Chemistry Reference
In-Depth Information
Fig. 13 Energy
dependence of the
quantities A and B entering
Eqs. (
5
) and (
6
) reported in
text, for some
semiconductors: silicon,
germanium, gallium
arsenide, and gallium
phosphide. The bulk optical
functions have been taken
from Palik [
47
]. Note that
here A and B are reported in
ʼ
m
1
, according to the
definition for these
coefficients used in Selci
et al. [
13
], slightly different
from formulas (
7
) for the
multiplicative factor “
d
.”
This fact changes only the
vertical scale: the overall
line shape expressing the
dependence upon photon
energy is the same (From
Selci et al. [
13
]. Reproduced
with permission. Copyright
1987, American Vacuum
Society.)
0
s
00
s
ε
1
ε
A
¼
and B
¼
;
ð
6
Þ
2
s
2
1
ε
0
s
þ ε
00
2
1
ε
0
s
þ ε
00
2
s
ε
s
00
are, respectively, the real and the imaginary parts of the dielectric
function of the substrate. The values of A and B can be computed by using data
reported in the literature [
47
]. Some examples are reported in Fig.
13
.
From formula
4
, two remarkable cases are considered and discussed:
ε
s
0
and
where
a) In the photon energy range where the substrate is transparent (B
¼
0) or weakly
absorbing (A
B), the RAS signal is given mainly (or only) by the anisotropy of
the layer absorption. The anisotropy of the dielectric function imaginary part
Δε
2
00
should be then computed by formula
4
(with B
¼
0) to value correctly the
peak position and the line shape details, but the interpretation of the results is
straightforward. An example is reported in Fig.
14
, for the cleavage diamond
surface C(111)2
1. The B coefficient (not reported here, computed from Palik
[
47
]) is zero below 6.5 eV [
21
]. The reader can evaluate how the line shape of
Δ
Δε
2
00
is extracted.
b) If the substrate absorption is not negligible, the real and the imaginary parts of
the layer anisotropic dielectric function are entangled, and a careful
deconvolution via Kramers-Kronig analysis is necessary. An alternative
R
/
R
RAS
is preserved when
