Damage formation and annealing studies of low energy ion implants ...

dE/dx (eV/Ang)
125
100
75
50
25
0
2.4 Ion range
Ions travelling through a solid will undergo collisions with different lattice
atoms and as such the path taken by all the implanted ions will vary. The final depth
that implanted ions will come to rest at will vary as with any statistical process, and as
such will usually follow a Gaussian distribution. The average depth of implanted ions is
known as the mean projected range (Rp), and the spread of the implanted ions about the
mean depth is known as straggling.
2.4.1 Range calculation
In dealing with the stopping power it is often convenient to define a stopping
cross section, S, where;
1 ⎛ dE ⎞
= and
Se ⎜ ⎟
n ⎝ dx ⎠e
26
1 ⎛ dE ⎞
= (2.12 a and b)
Sn ⎜ ⎟
n ⎝ dx ⎠ n
where N is the density (15). Stopping cross sections are often used in range calculations.
The rate of energy loss of an ion as it travels through a solid is the sum of the
nuclear and electric stopping, i.e.:
dE
dx
He
1 10 100 1000
⎛ dE ⎞
⎜ ⎟
⎝ dx ⎠
e
⎛ dE ⎞
+ ⎜ ⎟
⎝ dx ⎠
Electronic stopping
Nuclear stopping
MEIS
= or N(
S ( E)
+ S ( E)
)
n
Implantation
Energy (keV)
As
1 10 100 1000
Figure 2.4 Electronic and Nuclear stopping powers for He and As in Si. The energy
regimes used in MEIS and for the implants are indicated.
dE
= n e (2.13)
dx