Depletion layer thickness

Inspection of equations (33) and (45) confirms that the flux. 7, is maximal for 6 = 0. It decreases with increasing 6, and tends to zero for 6 = tt, where the depletion layer thickness is no longer small compared to r0. This result is not practically important, since the fluxes for 6 close to tt are relatively small and hardly count in the total transport rate. It may also be noted that, as a consequence of the approximations in the derivation, the limit v —> 0 of equation (45) does not approach the purely diffusional value given by ro. 

The concentration of constituent B becomes negligible at the surface of the mineral grain. Gradually, the rate of mass diffusion of B (Eq. 5.21) through an increasing depleted layer (y) becomes slower and is equal to the rate of surface-controlled dissolution of A (Eq. 5.22). Thus, a pseudosteady state is attained and the depleted layer thickness stabilizes. The rates of reaction of solid layer diffusion (Eq. 5.21) and of surface controlled dissolution become equal ... 

As a rule of thumb the optimum depletion layer thickness is that defined by half the period of the required modulation response, i.e., at 2 GHz bandwidth and a carrier velocity of 100,000 m/sec the optimum depletion layer thickness is ca. 50... 

In one of the most common types of photodiodes used for time-resolved work, the p-i-n photodiode (see Figure 12.24), the depletion layer thickness (i for intrinsic) is fabricated to obtain this optimum performance. Manufacturers usually give full specification sheets detailing, active area, time/frequency response, responsivity amps/watt (AAV) at a given wavelength, dark current, depletion layer capacitance, and bias volts such that with minimal external electronics devices can be made operative. 

Kiguchi M, Nakayama M, Fujiwara K, Ueno K, Shimada T, Saiki K (2003) Accumulation and depletion layer thickness in organic field effect transistors. Jpn J Appl Phys 42 L1408-L1410... 

Thus, for deep levels it is possible that the region x2 — X in which they are effective as traps is substantially less than the total depletion layer thickness W. For the case of a current transient the effect of the edge region is to change the expression given by Eq. (18) to (Grimmeiss, 1977)... 

Suppose that the rate of an electrode reaction at the interface with holes involved is sufficiently high so that each hole approaching the electrode surface is consumed. Under such conditions the change in the electrode potential affects the hole photocurrent mainly through a change in the depletion layer thickness Lsc, which depends on [see Eq. (20a)]. If the light is absorbed weakly (a"1 Lsc + Lp), the photocurrent must, obviously, be proportional to the region thickness, from which the surface collects holes,... 

Straight lines plotted in the coordinates iph — < sc or iph —

Mott-Schottky plots C 2 —

straight line segments intersect at a single point. For materials studied in the works cited below, this point coincides, within 0.2 V, with the value of q>tb measured independently by the differential capacity technique. 

Here, A is the depletion layer thickness (assumed equal to the radius of gyration of the polymer, RG). H = r - 2a is the surface-to-surface particle separation, V ° is the molar volume of the solvent, and ji and ji are the solvent chemical potentials for the polymer solution and the pure solvent. It appears that the assumption A = RG is generally acceptable providing that the polymer solution is in the dilute concentration regime. At higher polymer concentrations, however, the value of A is reduced according to the relationship (Vincent, 1990) ... 

Vincent, B. (1990). The calculation of depletion layer thickness as a function of bulk polymer concentration. Colloids and Surfaces, 50, 241-249. 

While experiments involving solution-phase reactants have provided deep insights into the dynamics of heterogeneous electron transfer, the magnitude of the diffusion-controlled currents over short timescales ultimately limits the maximum rate constant that can be measured. For diffusive species, the thickness of the diffusion layer, S, is defined as S = (nDt)1/2, where D is the solution-phase diffusion coefficient and t is the polarization time. Therefore, the depletion layer thickness is proportional to the square root of the polarization time. One can estimate that the diffusion layer thickness is approximately 50 A if the diffusion coefficient is 1 x 10-5 cm2 s-1 and the polarization time is 10 ns. Given a typical bulk concentration of the electroactive species of 1 mM, this analysis reveals that only 10 000 molecules or so would be oxidized or reduced at a 1 pm radius microdisk under these conditions The average current for this experiment is only 170 nA, which is too small to be detected with high temporal resolution. 

