-40. An interfadal potential, distributed to Msc in the space charge layer and to in the compact layer as a function of the concentration of surface states, D . [From Chandrasekaran-Kainthla-Bockris, 1988.]...

Fig. 5-42. Potential across an interlace of semiconductor electrode distributed to the space charge layer, At>sc, and to the compact layer,. as a function of total potential,...

In the same way as described in Sec. 5.2 for a diifiise layer in aqueous solution, the differential electric capacity, Csc, of a space charge layer of semiconductors can be derived from the Poisson s equation and the Fermi distribution function (or approximated by the Boltzmann distribution) to obtain Eqn. 5-69 for intrinsic semiconductor electrodes [(Serischer, 1961 Myamlin-Pleskov, 1967 Memming, 1983] ... 

Fig. 5-46. Differential capacity estimated for an electrode of intrinsic semiconductor of germanium by calculation as a function of electrode potential C = electrode capacity solid curve = capacity of a space charge broken curve = capacity of a series connection of a space charge layer and a compact layer. [From Goischer, 1961.)...

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.

Fig. 5-56. Capacity Csc of a space charge layer and capacity Ch of a compact layer calculated for an n-type semiconductor electrode as a function of electrode potential Ct = total capacity of an interfadal double layer (1/Ct = 1/ Csc+ 1/Ch). [From Gerisdier, 1990.]...

Fig. 8-28. Cathodic polarization curves for several redox reactions of hydrated redox particles at an n-type semiconductor electrode of zinc oxide in aqueous solutions (1) = 1x10- MCe at pH 1.5 (2) = 1x10 M Ag(NH3) atpH12 (3) = 1x10- M Fe(CN)6 at pH 3.8 (4)= 1x10- M Mn04- at pH 4.5 IE = thermal emission of electrons as a function of the potential barrier E-Et, of the space charge layer. [From Memming, 1987.]...

Fig. 6.3 Schematic picture of the electrochemical potential ( > as a function of distance x in an oxide semiconductor electrolyte system a) bulk semiconductor potential b) solid/solution interface potential c) space charge potential d) flat band potential e) potential in the double layer (White, 1990, with permission.

Fig. 13 Experimental (symbols) and theoretical (lines) data for the current-density as a function of applied voltage for a polymer film of a derivative of PPV under the condition of space-charge-limited current flow. Full curves are the solution of a transport equation that includes DOS filling (see text), dashed lines show the prediction of Child s law for space-charge-limited current flow assuming a constant charge carrier mobility. From [96] with permission. Copyright (2005) by the American Institute of Physics...

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