Damage formation and annealing studies of low energy ion implants ...

in terms of stopping power and stopping cross section respectively. Knowledge of the
stopping power allows the overall slowing down to be described in a quantitative way.
It therefore enables calculation of the range. Rearranging equation 2.13 and integrating
from the maximum energy E0 to zero yields the total path length, R(E), of the ion:
dE
∫ 0 +
dx e
E0
R ( E)
=
or ( E)
( dE ) ( dE )
2.4.2 Simulation of ion implantation (using SRIM)
dx
n
1 dE
R =
N ∫ (2.14)
S +
27
E0
( E)
S ( E)
0 n e
Several computer simulation codes have been developed to calculate parameters
such as the range and straggling of implanted ions. The Stopping and Range of Ions in
Matter (SRIM) (3) is a group of programs which calculate the stopping and range of
energetic ions into matter using a fit to a full quantum mechanical treatment of ion-atom
collisions. The most comprehensive of these programs is the Transport of Ions in Matter
(TRIM). The TRIM simulation code is widely used for simulating the effects of ion
implantation and has been useful within this study to compare theory to the
experimental depth profiles obtained from MEIS. Because of the statistical nature of the
paths of implanted ions simulations TRIM uses Monte Carlo methods and a binary
collision algorithm to calculate the ion trajectories of many implanted ions. It will
accept complex targets made of compound materials, and calculate the final 3D
distribution of implanted ions and also all kinetic phenomena associated with the ion’s
energy loss: target damage, sputtering, ionisation and phonon production. As an
example a simulation of the paths of twenty implanted As and B ions into Si with an
implant energy of 3 keV, is shown in Figure 2.5 a) and b) respectively. The shallower
implantation and smaller amount of straggling seen with As compared to B is due to the
higher nuclear stopping power. TRIM works on the basis of an amorphous matrix.