5.1 Effect of Scattering Layers

Before an implantation the crystalline silicon substrate is often covered by an amorphous layer, preferably silicon dioxide, to scatter the implanted ions and to reduce thereby the channeling effect. In the following the scattering behavior of silicon dioxide (SiO$_2$), silicon nitride (Si$_3$N$_4$) and of tungsten silicide (WSi$_2$) is analyzed, by evaluating the influence of the scattering layers on the motion of boron ions implanted with an energy of 30 keV and an energy of 90 keV.

In Fig. 5.1 to Fig. 5.3 the momentum distribution of the boron atoms leaving the scattering layer is analyzed. Even if an ion beam with ions with a single moment is implanted into a scattering layer the beam of particles leaving the scattering layer becomes divergent. This means that the distribution of the moments of the particles leaving the scattering layer is centered around the original ion beam direction, which is indicated by 0 $\,^\circ\;$in the figures Fig. 5.1 to Fig. 5.3.

If the ions were homogeneously distributed the probability $P_\theta$ for finding an ion momentum with an angle $\theta$ to a reference direction (0 $\,^\circ\;$) is

$$P_\theta = \frac{\sin(\theta)}{2\cdot \pi}.$$ (5.1)

The probability distributions plotted in Fig. 5.1 to Fig. 5.3 are related to such a homogeneous distribution. For instance as indicated by Fig. 5.1 (top) if the ion beam with an energy of 30 keV is scattered by a silicon dioxide layer with a thickness of 1 nm, which is approximately the thickness of a native oxide layer, the probability for ion momentums is higher compared to a homogeneous distribution for angles below 2.1 $\,^\circ\;$while it is lower for all larger angles.

In the analysis the thickness of the scattering layer is varied from 0.5 nm to 30 nm to evaluate the scattering efficiency and the influence of the layer thickness on the scattering efficiency. The scattering efficiency of the layer is all the higher the larger the divergence of the ion beam leaving the scattering layer. The scattering efficiency of two materials can be compared by comparing the divergence of the ion beam at a fixed layer thickness.

In Fig. 5.1 the scattering efficiency of SiO$_2$ is analyzed, while Fig. 5.2 and Fig. 5.3 demonstrate the scattering efficiency of Si$_3$N$_4$ and WSi$_2$, respectively. Two ion energies are analyzed for each material to see if also the ion energy has an influence on the scattering efficiency.

Figure 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).

Figure 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).

Figure 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).

According to the simulation results the divergence of the scattered ions is all the higher the thicker the scattering layer is. For instance if Si$_3$N$_4$ is used as a scattering layer and ions with an energy of 90 keV are implanted the momentum distribution equals the homogeneous momentum distribution at a scattering angle of 2.2 $\,^\circ\;$if the layer thickness is 1 nm, while it equals the homogeneous momentum distribution at a scattering angle of 6,7 $\,^\circ\;$if the layer thickness is 20 nm (Fig. 5.2 (bottom)).

Additionally it can be said that besides the layer thickness also the ion energy has an influence on the scattering efficiency. By decreasing the energy of the ions the scattering efficiency increases. For instance, the probability for finding an ion scattered by an angle of 2,5 $\,^\circ\;$is 1.4 times higher for an implantation energy of 30 keV than for an implantation energy of 90 keV, if a 3 nm thick WSi$_2$ scattering layer is used (Fig. 5.3).

Comparing the materials SiO$_2$, Si$_3$N$_4$ and WSi$_2$ it can be said that WSi$_2$ has the highest scattering capability while SiO$_2$ has the lowest scattering capability. While a WSi$_2$ layer with a thickness of more than 10 nm is sufficient to achieve an almost homogeneous momentum distribution if the implantation energy is 30 keV, a SiO$_2$ layer of even 30 nm is not sufficient. Layer thicknesses of approximately 20 nm SiO$_2$, 4 nm Si$_3$N$_4$ and 3 nm WSi$_2$ are comparable in their angular scattering capabilities.

As indicated by Fig. 5.4 the stopping behavior of all scattering layers is similar to the angular scattering capability. Fig. 5.4 shows the maximum energy $E_{max}$ of the ions leaving the scattering layer related to the implantation energy $E_0$. WSi$_2$ has the highest stopping capability while SiO$_2$ has the lowest stopping capability of the considered materials. The stopping capability of Si$_3$N$_4$ lies in between. Since the stopping power in the scattering layer is dominated by the electronic stopping (Sec. 3.3.1) as well for boron ions with an energy of 30 keV and of 90 keV, the relative energy of the scattered ions is higher for ions implanted with an energy of 90 keV (Fig. 5.4).

The reason is that the relative energy of an ion after scattering is

$$\mathcal{R}_E =\frac{E_0 - \Delta E}{E_0}$$ (5.2)

and

$$\Delta E \propto \sqrt{E}$$ (5.3)

$$\Longrightarrow\qquad \mathcal{R}_E \propto -\frac{1}{\sqrt{E}} .$$ (5.4)

Figure 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.

Figure 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.

