Films minces à base de Si nanostructuré pour des cellules ...

k(E) = f j(ω − ω g ) 2
(ω − ω j ) 2 + Γ 2 j
Eqn (2.12)
k(E) = 0 if w < w j Eqn (2.13)
where n ∞ is the refractive index of a material when energy tends to innity, w
is the wave energy in eV, f j is the fraction of electrons that oscillate at resonant
energy strength w j , G j is the damping coecient that gives rise to the phenomena
of optical absorption. The constants B and C are given as follows:
B = f j
Γ j
[
G
2
j − (w − w j ) 2] Eqn (2.14)
tel-00916300, version 1 - 10 Dec 2013
C = 2f j G j (w − w j ) Eqn (2.15)
The imaginary part of the refractive index k(E) is also known as the extinction
coecient because it represents absorption or attenuation of an electromagnetic
wave. Hence from k(E), the absorption coecient of the lm can be extracted using
the relation,
α= 4πk
λ =4πkω hc
Eqn (2.16)
where h is the Planck's constant and c is the velocity of the light.
Figure 2.17 explains the rst two steps involved in modelling an ellipsometric
spectra.
The measured (Y, D) spectra can be visualized in terms of n and k through
internal calculations in the software. Therefore a model is built according to our
structure under investigation also taking into account the possible surface roughness
in the material as shown in Step 1. The parameters involved in the dispersion
relation are adjusted to get an approximate shape of dispersion curve that matches
with the standard material as shown in Step 2. Following this, a data tting of the
measured spectra with the theoretically obtained spectra is performed. The value
of χ 2 is low if the extent of closeness between the two spectra is high. From this
tting, we deduce the optical constants from the new dispersion curve of the sample
under investigation. These are represented as Step 3 and Step 4 in gure 2.18. The
simulation results also include the thickness of the sample.
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