A multiple pass application of the Boltzmann transport equation for calculating ion implantation profiles at low energies

The Boltzmann transport equation is used to predict ion implantation profiles at low implantation energies, with particular attention to the effects of ions which are backscattered. In previous work the transport equation was applied stepwise into the target and all backscattered ions were considered stopped at the point where they were scattered. This gives good results when the scattering is forward-peaked. However, when the incident ion is much lighter than the target atoms, a large fraction of the incident ions are backscattered. For example, when boron is implanted into silicon at 15 keV, 60% of the ions are backscattered. To obtain greater accuracy under these conditions, the momentum distribution of the backscattered ions is stored after each step and their motion is followed by making a second pass backward through the implanted layer. Further passes back and forth can be used until all the ions have stopped. The extra ion motion considered will increase the calculated recoil generation. The effects are large at interfaces between light and heavy target layers, such as silicon nitride on gallium arsenide, and may lead to important mixing effects in certain sputtering situations. (orig.)