Charge random walk

Charge transport is an incoherent random walk described by a generalized... 

The diffusion of an impurity atom in a crystal, say K in NaCl, involves other considerations that influence diffusion. In such cases, the probability that the impurity will exchange with the vacancy will depend on factors such as the relative sizes of the impurity compared to the host atoms. In the case of ionic movement, the charge on the diffusing species will also play a part. These factors can also be included in a random-walk analysis by including jump probabilities of the host and impurity atoms and vacancies, all of which are likely to vary from one impurity to another and from one crystal structure to another. All of these alterations can be... 

To obtain a more complete description, we need to find an analytic expression for the pre-exponential factor Dq of the diffusion coefficient by considering the microscopic mechanism of diffusion. The most straightforward approach, which neglects correlated motion between the ions, is given by the random-walk theory. In this model, an individual ion of charge q reacts to a uniform electric field along the x-axis supplied, in this case, by reversible nonblocking electrodes such that dCj(x)/dx = 0. Since two... 

Since one starts off with a larger hole concentration in the //-type of material than exists in the //-type of material, there will initially be more holes taking the p — // random walk titan the n — // random walk. One has stated in microscopic language that there will be diffusion of holes in the// —> // direction [Fig. 7.21(b)]. What is the result of this p—m hole diffusion The net p transport of holes leaves a negative charge on the p material and confers a positive charge on the n material [Fig. 7.21(c)]. A potential difference develops [Fig. 7.21(d)]. Further, this charging of the two sides of the interface and the resultant potential difference acts precisely in such a manner as to oppose further //—>// hole diffusion (Fig. 7.22). 

The driving forces necessary to induce macroscopic fluxes were introduced in Chapter 3 and their connection to microscopic random walks and activated processes was discussed in Chapter 7. However, for diffusion to occur, it is necessary that kinetic mechanisms be available to permit atomic transitions between adjacent locations. These mechanisms are material-dependent. In this chapter, diffusion mechanisms in metallic and ionic crystals are addressed. In crystals that are free of line and planar defects, diffusion mechanisms often involve a point defect, which may be charged in the case of ionic crystals and will interact with electric fields. Additional diffusion mechanisms that occur in crystals with dislocations, free surfaces, and grain boundaries are treated in Chapter 9. 

The absorption of energy by the grains produces conduction electrons and either free or trapped holes. The conduction electrons and the holes diffuse initially by a three-dimensional random walk. In chemically sensitized crystals, the holes are trapped by products of chemical sensitization which thus undergo photo-oxidation. Rapid recombination between a trapped hole and an electron is avoided by the delocalization as an interstitial Ag ion of the nonequilibrium excess positive charge created at the trapping site. Latent pre- and sub-image specks are formed by the successive combination of an interstitial Agi ion and a conduction electron at a shallow positive potential well. 

Once the uncapped NC is ionized (A + B state), we assume the ejected charge carrier undergoes a random walk on the surface of the NC or in the bulk. 

Another refinement of the VRH model consists in assuming that the charges are delocalized over segments of length L, instead of being strictly localized on point sites [40]. This is indeed a more realistic picture, leading to better fits with the data, but it has the drawback that an extra parameter has been added. Note that the temperature dependence, log o- -T y, can be found by other approaches, such as the percolation model, the effective medium approximation (EMA), the extended pair approximation (EPA) [41], the random walk theory, and so on. 

The choice of a Gaussian distribution can be justified by the observation that the optical absorption profiles of well-defined conjugated moieties are Gaussian. Charge transport is treated as a biased random walk amongst the conjugated moieties, which have random site energies described by Equation... 

As described above, the electrons in a semiconductor can be described classically with an effective mass, which is usually less than the free electron mass. When no gradients in temperature, potential, concentration, and so on are present, the conduction electrons will move in random directions in the crystal. The average time that an electron travels between scattering events is the mean free time, Tm. Carrier scattering can arise from the collisions with the crystal lattice, impurities, or other electrons. However, during this random walk, the thermal motion is completely random, and these scattering processes will therefore produce no net motion of charge carriers on a macroscopic scale. 

Before presenting some additional experimental observations, we pause to discuss, qualitatively, how the foregoing trends and dependences may be understood. (A quantitative theory of charge transport in amorphous molecular solids will be discussed later.) In any charge transport process, whether the carriers are electronic or ionic, and whether the mediiun is crystalline, amorphous, or fluid, each individual carrier undergoes a random walk in which there is a preference (large or small, de-... 

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