THE idea of doping semiconductors by ionic bombardment was patented by William Shockley [Sho54] at Bell Laboratories in 1954. Later on, in the 1960s the method of Ion Implantation was developed and over the past 25 years it has become the method of choice for introducing dopants into semiconductors. Early work has been summarized by Gibbons [Gib68] covering developments up to 1968. An overview of work since then can be found in the proceedings of the International Conferences on Ion Implantation [Nam75] and the Conferences on Ion Beam Modification of Materials, and in various books [Rys86b], [Gil88].
During ion implantation dopant atoms are vaporized, accelerated, and directed at a substrate. The individual implanted ion enters the crystal lattice, collides with substrate atoms and electrons, loses gradually its kinetic energy and finally comes to rest at some depth within the lattice.
The average depth can be controlled by adjusting the acceleration energy. The dopant dose can be controlled by monitoring the ion current during the implantation. Both parameters - dose and energy - can be measured electrically, and therefore, the method of ion implantation largely satisfies the conditions of controllability and reproducibility [Rys86a], [Gil88]. In addition, ion implantation is a low temperature process step and for this reason already existing dopant profiles are not affected.
Nevertheless, implantation damages the target and displaces many substrate atoms for each implanted ion [Kin55], [Sig69], [Gib72]. The electrical behavior after implantation is dominated by deep level electron and hole traps which capture carriers and make the resistivity high. Annealing is required to repair lattice damage and put dopant atoms on substitutional sites where they are electrically active.
To repair lattice damage is a process with an activation energy of almost
[Mic87], while diffusion has an activation energy in the range
of 
to 
[Gil88]. Because of this energy difference
lattice repair increases more effective with increasing temperature than
diffusion. Therefore, Rapid Thermal Annealing (RTA) at high temperature
allows repairing of damage with minimal diffusion.
This chapter treats the Analytical Ion Implantation Module of PROMIS. First, we will give a brief outline of physically based simulation techniques for ion implantation, which may provide parameter values for our analytical models. In Section 2.2 we give an overview of one-dimensional distribution functions which are the basis for modeling two-dimensional profiles (Section 2.3). There, we explain the method we have implemented for analytical simulation of ion implantation into arbitrary structures. We summarize the models provided in the standard Model Library in Section 2.4. We close this chapter with some applications (Section 2.5). We compare two-dimensional results of the analytical model with Monte Carlo simulations and study the feasibility of a knock-in implantation method for producing ultra shallow profiles using Monte Carlo simulation. All simulations shown in this chapter have been performed with PROMIS.