The decision, whether to use the Monte Carlo simulation method or the
analytical ion implantation method, is a trade-off between CPU time
consumption and accuracy. The results obtained from Monte Carlo calculations
are based on probability decisions, hence the accuracy is limited within two
or three orders of magnitudes. The analytical method allows a more realistic
dopant profile description over the whole concentration range, but it cannot
cover physical effects like reflection of particles at the simulation
boundaries. Figure 2.3-1 shows the two-dimensional result of a
phosphorus implantation at 70keV and 30 degrees tilt angle. Comparing our
analytical results with Monte Carlo simulations (see Fig. 2.3-2)
we found good agreement. Due to the neglection of the reflected particles in
the mask sidewall region, the analytical method yields a lower peak
concentration in the silicon substrate. One major drawback of the Monte
Carlo ion implantation method is the enormous CPU time consumption for
amorphous and even for crystalline calculations. For a simple structure like
that shown in Figure 2.3-1 a two-dimensional crystalline Monte
Carlo simulation would consume approximately 
times the CPU time of
the analytical method. By performing a two-dimensional amorphous Monte Carlo
simulation this CPU time ratio is reduced by one magnitude
( 
). Therefore, the Monte Carlo method is not
suitable for optimization purposes, where several hundred implantations have
to be simulated within reasonable time.
Figure 2.3-1: Two-dimensional phosphorus implantation
profile obtained by the analytical ion implantation method at 70 keV
energy, 
dose, and 
tilt angle. Due to
neglection of reflective particles the sidewall mask concentration is
underestimated.
Figure 2.3-2: Two-dimensional phosphorus
implantation profile obtained from the amorphous Monte Carlo ion
implantation method at 70 keV energy, dose, and
tilt angle. The simulation was performed using 50.000 distinct
ions and consumed about 90 times the CPU time of the analytical simulation
method.