Quantitative Study of Near Equilibrium in Dissociative Mechanism of Nickel in Silicon

The dissociative mechanism of nickel in silicon has been studied experimentally, assuming the near equilibrium represented by eq s eq V eq i s V i / / C C C C C C = , where subscripts i, V, and s represent interstitial nickel atoms, vacancies, and substitutional nickel atoms, respectively, superscript eq represents the thermal equilibrium, and A C is the concentration of component A. However, the assumption of the near equilibrium has not yet been verified experimentally, because it is difficult to measure V C in silicon. In the present work, the simultaneous diffusion equations of the dissociative mechanism of nickel in silicon are solved numerically by double-precision FORTRAN without assuming the near equilibrium under the condition of in-diffusion of nickel into a silicon specimen, and the establishment of the near equilibrium is verified. It is also clarified that the near equilibrium is a transitional process which continues until the thermal equilibrium is reached. After the near equilibrium is reached, the very small difference of two nearly equal terms is an important factor in solving the diffusion equations. In other words, high accuracy is necessary to solve the diffusion equations. Concerning this, it is verified that the accuracy of double-precision FORTRAN is sufficiently high to solve the diffusion equations in the present work.