Electron diffusion velocity

Barrier, PE, and the Electron Diffusion Velocity, VD. Subscript o indicates H+ Adsorption has been Neglected. ... 

FIGURE 8.6 Evolution of the electron diffusion coefficient in LAr starting with an initial velocity 4.8 times the thermal velocity. Reproduced from Mozumder (1982). 

Up to now, only hydrodynamic repulsion effects (Chap. 8, Sect. 2.5) have caused the diffusion coefficient to be position-dependent. Of course, the diffusion coefficient is dependent on viscosity and temperature [Stokes—Einstein relationship, eqn. (38)] but viscosity and temperature are constant during the duration of most experiments. There have been several studies which have shown that the drift mobility of solvated electrons in alkanes is not constant. On the contrary, as the electric field increases, the solvated electron drift velocity either increases super-linearly (for cases where the mobility is small, < 10 4 m2 V-1 s-1) or sub-linearly (for cases where the mobility is larger than 10 3 m2 V 1 s 1) as shown in Fig. 28. Consequently, the mobility of the solvated electron either increases or decreases, respectively, as the electric field is increased [341— 348]. 

Woodall et al.36 have analyzed the relationship between surface recombination velocity and the steady state band gap luminescence in GaAs. They calculate for 534nm excitation that a decrease in vs from 106cm/sec to 104cm/sec will triple the quantum efficiency at a 2.5Mm deep p-n junction if the hole diffusion length, Lp, is 3jim, and the electron diffusion length, L is 4/im. 

Theory predicts that the mobility decreases as T 3/2 because of lattice scattering (8). But because electrons have higher velocities at high temperatures, they are less effectively scattered by impurities at high temperatures. Consequently, impurity scattering becomes less important with increasing temperature. Theoretical models predict that the mobility increases as T3/2/nj, in which nx is the total impurity concentration (8). The mobility is related to the electron diffusivity, Dn, through the Einstein relation... 

The uncertainty principle This principle (due to W. Heisenberg) states that the product of the uncertainties in the measured position and velocity of an electron is larger than a quantity, h, which is Planck s constant (very, very small, but not zero ). This principle excludes the possibility that the negatively charged electron will rest on the positively charge nucleus (in which case, there is no uncertainty in either its position or its velocity). Therefore, the electron diffuses in space (becomes delocalized) around the nucleus, and the position of its highest probability may be used to define the atomic radius. 

The solid solution KCl-RbCl differs basically from the solid solution NiO-MgO in two ways. Firstly, the system KCl-RbCl exhibits purely ionic conduction. The transport numbers of electronic charge carriers are negligibly small. Secondly, a finite transport of anions occurs. Because of these facts, the atomic mechanism of the solid state reaction between KCl and RbCl is essentially of a different sort than that between NiO and MgO. Once again, the diffusion profile exhibits an asymmetry (see Fig. 6-1). However, in this case the asymmetry arises not so much because of the variation of the defect concentration with composition, but rather because of the different mobilities of the ions at given concentration. Were the transport number of the chloride ions negligible, then the diffusion potential (which would be set up because of the different diffusion velocities of potassium and rubidium) would ensure that the motion of the two cations is coupled. If, on the contrary, the transference number of the chloride ions is one, then there is no diffusion potential, and the motion of the two cations is decoupled. 

Up until the early 1960 s the electron transport coefficients w (electron drift velocity) and (transverse electron diffusion coefficient) were considered to be independent of N. This is probably because the experimental studies were traditionally conducted at low N (gas pressures < 1 atm). The transport coefficients w and [actually D /y where ]i is the electron mobility (w=yE)] are functions of the gas, T, and E/N (e.g., see Hunter and Christophorou, 1984). 

The movement of the fast electrons leads to the fonnation of a space-charge field that impedes the motion of the electrons and increases the velocity of the ions (ambipolar diffusion). The ambipolar diffusion of positive ions and negative electrons is described by the ambipolar diffusion coefficient... 

Processing variables that affect the properties of the thermal CVD material include the precursor vapors being used, substrate temperature, precursor vapor temperature gradient above substrate, gas flow pattern and velocity, gas composition and pressure, vapor saturation above substrate, diffusion rate through the boundary layer, substrate material, and impurities in the gases. Eor PECVD, plasma uniformity, plasma properties such as ion and electron temperature and densities, and concurrent energetic particle bombardment during deposition are also important. 

