Dopants Diffusion Coefficient

Figure 9 Temperature dependences of dopant diffusion coefficients in 6H-SiC.

A report on doping of polyacetylene by metal halides 462-463) shows that the interplanar spacing increases with the size of the anion and clustering is inferred to occur at low dopant levels as the dopant reflection appears at about 3 mol% while much of the material is still undoped. It is not totally clear whether similar effects might be the result of a combination of slow dopant diffusion and a diffusion coefficient which is dependent on dopant concentration this is discussed in more detail below. 

In many cases the important property will actually be the permeability, which is the product of the diffusion coefficient and the solubility of the dopant in the polymer. The solubility is determined by the degree of interaction between the diffusant and the polymer. The picture is further complicated, since reactions may take place so that several different species are diffusing. The reaction of a gaseous dopant with a conducting polymer is a complicated diffusion and reaction process. We must consider the solubility and diffusion of the molecular gas, the charge-transfer reaction to dope the polymer, the diffusion of the resulting ions in the doped (intercalated) structure and any reaction between the dopant ions and the polymer which may lead to covalent bonding. 

The diffusion behaviour of Shirakawa polyacetylene is complicated by its fibrillar morphology and high surface area, so that weight changes depend on pore transport and surface adsorption, as well as on diffusion into the fibrils. Chien 6) has reviewed earlier studies of the diffusion of dopant counter-ions in Shirakawa polymer and has emphasised the wide range of values of diffusion coefficient which are reported and which depend a great deal upon the morphological model chosen to interpret experimental data. 

Oxygen is also a dopant for polyacetylene, but on exposure the conductivity rises to a maximum then rapidly declines as oxidation of the polymer backbone occurs, as shown in Fig. 21. We have no data on the diffusion coefficient as the process is rapid and is masked by the reaction of oxygen with the polymer. The kinetics are first-order, implying that the doping reaction is rapid, goes to less than 1 mol%, and is then followed by irreversible oxidation of the polymer. Based on the observa-... 

Table 3. Diffusion coefficients for dopant counter ions...

We have also estimated diffusion coefficients in Durham polymer using the electrochemical approach. Using this method the diffusion coefficient of Li+ was found to be 2.5 x 10 13 cm2 s-1 at a dopant level of 0.37 mol% and that of C104-1.3 x 10-14 cm2 s-1 at a level of 0.05 mol%. Increasing the doping level caused the diffusion coefficient to fall slightly. 

Purification of Solution. An approximate model for the purification of the solution can be developed by assuming that a stagnant melt initially contains an impurity at a uniform concentration, Cf°, and loss of dopant occurs by evaporation at the top surface. The rate of evaporation is assumed to be directly proportional to the difference in concentrations at the top surface and at equilibrium. If the proportionality constant is z, the diffusion coefficient of the impurity in the melt is D v and the depth of the melt is Z, then the following expression for the impurity concentration in the melt,... 

The analytical solutions to Fick s continuity equation represent special cases for which the diflusion coefficient, D, is constant. In practice, this condition is met only when the concentration of diffusing dopants is below a certain level ( 1 x 1019 atoms/cm3). Above this doping density, D may depend on local dopant concentration levels through electric field effects, Fermi-level effects, strain, or the presence of other dopants. For these cases, equation 1 must be integrated with a computer. The form of equation 1 is essentially the same for a wide range of nonlinear diffusion effects. Thus, the research emphasis has been on understanding the complex behavior of the diffusion coefficient, D, which can be accomplished by studying diffusion at the atomic level. 

Point Defect Models of Diffusion in Silicon. Under conditions of thermal equilibrium, a Si crystal contains a certain equilibrium concentration of vacancies, C v°, and a certain equilibrium concentration of Si self-interstitials, Cz°. For diffusion models based on the vacancy, Cv° Cf and the coefficients of dopant diffusion and self-diffusion can be described by equation 27 (15)... 

The hydrogen diffusion activation energy increases with time because of the dispersive hydrogen motion. The relaxation of defects and dopants typically involves a much shorter hydrogen diffusion distance than in measurements of the diffusion coefficient, so that the activation energy of t is smaller than of Dg and is given by... 

Oxygen migration in doped cerias has been recently studied with molecular dynamics methods by Inaba et al and Hayashi et These authors examined the systems (Ce02)i (A 203) /2 (where M = Y Gd La) with dopant contents in the range 0 — 15% mol. The diffusion coefficient of oxygen at 1273 K was evaluated from the simulations at different compositions with a maximum at around 10% mol of dopant. 

During growth, this phenomenon known as exodiffusion does not take place because the gas phase is deliberately saturated to dope the layer. However, it starts at the end of the growth during the cooling process. The importance of the phenomenon depends on the dopant species it varies with its diffusion coefficient, which is a function of temperature and with its saturation pressure in the gas phase. The nature of the carrier gas also affects the value of the diffusion coefficient [20]. 

This phenomenon is again guided by the diffusion parameters temperature and diffusion coefficient. The autodoping phenomenon combined with the exodiffusion, which occurs during the rise in temperature before the growth step, explains that the profile of the dopant concentration between the epitaxial layer and the substrate cannot be abrupt. The concentration profile at the junction shows a subdoping of the substrate and an overdoping of the epitaxial layer as shown in Fig. 10.7. 

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