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 ...
gure 5.11. It can be seen clearly that the population in the excited state N 3 follows the pump prole with regularly alternating maxima and minima as suggested before. 5.3.3 Dynamical losses and gain In the framework of this thesis, it is assumed that the real part of refractive index is a constant, while the imaginary part may depend on the absorption and gain dynamics according to the following equation, ñ = n(λ) − ik(λ, x) + ig(λ, x) Eqn (5.31) tel-00916300, version 1 - 10 Dec 2013 where n(λ) is the real part of refractive index which we assume to be unchanged with the absorption dynamics, k(λ, x) accounts for the dynamic losses (absorption) and g(λ, x) is the dynamic gain (emission). Gain refers to an increase in the emitted electromagnetic intensity due to energy transfers within the medium as compared to the incident pump. When the gain is higher than the absorption in the thin lm, we may expect to see emission. In order to simulate the gain and losses few assumptions are made: ˆ Dynamic losses k(λ, x): The dynamic losses which depend on the population of emitters, can be expressed using the following equation, k(λ, x)= σ abs(λ).N 1 (x).λ Eqn (5.32) 4π where σ abs is the absorption cross section, and N 1 is the population of emitters in the ground state. In order to estimate the absorption cross section (σ abs ), and to give a shape to it, Lorentzian functions are used. Therefore σ abs can be represented by, σ abs = σ abs.max. 1 1 + (ω 2 ij(abs) −ω2 ) 2 ω 2 ∆ω 2 (abs) Eqn (5.33) where σ abs.max is the maximum value of absorption cross sections, ω ij(abs) is the frequency of absorption between levels i to j, and ∆ω is the width of the Lorentzian curve of absorption. The parameters in equation 5.32 are obtained by giving a shape to k(λ, x) by tting the experimentally obtained k(λ) with lorentzian function in the energy range of investigation (1.1 - 2.05 eV) of the emission behaviours (Fig. 5.12). ˆ Dynamic gain g(λ, x) : Similar to dynamic losses, dynamic gain can also be represented as a function of emission cross section (σ emis ) and the population of emitters in the excited state (N 3 ) as follows, 150
Figure 5.12: The shapes of k(λ) and k (λ, x). Lorentzian t of the k(λ) obtained through experiments, gives the shape of k(λ, x). tel-00916300, version 1 - 10 Dec 2013 g(λ, x) dynamic = σ em(λ).N 3 (x).λ 4π Eqn (5.34) For a transition between i → j, the Lorentzian function for the emission cross sections is represented as, σ em. = σ em.max 1 1 + (ω 2 ij(em.) −ω2 ) 2 ω 2 ∆ω 2 (em.) Eqn (5.35) where σ em.max is the maximum value of emission cross sections, ω ij(em.) is the frequency of emission transitions and ∆ω is the width of the Lorentzian curve of emission. Figure 5.13 shows the typical shapes of σ(λ) abs. and σ(λ) em. 5 Figure 5.13: Illustration of emission and absorption cross-sections for arbitrary inputs. 151
- Page 117 and 118: tel-00916300, version 1 - 10 Dec 20
- Page 119 and 120: (a) FTIR spectra of NRSN, Si 3 N 4
- Page 121 and 122: tel-00916300, version 1 - 10 Dec 20
- Page 123 and 124: Figure 4.15: Absorption coecient sp
- Page 125 and 126: A multilayer composed of 100 patter
- Page 127 and 128: multilayered conguration. Therefore
- Page 129 and 130: around 1250 cm −1 . The blueshift
- Page 131 and 132: tel-00916300, version 1 - 10 Dec 20
- Page 133 and 134: tion but within a dierence of one o
- Page 135 and 136: sample peak 1 (eV) peak 2 (eV) peak
- Page 137 and 138: (a) 1min annealing vs. T A . (b) 1h
- Page 139 and 140: tel-00916300, version 1 - 10 Dec 20
- Page 141 and 142: (a) Brewster incidence. (b) Normal
- Page 143 and 144: tel-00916300, version 1 - 10 Dec 20
- Page 145 and 146: increases for the 50 patterned samp
- Page 147 and 148: - Peak (3) and (c): 1.8-1.95 eV Die
- Page 149 and 150: 4.10.2 Eect of Si-np Size distribut
- Page 151 and 152: tel-00916300, version 1 - 10 Dec 20
- Page 153 and 154: tel-00916300, version 1 - 10 Dec 20
- Page 155 and 156: Chapter 5 Photoluminescence emissio
- Page 157 and 158: As seen from gure 5.1, a part of th
- Page 159 and 160: function of wavelength consists of
- Page 161 and 162: tel-00916300, version 1 - 10 Dec 20
- Page 163 and 164: In the case of our multilayers, the
- Page 165 and 166: ⎛ ⎜ ⎝ A ′ 2 B ′ 2 1 ⎞
- Page 167: dN 3 dt = N 2 τ 23 − (σ em. φ
- Page 171 and 172: 5.4 Discussion on the choice of inp
- Page 173 and 174: tting operations show the presence
- Page 175 and 176: (a) 270nm. (b) 300nm. tel-00916300,
- Page 177 and 178: (a) σ emis.max. = 8.78 x 10 −18
- Page 179 and 180: (a) 50(3/1.5) (b) 50(3/3) tel-00916
- Page 181 and 182: (a) Integrated population of excite
- Page 183 and 184: two kinds of emitters in SRSO subla
- Page 185 and 186: Conclusion and future perspectives
- Page 187 and 188: 4. Investigating the origin of phot
- Page 189 and 190: Bibliography [Abeles 83] B. Abeles
- Page 191 and 192: [Carlson 76] D. E. Carlson & C. R.
- Page 193 and 194: [Di 10] D. Di, I. Perez-Wur, G. Con
- Page 195 and 196: [Gritsenko 99] V. A. Gritsenko, K.
- Page 197 and 198: [Kaiser 56] W. Kaiser, P. H. Kech &
- Page 199 and 200: [Mandelkorn 62] J. Mandelkorn, C. M
- Page 201 and 202: [Pavesi 00] L. Pavesi, L. D. Negro,
- Page 203 and 204: [Sopori 96] B. L. Sopori, X. Deng,
- Page 205 and 206: [Weng 93] Y. M. Weng, Zh. N. fan &
- Page 207 and 208: and the tangential components of th
- Page 209 and 210: Appendix II Trials σ em.max (x10
- Page 211: Résumé tel-00916300, version 1 -
Figure 5.12: The shapes of k(λ) and k (λ, x). Lorentzian t of the k(λ) obtained through<br />
experiments, gives the shape of k(λ, x).<br />
tel-00916300, version 1 - 10 Dec 2013<br />
g(λ, x) dynamic = σ em(λ).N 3 (x).λ<br />
4π<br />
Eqn (5.34)<br />
For a transition between i → j, the Lorentzian function for the emission cross<br />
sections is represented as,<br />
σ em. = σ em.max<br />
1<br />
1 +<br />
(ω 2 ij(em.) −ω2 ) 2<br />
ω 2 ∆ω 2 (em.)<br />
Eqn (5.35)<br />
where σ em.max is the maximum value of emission cross sections, ω ij(em.) is the<br />
frequency of emission transitions and ∆ω is the width of the Lorentzian curve of<br />
emission. Figure 5.13 shows the typical shapes of σ(λ) abs. and σ(λ) em.<br />
5<br />
Figure 5.13: Illustration of emission and absorption cross-sections for arbitrary inputs.<br />
151