Depletion layer, semiconductors

In ideal semiconductor/electrolyte junctions, the presence of an energetic barrier in the semiconductor phase, originated from the equilibrium of the Fermi level in the solid and liquid phases, can be approached by the semiconductor depletion layer capacitance or space charge capacitance, Cgc- Measurement of capacitance versus... 

The E0 transition in GaAs is the simplest single transition that can be investigated within the III/V materials and a detailed quantitative fit has been attempted to the data of Fig. 29. A careful analysis of these data lead to the fit shown in Fig. 17 and it is clear that all the features of the experimental spectrum can be reproduced with some precision provided that the manufacturer s acceptor density be taken as the basis for the analysis. By comparing the changes in the Franz-Keldysh oscillation near 820 nm with those calculated using the intermediate field model with a presumed parabolic decay of potential inside the semiconductor depletion layer, it is found that some 70 10% of the potential is dropped inside the depletion layer of this n-type material, as can be seen in Fig. 30, and there is no evidence for the phenomenon described in the previous paragraph whereby the band... 

In the simplest case as more fully discussed elsewhere [14, 15, 29], one obtains the Mott-Schottky relation (for the specific instance of a n-type semiconductor) of the semiconductor depletion layer capacitance (Csc), again by invoking the Poisson equation... 

The electrochemical impedance for surface state-mediated charge transfer has been computed recently [78]. The key results are summarized in Fig. 16. Figure 16(a) contains the proposed equivalent circuit for the process and features a parallel connection of the impedance for the Faradaic process [Zf( )] (co = angular frequency, 2nf) and the capacitance of the semiconductor depletion layer, Csc- The... 

Solution of semiconductor depletion layer as a BV problem require"odebvfd" exp math.exp... 

As we have discussed earlier in the context of surfaces and interfaces, the breaking of the inversion synnnetry strongly alters the SFIG from a centrosynnnetric medium. Surfaces and interfaces are not the only means of breaking the inversion synnnetry of a centrosynnnetric material. Another important perturbation is diat induced by (static) electric fields. Such electric fields may be applied externally or may arise internally from a depletion layer at the interface of a semiconductor or from a double-charge layer at the interface of a liquid. 

Figure Bl.28.10. Schematic representation of an illuminated (a) n-type and (b) p-type semiconductor in the presence of a depletion layer fonned at the semiconductor-electrolyte interface.

A useftil applicadon of time-dependent PL is the assessment of the quality of thin III-V semiconductor alloy layers and interfaces, such as those used in the fabri-cadon of diode lasers. For example, at room temperature, a diode laser made with high-quality materials may show a slow decay of the acdve region PL over several ns, whereas in low-quality materials nonradiative centers (e.g., oxygen) at die cladding interface can rapidly deplete the free-carder population, resulting in much shorter decay times. Measurements of lifetime are significandy less dependent on external condidons than is the PL intensity. 

Figure 14-7. A MISFET in operation, (a) VK>V l/j=0 an n-lypc channel of constant thickness forms at the insulator-semiconductor interlace, (b) V, > V , Vlt - Vy, the channel is pinched ofl at the drain contact. The white area that separates the p-lype substrate from the ii-lypc contacts and channel represents the depletion layer.

Otherwise, the effect of electrode potential and kinetic parameters as contained in the relevant expression for the PMC signal (21), which controls the lifetime of PMC transients (40), may lead to an erroneous interpretation of kinetic mechanisms. The fact that lifetime measurements of PMC transients largely match the pattern of PMC-potential curves, showing peaks in accumulation and depletion of the semiconductor electrode and a minimum at the flatband potential [Figs. 13, 16-18, 34, and 36(b)], demonstrates that kinetic constants are accessible via PMC transient measurements, as indicated by the simplified relation (40) derived for the depletion layer of an n-type electrode. 

More subtle effects of the dielectric constant and the applied bias can be found in the case of semiconductors and low-dimensionality systems, such as quantum wires and dots. For example, band bending due to the applied electric field can give rise to accumulation and depletion layers that change locally the electrostatic force. This force spectroscopy character has been shown by Gekhtman et al. in the case of Bi wires [38]. 

In Eq. (4.5.5), describing an n-type semiconductor strongly doped with electron donors, the first and third terms in brackets can be neglected for the depletion layer (Af0 kT/e). Thus, the Mott-Schottky equation is obtained for the depletion layer,... 

When Es > FB, region (b), a depletion layer forms in the semiconductor due to the bending of the bands under the influence of the electric field. Increasing the potential increases this band bending and so increases the effective barrier to tunnelling it represents. However, the high doping level... 

A constant bias potential is applied across the sensor in order to form a depletion layer at the insulator-semiconductor interface. The depth and capacitance of the depletion layer changes with the surface potential, which is a function of the ion concentration in the electrolytic solution. The variation of the capacitance is read out when the semiconductor substrate is illuminated with a modulated light and the generated photocurrent is measured by means of an external circuit. 

Mutatis mutandis the same terminology is applied to the surface of p-type semiconductors. So if the bands bend upward, we speak of an enrichment layer if they bend downward, of a depletion layer. 

Figure 7.4 Band bending at the interface between a semiconductor and an electrolyte solution (a)-(c) n-type semiconductor (a) enrichment layer, (b) depletion layer, (c) inversion layer (d)-(f) p-t.ype semiconductor (d) enrichment layer, (e) depletion layer, (f) inversion layer.

Figure 7.5 Mott-Schottky plot for the depletion layer of an n-type semiconductor the flat-band potential Eft, is at 0.2 V. The data extrapolate to Eft, + kT / eo-...

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

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