Thin-source diffusion

The purpose of most experimental studies of diffusion is to obtain accurate diffusion coefficients as a function of temperature, pressure, and composition of the phase. For this purpose, the best approach is to design the experiments so that the diffusion problem has a simple anal3hical solution. After the experiments, the experimental results are compared with (or fit by) the anal3hical solution to obtain the diffusivity. The method of choice depends on the problems. The often used methods include diffusion-couple method, thin-source method, desorption or sorption method, and crystal dissolution method. 

The thin-source method is also referred to as the thin-film method. One surface is cut into a plane surface and polished. A very thin layer is then sprayed or spread onto the surface. The thin layer contains the component of interest, which at high temperature diffuses into the interior of the sample from the polished surface. After the experiment, a section is cut perpendicular to the polished surface. Concentration profile is measured as a function of distance away from this surface. If the length of the concentration profile is much greater than (> 100 times) the thickness of the thin layer on the surface, the problem may be treated as a... 

Tracer diffusivities are often determined using the thin-source method. Self-diffusivities are often obtained from the diffusion couple and the sorption methods. Chemical diffusivities (including interdiffusivity, effective binary diffusivity, and multicomponent diffusivity matrix) may be obtained from the diffusion-couple, sorption, desorption, or crystal dissolution method. 

The form of the solution for one-dimensional diffusion is illustrated in Fig. 5.3. The solution c(x,t) is symmetric about x = 0 (i.e., c(x,t) = c(—x,t)). Because the flux at this location always vanishes, no material passes from one side of the plane to the other and therefore the two sides of the solution are independent. Thus the general form of the solution for the infinite domain is also valid for the semi-infinite domain (0 < x < oo) with an initial thin source of diffusant at x = 0. However, in the semi-infinite case, the initial thin source diffuses into one side rather than two and the concentration is therefore larger by a factor of two, so that... 

Suppose that a very thin planar layer of radioactive Au tracer atoms is placed between two bars of Au to produce a thin source of diffusant as illustrated in Fig. 5.8. A diffusion anneal will cause the tracer atoms to spread by self-diffusion as illustrated in Fig. 5.3. (A mathematical treatment of this spreading out is presented in Section 4.2.3.) Suppose that the diffusion ex-... 

Tracer diffusion coefficients for Li were determined by deposition of a thin source onto polished glass wafers, annealing at 300 to 900C and ion-microprobe determination of the concentration profile. The results conformed to an Arrhenius-type relationship ... 

Dispersion equations, typically the van Deemter equation (2), have been often applied to the TLC plate. Qualitatively, this use of dispersion equations derived for GC and LC can be useful, but any quantitative relationship between such equations and the actual thin layer plate are likely to be fraught with en or. In general, there will be the three similar dispersion terms representing the main sources of spot dispersion, namely, multipath dispersion, longitudinal diffusion and dispersion due to resistance to mass transfer between the two phases. 

Conventional electronic devices are made on silicon wafers. The fabrication of a silicon MISFET starts with the diffusion (or implantation) of the source and drain, followed by the growing of the insulating layer, usually thermally grown silicon oxide, and ends with the deposition of the metal electrodes. In TFTs, the semiconductor is not a bulk material, but a thin film, so that the device presents an inverted architecture. It is built on an appropriate substrate and the deposition of the semiconductor constitutes the last step of the process. TFT structures can be divided into two families (Fig. 14-12). In coplanar devices, all layers are on the same side of the semiconductor. Conversely, in staggered structures gate and source-drain stand on opposing sides of the semiconductor layer. 

Experimental measurements of DH in a-Si H using SIMS were first performed by Carlson and Magee (1978). A sample is grown that contains a thin layer in which a small amount (=1-3 at. %) of the bonded hydrogen is replaced with deuterium. When annealed at elevated temperatures, the deuterium diffuses into the top and bottom layers and the deuterium profile is measured using SIMS. The diffusion coefficient is obtained by subtracting the control profile from the annealed profile and fitting the concentration values to the expression, valid for diffusion from a semiinfinite source into a semi-infinite half-plane (Crank, 1956),... 

K. Fushinobu, D. Takahashi, and K. Okazaki. Micromachined metallic thin films for the gas diffusion layer of PEFCs. Journal of Power Sources 158 (2006) 1240-1245. 

Figure 24. Models illustrating the source of chemical capacitance for thin film mixed conducting electrodes, (a) Oxygen reduction/oxidation is limited by absorption/de-sorption at the gas-exposed surface, (b) Oxygen reduction/ oxidation is limited by ambipolar diffusion of 0 through the mixed conducting film. The characteristic time constant for these two physical situations is different (as shown) but involves the same chemical capacitance Cl, as explained in the text.

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