Nonlinear Many-Staged Diffusion

Abstract

We considered and solved the nonlinear diffusion equation formerly. The more complicated but more useful task of many-staged diffusion is solved in this paper. The obtained solution satisfies the initial distribution of the impurities and can be generalized for many-staged diffusion. Using these solutions we can take into account all the stages of a planary transistor formation.

Superdiffusion in Si Crystal Lattice Irradiated by Soft X-Rays

“…∆E/N V = 1.05 eV at the surface of sample. The number of vacancies introduced into the sample can be expressed using a slightly modified formula for the number of impurity atoms introduced by the diffusion process [15]:…”

“…1 we can see that in all experiments with periods of irradiation longer than 15 min the saturation of the sample with vacancies was achieved and that the vacancies acting on the conductivity left the sample during the same time t = 87 min. This process can be described by drive in or second stage diffusion of vacancies from the samples surface [15]. For the second-stage diffusion [15], we have the following relation between the constant vacancy concentration N s1 on the irradiated surface during time t 1 of the first-stage diffusion (until saturation of the sample with the vacancies) and vacancies concentration N s2 at the surface after time t of the second stage of diffusion until vacancies leave the sample…”

“…The number of vacancies introduced into the sample can be expressed using the nonlinear diffusion theory [15] …”

“…Here N is the concentration of vacancies at the surface of the irradiated side (N s1 is the concentration of impurity atoms on the surface after diffusion from the constant source [15] (19) Now we can make an important conclusion that diffusion conditions in the irradiated sample of Si are essentially different from thermal diffusion.…”

Modeling of Thermodiffusion Inertia in Metal Films Heated with Ultrashort Laser Pulses

“…The heat source term Q(x, y, t) can be included as the first stage [11] of thermal diffusion. We use the approximation [12] where electron-phonon coupling constant g for subpicosecond scale of time can be neglected.…”