Chemistry Reference
In-Depth Information
material it is possible to determine the elemental composition as a function of depth.
The energy of the scattered projectile is
M
T
−
2
M
P
sin
2
θ
1
/
2
+
M
P
cos θ
E
1
=
E
0
,
(7.20)
M
P
+
M
T
where
M
P
is the mass of the projectile with initial energy
E
0
M
T
is the mass of the target nucleus
θ describes the scattered angle of the scattered particle with the mass
M
P
relative
to the incident trajectory
While this equation correctly determines the backscattered energies relative to mea-
surement angle, it does not describe the angular distribution of the backscattering
probability. For the backscattering probability the differential cross-section of the
backscattering will be needed [48]
1
cos θ
2
sin
2
θ
2
1
/
2
−
(
Z
T
Z
P
e
2
16πε
0
E
2
M
P
/
M
T
)
+
(
)
d
σ
θ
1
sin
4
θ
=
·
, (7.21)
1
1
/
2
d
/
2
2
−
((
M
P
/
M
T
)
sin
2
θ
)
where
Z
P
and
Z
T
are the atomic numbers of the incident and the target nuclei. Layer
thickness and concentration profile can be determined from the energy difference
E
1
−
E
0
, see (7.20), of the backscattered projectile. The number of the detected
backscattered projectile ions gives information about the concentration of the target
element. From the differential Rutherford cross section (7.21) the atomic number
Z
T
of the target atom can be calculated. RBS is a standard free and absolute method. It
is more sensitive for heavier components of a the sample.
7.3.2 E
LASTIC
R
ECOIL
D
ETECTION
A
NALYSIS
The sample which should be analyzed is irradiated with high energetic heavy ions
under grazing incidence conditions (see [49,50]). Light elements (e.g., H, D) from
the sample are scattered in forward directions. The energy as well as the number
of outscattered atoms (recoils) of the sample components are measured at a fixed
angle relative to the beam direction, see Figure 7.14b. The mass identification can be
done by ToF (time of flight) methods (
E
ν
2
). The element concentration can
be estimated from the number of the forward scattered atoms. Layer thickness and
concentration profile will be determined from the energy difference
E
2
−
=
M
/
2
·
E
0
of the
forward scattered sample atoms
E
0
4
M
P
M
T
cos
2
φ
(
E
2
=
.
(7.22)
2
M
P
+
M
T
)
