Impurity Profiles

Based on the LSS theory the implant profile (projected ranges $R_p$ of a huge number of ions) in an amorphous material can be described by a gaussian distribution due to the statistical nature of the ion stopping process.

$$n(x) = n_0 \exp{\left( \frac{-(x - R_p)^2}{2 {\ensuremath{\... ...h}    n_0 = \frac{\Phi}{\sqrt{2\pi} {\ensuremath{\Delta R_p}}}$$ (3)

The profile is defined by the implanted dose $\Phi$, the projected range $R_p$ and the projected straggle ${\ensuremath{\Delta R_p}}$. $R_p$ and ${\ensuremath{\Delta R_p}}$ are tabulated for various materials and dopants relevant in silicon technology in e. g. [3]. Of course they also depend on the implant energy $E$.

Figure: implant profile by SIMPIMPLANT

In real applications many times the implantation is done through composite layers of different materials. In this case a simple approximation of the implant profile can be calculated as follows:

• Convert all individual layer thicknesses $t_i$ to equivalent silicon thickness by:

  
  

  $$t_{eqSi} = t_i \frac{R_{p_{Si}}}{R_{p_i}}$$ (4)

  
  

• Calculate the implant profile in silicon and scale it back using the transformation above.

The described procedure yields continous, but abrupt changing profiles which are no real, but usable as first approximations (fig. ).

Figure: implant in composite structure by SIMPIMPLANT