Three-Dimensional Mathematical Modeling and Simulation of the Impurity Diffusion Process Under the Given Statistics of Systems of Internal Point Mass Sources

A three-dimensional mathematical model and simulation of the impurity diffusion process are developed under the given statistical characteristics of the system of internal stochastically disposed point sources of mass. These sources, possessing varying intensities, are located within the sub-strip according to a uniform distribution. The random source statistics are known, and the problem solution is expressed as the sum of the solution to the homogeneous problem and the convolution of Green’s function with the random point source system. The impurity concentration is averaged. Diffusive fluxes and the total amount of substance passing through any cross-sectional area over a specified time period are modeled using Fick’s laws. General and calculating formulas for averaged diffusive fluxes, including those applicable to steady-state regimes, are derived. A calculating formula for the total substance that has passed through the strip within a given time interval is obtained. A comprehensive software suite is developed to simulate the behavior of the averaged characteristics of the diffusion process influenced by the point source system. The second statistical moments of the impurity concentration are obtained and studied.