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4.4.2 Nuclear Stopping Process

For the simulation of the nuclear stopping process it is assumed that the scattering process can be described by its asymptotic behavior. Therefore neither the position of the ion nor the position of the target atoms is changed. Just the momentum vectors of the particles are modified. Before the scattering event the ion is placed at the closest distance to the collision partner, which is equal to the impact parameter. In reality the minimum distance between the collision partners is larger than the impact parameter as shown in Fig. 4.7. According to Fig. 4.7 the error in the particle distance is low (below 10%) as long as the particle energy and the impact parameter are not too low. At the moment it is not possible to quantify the influence of the error in the particle distance on the simulation result. Therefore a rigorous treatment of the scattering process had to be implemented in the simulator, to be able to compare simulation results obtained by applying a rigorous treatment to simulation results generated by applying the asymptotic approximation.

Figure 4.7: Relative difference between the distance of closest approach and the impact parameter as a function of the energy. The function is plotted for several reduced impact parameters in the interval 0.5 to 9.0.
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Figure 4.8: Tabulated scattering angle as a function of the reduced energy and the reduced radius.
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The asymptotic scattering process is implemented by a table based representation of the scattering process % latex2html id marker 20890 \setcounter{footnote}{2}\fnsymbol{footnote} as described by (3.88), (3.89) and (3.90). A bicubic spline interpolation is performed in between. The tabulated scattering function is plotted Fig. 4.8.

Knowing the scattering angle in the center-of mass system, the scattering angles of the incident particle and of the recoil are calculated by (3.73) and (3.74) for the laboratory system and the energy transfer to the target atom is determined by (3.75).


Footnotes

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The asymptotic scattering angle is tabulated in the file SCATTAB.DAT (located in $CWD,$VPROJECT, $VROOT) as a function of the reduced impact parameter $ \frac{p}{a_U}$ (3.92) and the reduced energy (3.95) for 28 energy values and 17 impact parameter values.
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A. Hoessiger: Simulation of Ion Implantation for ULSI Technology