Depletion-layer width

Figure 13. Absorption length La and depletion layer width W of an ideally smooth WSe2 electrode in contact with an electrolyte, assuming e = 9 and n,= X 106...

Figure 15. Schematic of trajectories of minority carriers for a surface with a step exposed to the electrolyte (the step height d is assumed to equalize approximately the depletion layer width)...

It thus appears that even on metal-free SrTi03 conduction-band electrons are the primary reductants. Since similar reaction rates occur on pre-reduced and stoichiometric crystals with disparate depletion layer widths, the electrons do not tunnel through the depletion layer. With no Pt to provide an outlet for electrons at potentials far positive of the flatband potential, strong illumination would flatten the bands almost completely and allow electrons to reach the semiconductor surface. The presence of both electrons and holes at the surface could lead to unique chemistry as well as high surface recombination rates. 

The sensing mechanisms of the tin oxide based sensors have been discussed in many publications (9,10,11). The most widely accepted model for tin oxide based sensors operated at temperatures <400°C is based on the modulation of the depletion layer width in the semiconductor (sensor) due to chemisorption as illustrated schematically in Figure 6. For C2H 0H and Sn0x (or PdAu/Sn0x) interaction, the possible reaction steps may be expressed by the following equations ... 

H reacts with 0"2, and the released electrons are injected back to the SnOx conduction band, causing the depletion layer width to decrease. Hence, both the carrier concentration and carrier mobility increase. 

Another possible effect of PdAu deposits on PdAu/SnOx sensors is through the formation of a Schottky barrier between PdAu and SnOx, as in the case of the Pd/CdS hydrogen sensor. If such a barrier is formed, then a depletion layer is created inside the semiconductor tin oxide. Since the Pd work function can be reduced by hydrogen absorption through dipole or hydride formation (14,15), the width of the depletion layer in tin oxide may be reduced. The reduction of the depletion layer width causes the sample resistance to decrease. Such a possibility was checked and was ruled out, because a good ohmic contact was obtained between Pd (-50 nm thick) and SnOx- It is also commonly known that gold forms an ohmic contact with tin oxide. 

The barrier is characterized by the barrier height, O3, the built-in potential V, and the depletion layer width. An ideal Schottky contact has a barrier height and built-in potential given by,... 

The depletion layer profile contains information about the density of states distribution and the built-in potential. The depletion layer width reduces to zero at a forward bias equal to and increases in reverse bias. The voltage dependence of the jimction capacitance is a common method of measuring W V). Eq. (9.9) applies to a semiconductor with a discrete donor level, and 1 is obtained from the intercept of a plot of 1/C versus voltage. The 1/C plot is not linear for a-Si H because of the continuous distribution of gap states-an example is shown in Fig. 4.16. The alternative expression, Eq. (9.10), is also not an accurate fit, but nevertheless the data can be extrapolated reasonably well to give the built-in potential. The main limitation of the capacitance measurement is that the bulk of the sample must be conducting, so that the measurement is difficult for undoped a-Si H. 

The structure of a p-4-n device is shown in Fig. 10.1. The depletion layer width of low defect density undoped a-Si H at zero bias is about 1 pm, but is less than 100 A in heavily doped material (see Fig. 9.9). The p and n layers provide the built-in potential of the junction but contribute virtually nothing to the collection of carriers. Therefore the doped layers need be no more than the width of the depletion layer to establish the junction-any additional thickness unnecessarily reduces the charge collection by absorbing incident light. An efficient sensor usually requires that the undoped layer be as thick as possible to absorb the maximum flux of photons, but it cannot be thicker than... 

Based on these characteristics, porous silicon may be described as a random array of channel-like pores or etch tunnels growing in <100) directions. For the case of n-type silicon these channels are isolated from each other and, for etching in the dark, the pore spacing is approximately equal to the depletion layer width at a planar surface [83-86]. For the case of p-type silicon the channels are interconnected. The... 

Understanding of the electrostatics across nanocrystalline semiconductor film-electrolyte junctions presents interesting challenges, particularly from a theoretical perspective. Concepts related to space-charge layers, band-bending, flat-band potential and the like (Section 1.3) are not really applicable here because the crystallite dimensions comprising these layers are comparable to (or even smaller than) nominal depletion layer widths. 

Impedance spectroscopy and electrochemical dye desorption experiments have been employed [339] to study the electrical characteristics of Ti02 nanocrystalline films in the dark. This study and the others cited above demonstrate how the conductivity changes (as a result of electron injection from the support electrode) can cause the porous/nanocrystalline layer to manifest itself electrically, such that the active region moves away (i.e., outward) from the support as the forward bias voltage is increased. The potential distribution has also been analyzed depending on whether the depletion layer width exceeds or is smaller than the typical dimension of the structural units in the nanocrystalline network [338]. 

Fig. 1. Potential distribution at the interface between a concentrated electrolyte and (a) a metal (b)-(e) a semiconductor. In (c) (e), the (positive) potential applied to the interface increases this potential is accomomodated entirely within the semiconductor and is manifested in a steadily increasing depletion-layer width.

The redistribution of the space charges N and the built-in potential Vbi with a depletion region are governed by the Poisson equation. Analogous to inorganic semiconductor, the depletion layer width W is expressed as... 

If a negative potential is applied across the sensor, electrons are repelled from the semiconductor -insulator interface forming a layer depleted in majority carriers. The depletion layer can be modeled as an insulator with a width (and therefore capacitance, Cd) that is a function of the bias potential. As the bias potential becomes more negative, the depletion layer width increases, and Cd decreases, until the maximum depletion layer width is attained. 

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