Semiconductor equivalent circuit

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... 

Fig. 10.1 Equivalent circuits used to represent the semiconductor-electrolyte interface, (a) A more complete approach taking into account the series resistance (Ry), the depletion layer (Csc, Rsc), an oxide surface film...

Fig. 5-60. Equivalent circuit for an interfacial electric double layer comprising a space charge layer, a surface state and a compact la3 er at semiconductor electrodes Csc = capacity of a space charge layer C = capacity of a surface state Ch = capacity of a compact layer An = resistance of charging and discharging the surface state.

Fig. 19 (a) The device schematic for a pseudo Y-junction transistor, (b) SEM micrograph of the overall circuit arrangement used in the measurement of the electrical characteristics, with Au contact pads and an FIB-patterned Pt wire contacting the Au pads and the Y-junction. (c) The ambipolar I-V curves resemble that of an n-type semiconductor at a positive gate potential, and a p-type semiconductor at a negative gate potential top), and the equivalent circuit for a pseudo Y-junction SWNT device bottom). (Reprinted with permission from [170, 171])... 

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

A similar procedure can be used to determine the space charge distribution in n-type Si in the dark with a positive bias polarization so as to generate a depletion layer within the semiconductor substrate. In this case, the situation is somewhat different because the positive polarization in HF results in an anodic etching of the sample with a nonnegligible current density near 7 pA cm . Nevertheless, similar results were obtained, the components of the equivalent circuit were a capacitance of a few 10 F cm , and a resistance term ranging from 1 to 10Mf2cm for a bias potential varying from —0.1 to -1-0.9 V vs. SCE. 

To a first approximation, the BLM can be considered to behave like a parallel plate capacitor immersed in a conducting electrolyte solution. In reality, even such a thin insulator as the modified BLM (designated by and R, in Fig. 108) could block the specific adsorption of some species from solution and/or modify the electrochemical behavior of the system. Similarly, System C may turn out to be a semiconductor(l)-insulator-semiconductor(2) (SIS ) rather than a semiconductor(l)-semiconductor(2) (SS ) junction. The obtained data, however, did not allow for an unambiguous distinction between these two alternative junctions we have chosen the simpler of the two [652], The equivalent circuit describing the working (Ew), the reference (Eg), and the counter (Ec) electrodes the resistance (Rm) and the capacitance (C of the BLM the resistance (R ) and capacitance (Ch) of the Helmholtz electrical double layer surrounding the BLM as well as the resistance of the electrolyte solution (RSO ) is shown in Fig. 108a [652],... 

Deposition of a particulate semiconductor on the cis side of the BLM (System A) alters the equivalent circuit to that shown in Fig. 108b, where Rf and... 

Fig. 108a-c. Proposed equivalent circuits for. a an empty and b a semiconductor-particle-coated BLM. Porous structure of the semiconductor particles allowed c the simplification of the equivalent circuit. Rm, RH, and Rsol are resistances due to the membrane, to the Helmholtz electrical double layer, and to the electrolyte solutions, while C and CH are the corresponding capacitances Rf and Cf are the resistance and capacitance due to the particulate semiconductor film R m and Cm are the resistance and capacitance of the parts of the BLM which remained unaltered by the incorporation of the semiconductor particles R and Csc are the space charge resistance and capacitance at the semiconductor particle-BLM interface and Rss and C are the resistance and capacitance due to surface-state on the semiconductor particles in the BLM [652]... 

Fig. 7.51. Equivalent circuits for a semiconductor/solution interlace, (a) Conventional equivalent circuit (b) Equivalent circuit used in this work.

Figure 2. Assumed generalized equivalent circuit of the semiconductor—electrolyte interface. Reduced equivalent circuit at high frequencies and the expression for the impedance at low and high frequencies.

Figure 7. Equivalent circuit for interphase (Raei) resistance of semiconductor (Retec) electrolyte resistance, (Rfar) fara-daic resistance (Csc) space charge capacitance (CDl) double-layer capacitance and (z) parallel impedances associated with surface states, faradaic reactions, etc.

Fig. 4.11. Optical images of a printed polymer TFT array at increasing magnification, showing the whole 128 x 128 array (a), small regions of the array (b), and a single device (c). Note the printed semiconductor confined to the channel region in (b) and (c). (d) Equivalent circuit for the pixel, showing the gate and data address lines, the TFT and different capacitances. In the...