According to Fig. 5.5 to Fig. 5.8 as well as the momentum distribution, the energy distribution is broadened by increasing the layer thickness or by using a material with a higher scattering capability. Fig. 5.5 shows the difference of the average energy and the maximum energy related to the maximum energy according to (5.5).

$$\mathcal{R}_{Emax} =\frac{E_{max} - E}{E_{max}}$$ (5.5)

Figure 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).

Figure 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).

Figure 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).

In Fig. 5.6 to Fig. 5.8 the energy distributions of the boron ions leaving the scattering layer are shown. The energy distribution is presented by a cumulative sum as a function of the relative energy $\mathcal{R}_{Emax}$ compared to the maximal energy $E_{max}$ of an ion leaving the scattering layer. Using Fig. 5.6 to Fig. 5.8 the scattering capabilities of the various materials (SiO$_2$, Si$_3$N$_4$ and WSi$_2$) can be analyzed in detail. As for the evaluation of the momentum distribution two implantation energies are considered for analyzing the energy distributions for each scattering material type.

The influence of the layer thickness and of the implantation energy on the energy distributions of the boron ions leaving the scattering layer is equivalent to the influence on the momentum distribution. As well by increasing the thickness of the scattering layer as by reducing the implantation energy, the energy distribution is broadened. Additionally the energy distribution is broadened by using a material with a higher scattering capability. For instance if the boron ions are implanted with an energy of 90 keV through a scattering layer with a thickness of 30 nm approximately 77% of all ions are within an energy interval of 1% around the maximal energy if the scattering layer material is SiO$_2$, while just 62% and 41% of the ions are within this interval if the scattering layer material is Si$_3$N$_4$ or WSi$_2$ respectively.

The influence of the scattering layers on the channeling behavior of the ions in the crystalline silicon substrate and thereby on the distribution of the implanted atoms is shown in Fig. 5.9 to Fig. 5.14 for implantations with energies of 30 keV and 90 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$. The implantations are performed on the one hand side with an ion beam tilted by 7$\;^\circ$ and on the other hand side with an ion beam aligned with the $<$100$>$ crystal direction.

In case of an implantation along the $<$100$>$ channeling direction as shown for instance in the bottom figure of Fig. 5.9 the depth of the implanted profile is successively reduced by increasing the thickness of the scattering layer. Tab. 5.1 summarizes the depth of the concentration level of $1{\cdot }10^{15}$cm$^{-3}$ after an implantation through a scattering layer with a thickness of 30 nm. Various scattering materials and two implantation energies are used. A depth of 0 nm in Fig. 5.9 to Fig. 5.14 and in Tab. 5.1 corresponds to the surface of the silicon substrate. The values of the depth in Tab. 5.1 are extracted from the top figures in Fig. 5.9 to Fig. 5.14.

Figure 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.

Figure 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.

Figure 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.

Figure 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.

Figure 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.

Figure 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.

Figure 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.

If the ion beam is tilted by 7 $\,^\circ\;$the ions first penetrate deeper into the target if the thickness of the scattering layer is increased, because the probability that an ion is scattered into a channel increases as shown in Fig. 5.1 to Fig. 5.3. At a certain scattering layer thickness the penetration depth reaches a maximum until it decreases again. If thick scattering layers are used the impurity distributions become independent on the tilt of the ion beam. To achieve that a thickness of 30 nm, which is the largest layer thickness in the analysis presented here is sufficient as well for an implantation with an energy of 30 keV and of 90 keV and for all scattering layer materials analyzed. Since the effects observed do not depend on the material type of the scattering layer a presentation just of Fig. 5.9 would be sufficient, but Fig. 5.10, Fig. 5.11, Fig. 5.12, Fig. 5.13 and Fig. 5.14 are added for the sake of completeness. In this series of figures first the tilt angle then the material type and finally the implantation energy is varied.

In order to demonstrate that such an analysis is not restricted to one-dimensional problems, the effect of a silicon dioxide scattering layer on the doping profile in the vicinity of a gate corner of a MOS transistor is shown in Fig. 5.15. The scattering layer covers the whole surface and has a thickness of 1 nm in the top figure and of 16 nm in the bottom figure.

Boron ions with an energy of 30 keV and a dose of $5{\cdot }10^{13}$cm$^{-2}$ were implanted into this structure. The ion beam was tilted by 10 $\,^\circ\;$to move the boron atoms slightly under the gate.

By using a thicker scattering oxide the shape of the doping profile below the gate corner changes from a rectangular shaped structure to a circular shaped structure. Additionally a shallower doping profile is generated by implanting through a scattering oxide with a thickness of 16 nm. The iso-concentration line of $1{\cdot }10^{17}$cm$^{-3}$ has a depth of approximately 280 nm and its maximal distance from the gate corner is 90 nm. In case of an implantation through a scattering layer with a thickness of just 1 nm the depth of the iso-concentration line of $1{\cdot }10^{17}$cm$^{-3}$ is 355 nm and the distance from the corner is 100 nm. Therefore the aspect ratios of the doping profiles are 3.1 and 3.55 respectively.