Some Definitions

The two key parameters defining the final implant profile are dose $\Phi$ (usually given in $atoms/cm^2$) and energy $E$ (in $keV$). The dose is related to the beam current $I$ by the following formula:

$$\Phi = \frac{I t}{q_i A},$$ (1)

were $t$ denotes implantation time, $A$ beam area and $q_i$ is the charge per ion. Typical beam currents and implantation doses range from $1 \mu A - 30mA$ and $10^{11} - 10^{16} atoms/cm^2$. The lowest energies used start at the sub $keV$ area for ultrashallow junctions to the $MeV$ range for deep wells.

Figure: Range $R$ and projected Range $R_p$

When the ions enter the substrate they continously loose energy and change direction by collisions with the target atoms (see also fig. ). Due to the random nature of the collisions the total distance travelled (range) and its projection on the direction parallel to the ion beam (projected range) are random variables. $R_p$ denotes the projected range, the depth were most ions stop. The projected straggle ${\ensuremath{\Delta R_p}}$ describes the statistical fluctuation of $R_p$.