List of Figures

• 2.1. Schematic of a Harwell Freeman ion source.
• 2.2. Spectrum from an SiF$_4$ ion source spectrum [91].
• 2.3. Schematic of the Eaton NV8200 medium current implanter [91].
• 2.4. Projected ranges in silicon of various ion species as a function of the implantation energy.
• 2.5. Projected ranges in silicon dioxide of various ion species as a function of the implantation energy.
• 2.6. Projected ranges in silicon nitride of various ion species as a function of the implantation energy.
• 2.7. Projected ranges in aluminum of various ion species as a function of the implantation energy.
• 2.8. Projected ranges in the photo resists KTFR of various ion species as a function of the implantation energy.
• 2.9. Projected ranges in the photo resist AZ-7500 of various ion species as a function of the implantation energy.
• 2.10. Comparison of the functional behavior of the stopping power in the low ion energy regime of two ion species.
• 2.11. Definition of the tilt and the twist angle of the ion beam (blue).
• 2.12. Wafer types identified by the orientation of the primary and the secondary flat. The name of the wafer type indicates the background doping and the orientation of the wafer normal.
• 2.13. Model of a silicon crystal seen along the $<$110$>$ direction.
• 2.14. Model of a silicon crystal seen along the $<$100$>$ direction.
• 3.1. Schematic figure of the calculation of the impurity concentration by a convolution of the point response functions.
• 3.2. Two particle scattering process in the laboratory system.
• 3.3. Two particle scattering process in the center-of-mass coordinate system.
• 3.4. Universal screening potential as a function of the reduced radius $x = \frac {r}{a_U}$.
• 3.5. Reduced radius as function of the real radius.
• 3.6. Reduced energy as function of the ion energy.
• 3.7. Reduced nuclear stopping power as function of the reduced energy.
• 3.8. Functional behavior of the electronic stopping power as a function of the ion velocity.
• 3.9. Amplitude of lattice vibration as a function of the temperature for three Debye temperatures.
• 3.10. Collision cascades resulting from an implantation of a boron (left) and arsenic (right) ion into bare $<$100$>$ silicon. The implantation energy is 40 keV and a tilt of 0 $\,^\circ\;$is used. The green line denotes the trajectory of the implanted ion. The length unit used is Å.
• 3.11. Number of silicon vacancies and interstitials generated by the primary recoil as a function of the primary recoil energy assuming a displacement energy of 15 eV.
• 3.12. Enlargement of a recoil cascade originating from one primary recoil.
• 3.13. Interstitial and vacancy distribution resulting from an implantation of arsenic ions with an energy of 50 keV and a dose of $1{\cdot }10^{14}$cm$^{-2}$. The total concentration of the point defects is shown.
• 3.14. Interstitial and vacancy distribution resulting from an implantation of arsenic ions with an energy of 50 keV and a dose of $1{\cdot }10^{14}$cm$^{-2}$. The difference of the interstitial and vacancy distribution is shown.
• 3.15. Schematic figure of the position of tetrahedral interstitial sites in the diamond lattice. The black spheres denote silicon atoms while the patterned spheres represent the tetrahedral interstitial positions.
• 3.16. Schematic picture of crystalline silicon with some interstitials (yellow spheres) placed at tetrahedral interstitial positions. The view in the left figure is parallel to the $<$100$>$ direction while it is parallel to the $<$110$>$ direction in the right figure.
• 4.1. Illustration how the input structure is expanded to the simulation structure. The solid lines outline the original geometry while the dashed lines denote the expanded geometry.
• 4.2. Illustration how the automatic implantation window is generated.
• 4.3. Schematic figure of the trajectory calculation procedure for a simulated ion.
• 4.4. Schematic figure how the collision partner is determined in amorphous targets.
• 4.5. Schematic figure for the selection of collision partners for simultaneous collisions in crystalline materials.
• 4.6. Schematic figure for the selection of collision partners in crystalline materials.
• 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.
• 4.8. Tabulated scattering angle as a function of the reduced energy and the reduced radius.