Occasionally, the impedance spectra of diamond electrodes are well described by the Randles equivalent circuit with a frequency-independent capacitance (in the 1 to 105 Hz range) [66], Shown in Fig. 11 is the potential dependence of the reciprocal of capacitance squared, a well-known Mott-Schottky plot. Physically, the plot reflects the potential dependence of the space charge region thickness in a semiconductor [6], The intercept on the potential axis is the flat-band potential E whereas the slope of the line gives the uncompensated acceptor concentration NA - Nd in what follows, we shall for brevity denote it as Na ... 

Power law behaviour has also been observed by Dutoit et al. [73] and ascribed to more general relaxation processes within a narrow layer at the surface of the semiconductor. It is, of course, not possible to distinguish by a.c. techniques alone the model put forward by Dutoit et al. [73] and that described above since the mathematical development is the same and the differences may, in any case, be largely semantic. Nevertheless, Dutoit et al. s analysis is of considerable interest. An equivalent circuit of the form... 

It is all but impossible to prepare any semiconductor electrode without some surface film being present. The III/V semiconductors, for example, will normally possess oxide films whose thickness will vary from less than 10 A to more than 40 A after exposure to air and similar observations have been reported for silicon [77], Although the capacitance of these films will normally be considerably larger than that of the depletion layer, the film may affect the a.c. response both by virtue of the analysis leading to eqn. (72) and, if Css becomes sufficiently large, that the impedance of the depletion layer falls to a value comparable with that of the film. If the film has a finite resistivity, which may be ionic in character, then the equivalent circuit takes the form... 

Fig. 37, Equivalent circuit for surface conductivity studies. ZY = faradaic impedance, Rel = electrolyte resistance, RB = bulk resistance of the semiconductor, and Rm. = surface resistance of semiconductor.

The equivalent circuit of Fig. 37 clearly demonstrates the main experimental difficulties encountered in determining Rac it is evident that only d.c. measurements are likely to prove practical else ZF will be too small and the semiconductor will be shunted by Rel (which is likely to be very small). The bulk resistor RB is only larger than Rac for intrinsic semiconductors and it has proved difficult to extend the technique to extrinsic materials as R becomes effectively shunted by RB. Evidently, only Rsc and Rel vary with potential applied across the semiconductor between the back contact and the reference electrode in solution however, the change in Rel is normally much smaller than Rsc as the mobility of the ions in solution is so much smaller than that of the carriers in the semiconductor. 

Fig. 97. (a) Electrical equivalent circuit of an illuminated semiconductor electrolyte interface, (b), (c) Experimental impedance plots for n-GaAs/selenide under 22mWcnT2 illumination at different potentials, (b) V = -0.60V/SCE (in the photocurrent saturation region) (c) V = - 1.575 V/SCE (in the onset region). The circles are experimental points and the dotted curve is the best fit to (a). 

The first of these can be treated with a simple equivalent circuit of the form shown in Fig. 104. It is normally assumed that processes (b) and (c) are very fast compared with (d) and (e) and that, if a direct bandgap semiconductor is used, (a) can also be minimised. Under these circumstances, the initial condition is... 

Figure 6. Electrostatics at a semiconductor-electrolyte interface. A very simplified equivalent circuit for the interface at equilibrium is shown at the bottom. The Gouy layer is neglected in the latter case (see text).

The Mott-Schottky regime spans about 1 V in applied bias potential for most semiconductor-electrolyte interfaces (i.e., in the region of depletion layer formation of the semiconductor space-charge layer, see above) [15]. The simple case considered here involves no mediator trap states or surface states at the interface such that the equivalent circuit of the interface essentially collapses to its most rudimentary form of Csc in series with the bulk resistance of the semiconductor. Further, in all the discussions above, it is reiterated that the redox electrolyte is sufficiently concentrated that the potential drop across the Gouy layer can be neglected. Specific adsorption and other processes at the semiconductor-electrolyte interface will influence Ffb these are discussed elsewhere [29, 30], as are anomalies related to the measurement process itself [31]. Figure 7 contains representative Mott-Schottky... 

Fig. 5.30. Equivalent circuit of semiconductor detector I(t) = current generator C = capacitance of the depletion region Z = series impedance is the resistance of the depletion region.

The equivalent circuit of a semiconductor detector operated as a spectrometer is shown in Fig. 5.30. In most cases, effects of high resistance of the reverse-biased junction are negligible. If a zero-electric-field radiation-insensitive region is present in the detector, its impedance (a parallel RC combination) appears in series with the circuit and is indicated in Fig. 5.30 by the impedance Z. The impedance also accounts for any resistance (or resistance-capacitance combination) appearing in series with the contacts. 

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