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On the basis of the Green function method, analytical solutions of thediffusion equation which describes nonstationary migration of nonequilibriuminterstitial impurity atoms have been derived. It is supposed that the initialdistribution of nonequilibrium impurity interstitials is formed due to ionimplantation and, therefore, is described by the Gaussian function. Thecondition of the constant concentration of impurity interstitials (theDirichlet boundary condition) or reflecting boundary condition was imposed onthe surface of a semiconductor. The Dirichlet boundary condition was alsoenforced for the concentration of impurity interstitials in the infinity, i.e.,in the bulk of a semiconductor. On the basis of the solutions derived theredistribution of ion-implanted boron in silicon substrate duringlow-temperature thermal treatment has been simulated. The calculated profile ofboron atoms after annealing agrees well with experimental data. It means thatthe analytical solutions derived can be used both for verifying the numericalresults and for modeling the long-range migration of nonequilibrium impurityinterstitials during low-temperature thermal treatments.

Solution of the nonstationary diffusion equation for interstitial impurity atoms by the method of Green functions