• 4.9. Schematic figure of an implantation with a molecular ion like BF$_2$. One trajectory is calculated for each atom species while the effects generated by each particle species (damage generation, doping concentration) are multiplied by a weighting factor.
• 4.10. Illustration how the point response compression method works.
• 4.11. Two cuts through a compressed (top) and an uncompressed (bottom) point response function resulting from an implantation into crystalline silicon covered with 15 nm silicon dioxide. An implantation window with a size of 300 nm was used.
• 4.12. Two iso-surfaces ( $1{\cdot }10^{17}$cm$^{-3}$ (a) and $1{\cdot }10^{18}$cm$^{-3}$ (b)) of a compressed point response function resulting from an implantation into crystalline silicon covered with 15 nm silicon dioxide with boron ions with an energy of 70 keV and a dose of $4{\cdot }10^{15}$cm$^{-2}$.
• 4.13. Two iso-surfaces ( $1{\cdot }10^{17}$cm$^{-3}$ (a) and $1{\cdot }10^{18}$cm$^{-3}$ (b)) of a compressed point response function resulting from an implantation into crystalline silicon covered with 15 nm silicon dioxide with boron ions with an energy of 40 keV and a dose of $5{\cdot }10^{14}$cm$^{-2}$.
• 4.14. Comparison of three iso-lines ( $5{\cdot }10^{19}$cm$^{-3}$, $5{\cdot }10^{18}$cm$^{-3}$ and $5{\cdot }10^{17}$cm$^{-3}$) for point response functions generated by using implantation windows with sizes of 50 nm, 100 nm, 200 nm and 300 nm.
• 4.15. Header of a point response file.
• 4.16. Illustration of the shielding effect by a mask edge.
• 4.17. Schematic figure how the Trajectory-Split method works especially in combination with the molecular method.
• 4.18. Default values for $\mathcal{R}_{Emax}$ for the particle species boron, phosphorus, silicon and arsenic.
• 4.19. Default values for $\mathcal{R}_{Lmin}$ for the particle species boron, phosphorus, silicon and arsenic.
• 4.20. Illustration of the functionality of the Trajectory-Reuse method.
• 4.21. Schematic description of the trajectory copying method.
• 4.22. Schematic presentation of the splitting of the simulation domain into subdomains and of the distribution of the subdomains among several processors. The small dashed lines denote the subdomains while the thick lines denote the scopes of responsibility of the slaves.
• 4.23. Average idle times of the slaves for a simulation with five identical CPUs, using an arbitrary (black blocks) and an optimized (yellow blocks) subdomain distribution.
• 4.24. Distribution of 63 $\times$ 63 subdomains on a workstation cluster consisting of 19 CPUs with four different CPU speeds. Areas with different grey levels denote scopes of responsibility of different slave.
• 4.25. Schematic description of the simulation flow of the master process and of a slave process. The thick arrows denote communication events between the master and the slave.
• 4.26. Schematic presentation of the slave to slave communication events. Transfer of an ion (a), storing simulation results outside the local memory (b), accessing simulation results from outside (c).
• 4.27. Speedup as a function of the number of slaves compared to an ideal speedup.
• 5.1. Angular distribution $\frac {dN}{d\theta }$ of boron ions scattered by an SiO$_2$ layer compared to a spherical homogeneous momentum distribution. 0 $\,^\circ\;$corresponds to the initial momentum of the implanted ions. An ion beam without any divergence was assumed and the implantation energies of the ions were 30 keV (top) and 90 keV (bottom).
• 5.2. Angular distribution $\frac {dN}{d\theta }$ of boron ions scattered by an Si$_3$N$_4$ layer compared to a spherical homogeneous momentum distribution. 0 $\,^\circ\;$corresponds to the initial momentum of the implanted ions. An ion beam without any divergence was assumed and the implantation energies of the ions were 30 keV (top) and 90 keV (bottom).
