Films minces à base de Si nanostructuré pour des cellules ...
Films minces à base de Si nanostructuré pour des cellules ... Films minces à base de Si nanostructuré pour des cellules ...
where( D α is the ) passage matrix ( whose ) shape depends on the ( polarization (TE ) and A TM) and 2 A ′ 2 e is linked to by propagation matrix ikαd 0 (refer B 2 B ′ 2 0 e −ikαd Appendix I). From equation 5.8, the reected amplitude can be obtained for known A 1 since, B 1 = r glob A 1 . Hence, ( From the values of the following form: ( A ′ 2 B ′ 2 A ′ 2 B ′ 2 ) ) = D −1 2 D ( ) A 1 r glob A 1 Eqn (5.10). , the stationary eld of the pump is obtained with E p (x)= A ′ 2e −jk 2x + B ′ 2e jk 2x Eqn (5.11) tel-00916300, version 1 - 10 Dec 2013 5.2.2 Incident electric eld amplitude, A 1 A realistic value for the incident electric eld amplitude has to be determined to be fed as an input for simulations. In the PL experiments, we have access to the intensity (I) of the laser which is the square amplitude of the incident electric eld (Poynting vector). The intensity of the laser is calculated as 100 mW/mm 2 = 10 5 W/m 2 , in our case. This intensity is linked to the electric eld amplitude E p (x) by, I = cε on | E p (x) | 2 2 From this, the amplitude of the incident electric eld is calculated by, E p (x) = Eqn (5.12) √ 2I cnε 0 Eqn (5.13) where, n = refractive index of air = 1, c = 2.99 x 10 8 m/s is the speed of light and e o = 8.85 x10 −12 C 2 /N.m 2 is the dielectric constant. Thus, the amplitude of the electric eld calculated from equation 5.13 leads to a value of 8x10 3 V/m. This value is fed as input A 1 in the code developed by our team 1 . 5.2.3 Pump prole in the thin lm The pump prole is simulated with regard to the angle of incidence, thickness of the lm, and complex refractive index. The complex refractive index which vary as a 1 Dr. J. Cardin and Prof. C. Dufour devoloped the code for simulations. 140
function of wavelength consists of the real part n and imaginary part k, known as the extinction coecient. This is represented by, Complex refractive index ñ = n(λ) − ik(λ) Eqn (5.14) Figure 5.2 shows the shapes of simulated n(λ) and k(λ) by using the parameters from our ellipsometry results on the corresponding thin lm, as the input. tel-00916300, version 1 - 10 Dec 2013 Figure 5.2: The variation of complex refractive index (ñ = n(λ) − ik(λ)) of a thin lm, as a function of wavelength. The pump wavelength was xed at 488 nm in all the simulations, relating to the Ar laser used in the PL experimental set-up. (a) Inuence of Angle of incidence The simulations consist of focussing the pump on a 500 nm thin lm with complex refractive index described in gure 5.2. The pump pro- le is investigated as a function of depth (x) from the lm surface, for two angles of incidence: normal incidence and 45° incidence (Fig. 5.3). This gure clearly indicates that the incident pump intensity oscillates between maxima and minima along the depth (x). As a consequence, even if the emitters are homogeneously distributed within a thin lm, they are subjected to a variable pump prole. Figure 5.3: Pump intensity prole with regard to its angle of incidence on the thin lm. 141
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function of wavelength consists of the real part n and imaginary part k, known as<br />
the extinction coecient. This is represented by,<br />
Complex refractive in<strong>de</strong>x ñ = n(λ) − ik(λ) Eqn (5.14)<br />
Figure 5.2 shows the shapes of simulated n(λ) and k(λ) by using the parameters<br />
from our ellipsometry results on the corresponding thin lm, as the input.<br />
tel-00916300, version 1 - 10 Dec 2013<br />
Figure 5.2: The variation of complex refractive in<strong>de</strong>x (ñ = n(λ) − ik(λ)) of a thin lm,<br />
as a function of wavelength.<br />
The pump wavelength was xed at 488 nm in all the simulations, relating to the<br />
Ar laser used in the PL experimental set-up.<br />
(a) Inuence of Angle of inci<strong>de</strong>nce<br />
The simulations consist of focussing<br />
the pump on a 500 nm thin lm<br />
with complex refractive in<strong>de</strong>x <strong>de</strong>scribed<br />
in gure 5.2. The pump pro-<br />
le is investigated as a function of<br />
<strong>de</strong>pth (x) from the lm surface, for<br />
two angles of inci<strong>de</strong>nce: normal inci<strong>de</strong>nce<br />
and 45° inci<strong>de</strong>nce (Fig. 5.3).<br />
This gure clearly indicates that<br />
the inci<strong>de</strong>nt pump intensity oscillates<br />
between maxima and minima<br />
along the <strong>de</strong>pth (x). As a consequence,<br />
even if the emitters are<br />
homogeneously distributed within a<br />
thin lm, they are subjected to a variable pump prole.<br />
Figure 5.3: Pump intensity prole with regard<br />
to its angle of inci<strong>de</strong>nce on the thin lm.<br />
141