# Monte Carlo Ion Implantation

**Part II**

*By Dr. A.Burenkov, Dr. M.Temkin, and Dr. T.Crandle*

Monte Carlo implant models have been successfully applied within 1D process simulation tools.[1] In Part I[2], we discussed a modified Monte Carlo algorithm that extended implant modeling to 2D problems by overcoming calculation speed problems. Here we discuss further modifications that allow accurate implant modeling in crystalline target materials such as silicon.

Incorporation of crystal structure is needed primarily to account for the effects of channeling. Channeling is the preferential penetration of ions along crystalline axes or planes that results in a deep tail beyond the profile predicted for amorphous materials.

Figure 1 illustrates the channeling effect modeled by explicitly including an idealized crystal structure in the ion-atom collision calculation. The channeling knee results from on-axis implantation. The position of the implanted ion is calculated as it collides with a series of atoms in the crystal. Collisions tend to guide ions into channeling directions resulting in the channeling tail. Ions lose significantly less energy through electronic and nuclear collisions as they travel along crystalline channels.

Figure 1.

Crystal damage accumulates as implantation proceeds. The formation of damage occurs when ions have a collision that provides sufficient energy to a lattice atom to cause it to leave its original site in the lattice. The accumulation of defects will eventually amorphize the crystal. This produces two important effects:

*Reduction in channeling effect with increasing dose.*

*Anomalous defect driven diffusion following implantation.*

The implant model accounts for the first effect
by treating the material as partially amorphous based on accumulated
damage producing channeling saturation as measured experimentally.
Subsequent diffusion steps model the second effect using either
the point-defect-based diffusion models of **SSuprem4** or the
empirically based calculations of **PREDICT** (bundled with **SSuprem4**
).

For amorphous target materials [2],[3], approximations allow calculation of collision events in steps that are an increasing function of ion energy. When ion energy is high, steps are long and calculation time increases only slightly as energy increases. Unfortunately, for crystalline target materials, channeling must be considered and such approximations are invalid.

In crystals[4], the distance between collision
calculations is typically on the order of the interatomic spacing
independent of energy, resulting in lengthy calculations that increase
dramatically with implant energy. Accounting for the anomalous post-implant
diffusion effect used to make implant calculation time prohibitive.
However, a number of special algorithms greatly increase **SSuprem4**
calculation speed to make 2D implant modeling practical in **SSuprem4**.

**References:**

[1] B.J. Mulvaney, W.B. Richardson, and T.L.Crandle, PEPPER: A process simulator for VLSI, IEEE Trans.Computer-Aided Design, Vol. 8, No. 4, 1989.

[2] A.Burenkov, M.Temkin, and T.Crandle, Monte Carlo Ion Implantation, Part I, vol. 2, No.6, The Bug Exterminator, p.1, Nov/Dec 1991.

[3] J.F. Ziegler, J.P. Biersack, and U. Littmark, The Stopping and Range of Ions in Solids, New York; Pergamon, 1985.

[4] J. Lindhard <169> Influence of crystal lattice on motion of energetic charged particles, Mat.-fys. Medd. Dan. Vid. Selsk. vol. 34, Nr.14, pp. 1 - 64.

editors, World Scientific, 1992).