• 5.3. Angular distribution $\frac {dN}{d\theta }$ of boron ions scattered by an WSi$_2$ layer compared to a spherical homogeneous momentum distribution. 0 $\,^\circ\;$corresponds to the initial momentum of the implanted ions. An ion beam without any divergence was assumed and the implantation energies of the ions 30 keV (top) and 90 keV (bottom).
• 5.4. Maximal energy of ions leaving a scattering layer, related to the implantation energy. Implantation energies of 30 keV and 90 keV are used.
• 5.5. Average energy of ions leaving a scattering layer, related to the maximal energy of ions leaving the scattering layer. Implantation energies of 30 keV and 90 keV are used.
• 5.6. Cumulative energy distribution of boron ions scattered by an SiO$_2$ layer. The initial energies of the ion beam were 30 keV (top) and 90 keV (bottom).
• 5.7. Cumulative energy distribution of boron ions scattered by an Si$_3$N$_4$ layer. The initial energies of the ion beam were 30 keV (top) and 90 keV (bottom).
• 5.8. Cumulative energy distribution of boron ions scattered by an WSi$_2$ layer. The initial energies of the ion beam were 30 keV (top) and 90 keV (bottom).
• 5.9. Simulated ion implantation of boron ions into $<$100$>$ silicon through a scattering layer of SiO$_2$. The implantation was performed with an energy of 30 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. A tilt of 7 $\,^\circ\;$(top) and of 0 $\,^\circ\;$ (bottom) were used. The scattering layer thickness was varied from 0.5 nm to 30 nm.
• 5.10. Simulated ion implantation of boron ions into $<$100$>$ silicon through a scattering layer of Si$_3$N$_4$. The implantation was performed with an energy of 30 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. A tilt of 7 $\,^\circ\;$(top) and 0 $\,^\circ\;$ (bottom) were used. The scattering layer thickness was varied from 0.5 nm to 30 nm.
• 5.11. Simulated ion implantation of boron ions into $<$100$>$ silicon through a scattering layer of WSi$_2$. The implantation was performed with an energy of 30 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. A tilt of 7 $\,^\circ\;$(top) and 0 $\,^\circ\;$ (bottom) were used. The scattering layer thickness was varied from 0.5 nm to 30 nm.
• 5.12. Simulated ion implantation of boron ions into $<$100$>$ silicon through a scattering layer of SiO$_2$. The implantation was performed with an energy of 90 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. A tilt of 7 $\,^\circ\;$(top) and 0 $\,^\circ\;$ (bottom) were used. The scattering layer thickness was varied from 0.5 nm to 30 nm.
• 5.13. Simulated ion implantation of boron ions into $<$100$>$ silicon through a scattering layer of Si$_3$N$_4$. The implantation was performed with an energy of 90 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. A tilt of 7 $\,^\circ\;$(top) and 0 $\,^\circ\;$ (bottom) were used. The scattering layer thickness was varied from 0.5 nm to 30 nm.
• 5.14. Simulated ion implantation of boron ions into $<$100$>$ silicon through a scattering layer of WSi$_2$. The implantation was performed with an energy of 90 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. A tilt of 7 $\,^\circ\;$(top) and 0 $\,^\circ\;$ (bottom) were used. The scattering layer thickness was varied from 0.5 nm to 30 nm.
• 5.15. Simulated boron concentration resulting from an implantation of boron ions into a MOS transistor structure. In the top figure the surface is covered by a 1 nm thick SiO$_2$ layer while the layer thickness in the bottom figure is 16 nm. The implantation was performed with an energy of 30 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. A tilt of 10 $\,^\circ\;$and a twist of 90 $\,^\circ\;$was used. The figure shows the doping profile in the vicinity of the gate corner.
• 5.16. Simulated boron concentration resulting from an implantation with boron ions with an energy of 90 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$ after an implantation of silicon ions with doses of $5{\cdot }10^{14}$cm$^{-2}$ (top) and $1{\cdot }10^{15}$cm$^{-2}$ (bottom) and with various ion energies. Both ion beams were tilted by 7 $\,^\circ\;$and rotated by 90 $\,^\circ\;$.
