Analytical calculations of some ion-implantation depth distributions

Power-law range, damage, and ionization distributions are calculated analytically in the path-length approximation for the equal-mass case. An analytical expression is given for the asymptotic (large-depth) behaviour of the distributions, and the form of the small-depth behaviour is given. Also, the entire distribution is calculated as an inverse Mellin transform, both by numerical integration and by a numerical application of the stationary-phase method. The asymptotic expression is useful only in the extreme tail of the distribution, the numerical integration is generally valid, and the numerical stationary-phase method is useful except at very small depths. Results are shown for the power parameter m = 0.055, 0.311 and 0.48. (author)