ABSTRACT

There are two basic mechanisms for stopping of implanted ions in a material, electronic and ionic. When an energetic ion enters a semiconductor target, it interacts with the electrons and nuclei of the crystal. Implanted ions undergo a series of collisions until they finally stop. An example of trajectories of ions (calculated by Monte Carlo simulation) is shown in Fig. 9.1a [4]. The collision processes cause transfer of energy to the semiconductor, resulting in deflection of the projectile ions and dislodging of the target nuclei. Nuclear stopping also results in damage, and creation of point defects, line defects, and amorphous regions. A summarized version of the calculating range, etc., is given below. For details of the derivations, the reader is referred to textbooks on ion implantation (e.g., Refs. [1, 2]). If E is the energy of an ion at any point x along its path, the stopping power can be defined as Sn = ddExÊËÁ ˆ¯˜ n energy loss per unit length for nuclear stopping and Se = ddExÊËÁ ˆ¯˜ for electronic stopping. Electronic interaction causes generation of electron-hole pairs as the projectile ion energy is transferred to the crystal. The average rate of energy loss with distance can be written asddEx = N[Sn(E) + Se(E)] (9.1)where N is the number of target atoms per unit volume of the semiconductor. Figure 9.2 shows these two terms as a function of ion velocity (or energy). At typical ion energies used in ion implantation, nuclear stopping dominates. As energies increase into the mega-electron volt range, electronic stopping takes over. The nuclear stopping power can be treated as collisions between hard spheres. A more accurate model assumes the scattering to be Coulombic force at a distance interaction. The most successful model for predicting implantation profile is the Lindhard, Scharff, and Schiott (LSS) model [5], which utilizes a modified Thomas-Fermi screened potential for scattering. Calculations based on this show that nuclear stopping increases linearly at low energies, reaches a maximum, and then decreases at high energies, as shown in Fig. 9.2. Electronic stopping power is similar to viscous drag force and has been shown to be proportional to the ion velocity Se(E) = k E (9.2)

where the value of k depends upon the projectile and target material. For GaAs (nonion channeling case) k ≈ 0.52 10-15 ( eV)½ cm2.