Drift-current density

If we place an ionic conductor between parallel-plate blocking electrodes that produce an electric field E parallel to the x-axis, the electrostatic potential varies as — xE on passing from one electrode at x = 0 to the other. At equilibrium, the mobile-ion concentration Cj(x) is proportional to exp(qEx/kT), and the ionic drift-current density (7(E in the field is balanced by a diffusion current due to the concentration gradient (Fick s law) ... 

The electron current density J has units of A/cm and in a semiconductor results from drift and diffusion. In the absence of concentration gradients, equation 7 reduces to Ohm s law, = nqp E = [Pg.346]

The device model describes transport in the organic device by the time-dependent continuity equation, with a drift-diffusion form for the current density, coupled to Poisson s equation. To be specific, consider single-carrier structures with holes as the dominant carrier type. In this case,... 

In the binary-electrolyte experiments carried out at large, constant cell potentials, the cell current is ohmically limited. If the conductivity of the solution is proportional to the concentration of electrolyte, the current density at a given overpotential is then proportional to Cb. Under this regime, the concentration cancels out of Eq. (2.3), and the velocity is proportional to the applied potential. For this special case, the velocity can be expressed in terms of the anion drift velocity [27, 28]. For a binary solution, this is equivalent to replacing (1 — t+) by t and i by the ohmically limited current density. 

Charge-transfer resistance and the related exchange current density are the two most important factors in the operation of all electrochemical sensors. They play a role in selectivities, response times, baseline drift, and so on. In the following section, we take a closer look at what they are and how they are determined. 

In an exact calculation of the distribution of the electrostatic potential, the carrier densities and their currents, (4.81)-(4.87) are solved simultaneously, bearing in mind that only the sum of the diffusion and drift currents has physical significance. Due to the complexity of the above relations and in particular due to the coupling of electron and hole concentrations by Poisson s equation, analytical solutions exist only for a few, very specific conditions. Generally, the determination of local carrier concentrations, current densities, recombination rates, etc., requires extensive numerical procedures. This is especially true if they vary with time, but even in the steady state context. 

Recalling Eq. 12.13, it is seen that the second factor to be evaluated is j, the ion current density in the undistorted field. This is the product of the charge per unit volume and the drift velocity of the ions. The... 

Frohlich (1947) based his calculations on the hypothesis of the energy-level scheme shown in Fig. 6.1, where conduction electrons are derived from impurity levels lying deep (V = 1 eV or more) in the forbidden zone. There is also a set of shallow traps spread below the conduction-band edge (F> AF> kT). In outline, the theory of breakdown is then as follows. In an applied electric field E, energy is transferred directly to the conduction electrons (charge e, mass m) at a rate A = jE, where j is the current density. If we suppose that each electron is accelerated in the field direction for an average time 2r between collisions at which its energy is completely randomised, then the mean drift velocity of the conduction electrons in the field direction... 

The driving force for ionic drift, i.e., the electric field X, not only has a particular magnitude, it also acts in a particular direction. It is a vector. Since the ionic current density j, i.e., the flow of electric charge, is proportional to the electric field operating in a solution [Eq. (4.128)],... 

It can be concluded therefore that the total current density j is made up of two contributions, one due to a flux of positive ions and the other due to a flux of negative ions. Furthermore, assuming for the moment that the drift of positive ions toward the... 

Current Density Associated with the Directed Movement of Ions in Solution, in Terms of Ionic Drift Velocities... 

It is the aim now to show how the concept of drift velocity can be used to obtain an expression for the ionic current density flowing through an electrolyte in response to an externally applied electric field. Consider a transit plane of unit area normal to the direction of drift (Fig. 4.61). Both the positive and the negative ions will drift across this plane. Consider the positive ions first, and let their drift velocity be or simply v. Then, in 1 s, all positive ions within a distance cm of the transit plane will cross it. The flux 7+ of positive ions (i.e., the number of moles of these ions arriving in 1 second at the plane ofunit area) is equal to the number ofmoles ofpositive ions in a volume of 1 cm in area and v cm in length (with i = 1 s). Hence, 7 is equal to the volume in cubic centimeters times the concentration c. expressed in moles per cubic centimeter... 

Fig. 4.61. Diagram for the derivation of a relation between the current density and the drift velocity.

This drift velocity produces a current density given by [c/. Eq. (4.154)]... 

The fundamental equation for the current density (flux of charge) as a function of the drift velocity has been shown to be... 

If W is the electron drift velocity in the direction of the electric field, the current density or amount of (unit) charge transport per square centimeter per second is n W. Since P is defined as the reaction rate coefficient per unit charge transport, it follows that... 

The inward motion of anions is assumed to be the dominant ionic transport across the oxide. The ionic movement is field-assisted drifting and is the rate-limiting process. The diffusion of ions at room temperature is considered to be too slow to account for the oxide growth rates. The current density is written as... 

Let us calculate the correction to the proton polaron direct current density conditioned by light-induced transitions between the sites. This photocurrent calculation is analogous to that of the correction to the drift activation current carried out in the previous subsection [the analogy lies in the fact that operator (276) is similar to the correction to the Hamiltonian if the electric field is taken into account, with the correction being nondiagonal on the operator of the coordinate see expression (236)]. 

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