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

multilayers, absorption and emission cross-sections.
For all the simulations, it is considered that the thin lm is located between the
semi-innite Si substrate and semi-innte air medium.
5.2 Incident pump prole
tel-00916300, version 1 - 10 Dec 2013
5.2.1 Methodology : Matrix formulation for Isotropic layered
media
The incident Electro-Magnetic (EM) wave of the Ar laser is described by the electric
eld vector ( ⃗ E), magnetic eld vector ( ⃗ H) and the wave vector ( ⃗ k) perpendicular
to each other (Fig. 5.1). The calculations are perfomed in the cases of TE wave
(E y ≠ 0, E x = E z = 0). Figure 5.1 is a typical illustration of our thin lms of
thickness d, with two interfaces between the air and the substrate. The refractive
indices of the three media (air, thin lm and substrate) are denoted as n 1 , n 2 and n 3
respectively. The incident angle of the propagation wave vector, −→ k is denoted as θ inc .
The incident wave undergoes absorption, transmission and reection phenomena and
the intensity of the total EM wave that comes out of the sample is collected (in the
PL set-up and in simulations) with an angle of collection in the range, θ collect ±23°.
Figure 5.1: Schematic representation of external and internal components of our thin
lm samples under investigation. in TE mode. θ inc = 45 o and θ collect = ±23 o .
The electric eld amplitude of the incident plane wave is given by,
E y (x) =E(x)e i(ωt−βz) Eqn (5.1)
where β is the z component of the propagation wave vector and ω is the angular
frequency. The repartition of the incident pump eld in this thin lm is simulated
using transfer matrix formulation [Yeh 88, Weber 91, Boucher 06] that relates the
amplitude of the eld on either sides of the thin lm.
138