Analysis of the extended defects in 3C-SiC.pdf - Nelson Mandela ...

S n Td
(3.2)
25
and is also referred to as the stopping cross-section. T is the energy transferred and dσ
the differential cross-section. The electronic stopping power is proportional to the
velocity of the incoming ion and thus is proportional to E kin , the kinetic energy of
the particle. Using equation 3.1 the implanted range R is given by,
0
1
( ) ( )
E
dE
R (3.3)
N S E S E
0
n
e
with E0 being the energy of implantation.
3.2.2 Range Calculations
The first step taken in finding the equation relating the nuclear stopping power is by
solving the scattering integral (equation 3.4) for the centre of mass system scattering
angle θ given by,
U m
du
2 p
(3.4)
0 V ( u)
2 2
1
p u
E
r
where p is the impact parameter, u = 1/r with r the distance between colliding atoms.
V(u) the interatomic potential and
energy. Also Um satisfies the following,
1
V ( U
)
p
m 2 2
U m
E
r
0
E r
M 1M
2
E
with E the projectile’s
M M M )
1(
1 2
which represents the reciprocal of the minimum distance of approach.
(3.5)
Solving this integral the scattering angle θ is then used to obtain the energy
transferred to a struck atom by the relation,