A theoretical approach to study diffusion in semiconductors is introduced. A mass-energy model for diffusion atoms into target materials has been built up. The diffusion equation written in terms of the incident atom current density (fluence) is introduced. Laplace’s Integral Transform Technique is applied to get the solution. The concentration function is obtained using Fick’s first law that relates the mass transport with the concentration gradient, together with a flux balance equation. Computations for the case of time-independent incident atomic flux of different values of Phosphorus, Gallium, Indium and Arsenic diffused into Silicon target material are given as illustrative examples. Results show that
the penetration depth of Phosphorus atoms into Silicon is much greater than that for Indium atoms, while the concentration atoms of Phosphorus atoms in Silicon is much less than that for Indium atoms. The same behavior is shown with respect to Arsenic and Gallium atoms diffused in Silicon target. |
