Exact analytical solution to diffusion equation for ion-implanted dopant profile evolution during annealing

Moroi, D. S.; Hemenger, P. M.
January 1987
Applied Physics Letters;1/19/1987, Vol. 50 Issue 3, p155
Academic Journal
Exact solution in analytical form to the dopant diffusion equation for an arbitrary initial implanted profile is obtained with a judicious choice of variables. The diffusivity can be an arbitrary function of the dopant concentration and the temperature of a sample, provided only that their gradients at the front surface of an ion-implanted semi-infinite semiconductor wafer are zero. As an example, we derive a closed-form expression for the annealed concentration profile for the special case in which the diffusivity is a product of a certain power of the concentration and an arbitrary function of the temperature, the initial dopant concentration profile is a truncated Gaussian, and the temperature dependent part of the diffusivity is initially a Gaussian. The present calculation is a generalization of the data fitting analysis of ion-implanted dopant profile evolution during annealing by R. Ghez, A. S. Oehrlein, T. O. Sedgwick, F. F. Morehead, and Y. H. Lee [Appl. Phys. Lett. 45, 881 (1984)].


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