Electronic Stopping Power for Low Energy Ions

Abstract

A procedure to be used in ion implantation calculations has been developed to determine the stopping power of an ion at low energy as a function of its effective charge. The ion effective charge accounts for screening of the ion and has been found to have considerable effect on the stopping power through its dependence on the target electron density.Steps in the procedure include: the calculation of the Fermi momentum of the target, calculation of the relative velocity between the projectile and target electron cloud, determination of the screening distance for the ion, and calculation of the proton stopping power Sp according to the density-functional formalism. The ion stopping power is then S(ZI):(Z) 2Sp,• where Z* is the ion effective charge. The procedure can be applied to semiconductors and metals. Comparisons are reported with the predictions of the Firsov and Lindhard methods which do not include any effective charge or shell structure considerations. The computer program MARLOWE has been modified to include this method for calculating the stopping power. Results in the form of implanted boron profiles in silicon will be presented.

Phenomenological electronic stopping-power model for molecular dynamics and Monte Carlo simulation of ion implantation into silicon

“…Later, a purely local version of the BK theory was developed to take into account the charge distribution of the electrons 43,44 . Comparison with other electronic stopping models, such as Lindhard and Scharff 4 , Firsov 45 , and the above nonlocal implementation 42 , showed a marked improvement in modeling electronic stopping in the channel 7,43,44 . Good agreement between simulated dopant profiles and the SIMS profiles for boron implants into 100 single crystal silicon was obtained.…”

“…First, in comparison with other electronic stopping models used in Monte Carlo simulations based on the MAR-LOWE platform, we stress that in our model the effective charge is a nonlocal quantity, neither explicitly dependent on the impact parameter nor on the charge distribution, and the stopping power for a proton depends on the local charge density of the solid. A purely nonlocal version of the BK theory was implemented into MARLOWE 42 , in which both the effective charge and the stopping power for a proton depend on a single nonlocal parameter, namely, the averaged one electron radius. Its results demonstrated that energy loss for well-channeled ions in the keV region has high sensitivity to the one-electron radius in the channel.…”

“…Its results demonstrated that energy loss for well-channeled ions in the keV region has high sensitivity to the one-electron radius in the channel. It was pointed out that a correct density distribution is needed to account for the electronic stopping in the channel 8,42 . Later, a purely local version of the BK theory was developed to take into account the charge distribution of the electrons 43,44 .…”

Simulación de la implantación iónica en semiconductores

“…En un estado inicial la distribución de momentos en el plano de la superficie es una función delta, δ(E 0 ,v), dada por la energía de los iones E 0 y su dirección. El momento puede ser sustitudo por su energía E y elángulo θ si nos encontramos en un plano 6 . En cada paso del cálculo, la redistribución de las partículas en el espacio de momentos para una profundidad x y en un elemento dx se obtiene resolviendo la ecuación 3.70.…”