Under the same simplifying assumptions as for the PTC thermistor (where the surface states are shared between two grains) the depleted layer thickness d is given by... 

Sensitivity is a strongly microstructure-dependent property, the depletion layer thickness relative to the particle size of the sensing ceramic being the particularly important parameter. 

In both theta and good solvents, the exclusion of chains from the gap when h < 2L, with L as the depletion layer thickness, allows the interaction potential to be written as... 

Figure 5.9. Typical Interfaclal concentration profile of a nonadsorbing polymer. The correlation length which is a measure of the depletion layer thickness, is indicated.

To obtain high counting efficiencies for y or X rays, thick depleted layers (thick intrinsic regions) are needed. These are obtained by drifting Li into crystals of Ge or Si. Ge(Li) crystals are used as detectors for y rays, because of the high density of Ge,... 

There are, however, important differences between the phase behavior of sticky spheres and that of small molecules, which arise from differences in the relative ranges of the attractive potentials. These differences have been explored in a wonderful set of calculations and experiments by Cast et al. (1983) and Pusey and coworkers (Uett et al. 1995) for suspensions of spheres that are made to attract each other by the polymer-depletion mechanism. In such systems, the range of the attractive potential relative to the sphere size can be varied by controlling the ratio = Aj fa of the polymer depletion-layer thickness to the sphere radius. For 0 the potential is short-ranged, like that of sticky hard spheres,... 

The main approach to reach higher sensor sensitivity is based on maximization of the electron depletion layer compared with the semiconducting core this can be realized by decreasing the particle size down to the scale of the depletion layer thickness.6-8 Oxide semiconductors in the form of nanocrystalline powders,9-11 nanorods,12 nanowires,13-15 nanotubes,1617 and nanobelts18 with a high surface area/ volume ratio have been studied intensively as highly sensitive materials. 

At pseudo steady state, the thickness of the cation depleted layer is a function of pH. Thickness will decrease with increasing H+ ion concentration in bulk solution. Congruent dissolution will result immediately from low pH solutions. In practical situations, the depleted layer thickness has been estimated to be 2-17 A (Schott et al., 1979). For A1 or Si dissolving from a feldspar grain at pH 4, typical parameters for Eq. 4 are... 

Integration of Poisson s equation in the depletion layer, for example, results in a depletion layer thickness W in terms of the voltage drop V across the layer ... 

Fig. 16.11 Diagrammatic representation of the dependence of the overiap volume upon (a) the depletion layer thickness at constant particle radius and (b) particle radius at constant depletion layer thickness. Note that the separation between the particles (Ho) is held constant.

The potential dependence of the photocurrent is determined in the model by the dependence of the depletion layer thickness on the band-bending... 

Microelectrodes open up the possibility of probing redox processes in small sample volumes or physically small spaces. For example, the redox properties of sample volumes as small as a few picoliters have been interrogated. Experiments of this kind are possible because, as described by Eq. (10), for solution phase reactants, the depletion layer thickness, S, depends on the experimental timescale. 

The total amount of charge is related to the depletion layer thickness via... 

Fig. 3.16 Simulated impedance spectra (Bode plots) for the R(RC) circuit from Fig. 3.12c. The simulation includes a simple model that describes the bandwidth limitation of a (hypothetical) potentiostat. Several parameters are varied (a) the range resistor, Ri, (b) the depletion layer thickness W (c) the sample diameter ) (d) the resistance parallel to the space charge capacitance, Rsc- The series resistance Rs is fixed at 140 Q and Csc is calculated using Csc = (so Af h where Sr is the dielectric constant (25) and the surface area A is given by ll4nD. Note that the simulation in (a) does not show the increase in noise that one expects at less sensitive current ranges...

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