• 5.17. Simulated boron concentration resulting from an implantation with boron ions with an energy of 90 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$ after an implantation of silicon ions with doses of $5{\cdot }10^{15}$cm$^{-2}$ (top) and $1{\cdot }10^{16}$cm$^{-2}$ (bottom) and with various ion energies. Both ion beams were tilted by 7 $\,^\circ\;$and rotated by 90 $\,^\circ\;$.
• 5.18. Depth of the boron concentration levels of $1{\cdot }10^{15}$cm$^{-3}$ (top) and $5{\cdot }10^{16}$cm$^{-3}$ (bottom) resulting from an implantation with boron ions with an energy of 90 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$ after an implantation with silicon ions. The depth is plotted as the function of the energy and for different doses of the silicon implantation.
• 5.19. Simulated boron concentration resulting from an implantation of boron ions into a MOS transistor structure after the formation of the spacer. The implantation was performed with an energy of 80 keV and a dose of $1{\cdot }10^{15}$cm$^{-2}$. In the bottom figure the boron implantation is preceded by an implantation with silicon ions with an energy of 200 keV and a dose of $1{\cdot }10^{16}$cm$^{-2}$. Both ion beams were tilted by 10 $\,^\circ\;$and rotated by 270 $\,^\circ\;$. The figure shows the doping profile in the vicinity of the gate corner.
• 5.20. Distribution of oxygen atoms in the silicon substrate as a consequence of the implantation of arsenic ions with a dose of $3{\cdot }10^{15}$cm$^{-2}$ and with energies ranging from 10 keV to 150 keV through a 11 nm thick SiO$_2$ layer. A tilt of 7 $\,^\circ\;$and a twist of 90 $\,^\circ\;$was used.
• 5.21. Distribution of arsenic atoms in the silicon substrate as a consequence of the implantation of arsenic ions with a dose of $3{\cdot }10^{15}$cm$^{-2}$ and with energies ranging from 10 keV to 150 keV through a 11 nm thick SiO$_2$ layer. A tilt of 7 $\,^\circ\;$and a twist of 90 $\,^\circ\;$was used.
• 5.22. Depth of the concentration level of $1{\cdot }10^{21}$cm$^{-3}$ of the oxygen distribution after an implantation with arsenic ions with a dose of $3{\cdot }10^{15}$cm$^{-2}$ through a 10 nm thick SiO$_2$ layer. The depth is plotted as a function of the energy of the arsenic ions.
• 5.23. Distribution of oxygen atoms in the silicon substrate as a consequence of the implantation of arsenic ions with a dose of $3{\cdot }10^{15}$cm$^{-2}$ and with an energy of 75 keV through a 10 nm thick SiO$_2$ layer. A tilt of 7 $\,^\circ\;$ and a twist of 90 $\,^\circ\;$was used. For the displacement energy of the oxygen atom from a stable bound in the silicon dioxide is varied from 15 eV to 75 eV.
• 5.24. Structure of an 0.6 $\mu$m NMOS-transistor before the threshold voltage adjust implantation.
• 5.25. Simulated boron (top) and fluorine (bottom) profile resulting from a threshold voltage adjust implantation into a 0.6 $\mu m$ NMOS-transistor with BF$_2$ ions with an energy of 50 keV and a dose of $3{\cdot }10^{12}$cm$^{-2}$. The figure shows an outline of the transistor structure and the doping profile within three cuts through the gate and source/drain region.
• 5.26. Structure of an 0.6 $\mu$m NMOS-transistor before an implantation of the source and the drain region.
• 5.27. Simulated arsenic distribution resulting from a source/drain implantation with arsenic ions with an energy of 90 keV and a dose of $4{\cdot }10^{15}$cm$^{-2}$. The figure shows three cuts through the source/drain region.
• 5.28. Simulated amorphization of the source/drain region of a 0.6 $\mu m$ NMOS-transistor by a source/drain implantation with arsenic ions with an energy of 90 keV and a dose of $4{\cdot }10^{15}$cm$^{-2}$. The figure shows three cuts through the source/drain region. The light gray area denotes the amorphous region.