Spatial distribution of energy deposited into atomic processes in ion-implanted silicon

Abstract

A method is given for calculating the spatial distribution of the production of a quantity, Q, averaged over many ions incident randomly on a solid for any energy dependent interaction between the ions and target atoms. The method is basically a two step method. First, the spatial distribution of the ions in the solid is followed as the ions lose energy. Then, at each intermediate energy the spatial distribution of Q-production is obtained and the result is integrated over the range of intermediate energies assumed by the ions. Saturation effects are ignored in the procedure so that explicit consideration must be given to saturation effects when applying the method to high dose cases. Annealing and diffusion effects are also ignored, and the method is restricted in applicability to experimental conditions where annealing and diffusion are unimportant. Results of calculations by this method are presented of the depth distribution of energy ultimately deposited into atomic processes for Li⁷, B¹¹, C¹², N¹⁴, O¹⁶, Ne²⁰, Si²⁸, and P³¹ ions incident randomly on silicon with incident energies in the range of 30 to 400 keV. In this particular application of the method migration of the deposited energy through the recoil of struck target atoms has been neglected. Comparison of the results of calculations by this method with moments obtained by Sigmund and coworkers for the equal mass case indicate that for the ions listed above, and for the energy range considered, this approximation is valid. The calculated depth distributions thus represent the final depth distribution of energy deposited into atomic processes.