Figure 4. The following data were used leak radius r0 (40 micron), leak conductance F = 1 cc. sec.-1, gas pressure (air) p (20 torr), diffusion coefficient (26) for ions Di — 2 sq. cm. sec.-"1, for electrons De = 2000 sq. cm. sec.-1 (at 20 torr air). The flow velocities were assumed independent of 6 and (spherical polar coordinates). The spherically symmetrical flow pattern, which obviously overestimates the flow velocity for large values of 6 was chosen because of its simplicity. The velocity of the radially directed flow at a distance r is v = F/2irr2. The time re-...

In order to calculate the rates for electron impact collisions and the electron transport coefficients (mobility He and diffusion coefficient De), the EEDF has to be known. This EEDF, f(r, v, t), specifies the number of electrons at position r with velocity v at time t. The evolution in space and time of the EEDF in the presence of an electric field is given by the Boltzmann equation [231] ... 

Two other attempts, without the use of a distribution function, are worth mentioning, as these are operationally related to experiments and serve to give a rough estimate of the thermalization time. Christophorou et al. (1975) note that in the presence of a relatively weak external field E, the rate of energy input to an electron by that field is (0 = eEvd, where vd is the drift velocity in the stationary state. Under equilibrium, it must be equal to the difference between the energy loss and gain rates by an electron s interaction with the medium. The mean electron energy is now approximated as (E) = (3eD )/(2p), where fl = vd /E is the drift mobility and D is the perpendicular diffusion coefficient (this approximation is actually valid for a Maxwellian distribution). Thus, from measurements of fl and D the thermalization time is estimated to be... 

When applied to the motion of ions in a crystal, the term drift applies to motion of ions under the influence of an electric field. Although movement of electrons in conduction bands determines conductivity in metals, in ionic compounds it is the motion of ions that determines the electrical condu-ctivity. There are no free or mobile electrons in ionic crystals. The mobility of an ion, ji, is defined as the velocity of the ion in an electric field of unit strength. Intuitively, it seems that the mobility of the ion in a crystal should be related to the diffusion coefficient. This is, in fact, the case, and the relationship is... 

This is the regime of cathodic currents. The silicon atoms of the electrode do not participate in the chemical reaction in this regime. An n-type electrode is under forward bias and the current is caused by majority carriers (electrons). The fact that photogenerated minority carriers (holes) are detectable at the collector indicates that the front is under flat band or accumulation. A decrease of IBC with cathodization time is observed. As Fig. 3.2 shows, the minority carrier current at the collector after switching to a cathodic potential is identical to that at VQcp in the first moment, but then it decreases within seconds to lower values, as indicated by arrows in Fig. 3.2. This can be interpreted as an increase of the surface recombination velocity with time under cathodic potential. It can be speculated that protons, which rapidly diffuse into the bulk of the electrode, are responsible for the change of the electronic properties of the surface layer [A17]. However, any other effect sufficient to produce a surface recombination velocity in excess of 100 cm s 1 would produce similar results. 

The diffusion coefficient D can be thought of as the velocity of the analyte as it moves from the bulk of the solution towards the electrode just prior to the electron-transfer reaction. Because D is a velocity, larger values of D relate to a faster motion of analyte through the solution, while smaller values relate to slower motion. It is assumed, when deriving equation (6.3), that diffusion is linear... 

Diffusion coefficient, D A measure of the velocity of electroanalyte as its diffuses through solution prior to an electron-transfer reaction. 

Along with electronic transport improvements must come attention to substrate transport in such porous structures. As discussed above, introduction of gas-phase diffusion or liquid-phase convection of reactants is a feasible approach to enabling high-current-density operation in electrodes of thicknesses exceeding 100 jxm. Such a solution is application specific, in the sense that neither gas-phase reactants nor convection can be introduced in a subclass of applications, such as devices implanted in human, animal, or plant tissue. In the context of physiologically implanted devices, the choice becomes either milliwatt to watt scale devices implanted in a blood vessel, where velocities of up to 10 cm/s can be present, or microwatt-scale devices implanted in tissue. Ex vivo applications are more flexible, partially because gas-phase oxygen from ambient air will almost always be utilized on the cathode side, but also because pumps can be used to provide convective flow of any substrate. However, power requirements for pump operation must be minimized to prevent substantial lowering of net power output. 

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