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

u + = S + e −ik 2(d−x e)
and u − = S − e −ik 2x e
Eqn (5.22)
If there are N emitters placed at various positions x i (i = 1 to N ), then the
elds at the two ends of medium 2 becomes,
u + = ∑ N
i=1 S i(x i )e −ik 2(d−x i) at x = d − Eqn (5.23)
u − = ∑ N
i=1 S i(x i )e −ik 2x e at x = 0
+
Eqn (5.24)
In order to calculate the emission intensity of N emitters, the population rate
equations have to be known and are dened in the next section.
5.3.2 Population rate equations
tel-00916300, version 1 - 10 Dec 2013
In order to estimate the population density, the absorption and emission mechanisms
are described by a four level system. This system as illustrated in gure 5.10 is chosen
in order to relate to a Si-np system and to account for the dierence in energy levels
between the absorption and emission.
Figure 5.10: Four level system for modeling absorption and emission.
We assume the absorption of the incident photons (from laser) between energy
levels 1 to 2, fast non-radiative transition in level 2 to 3, reaching of a stationary
regime in level 3 where it stays for a time that denes the lifetime of the carriers, and
nally deexcitation to level 1 either by spontaneous or stimulated emission. If N − i
and N + i represent the population density of level i at time t and t + ∆t respectively,
the rate equations of each of the levels using the nite dierent method can be
written as follows:
dN 1
dt = −σ abs.φN 1 + N 4
τ 41
Eqn (5.25)
dN 2
dt = −N 2
τ 23
+ σ abs. φN 1 Eqn (5.26)
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