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

dN 3
dt = N 2
τ 23
− (σ em. φ + 1
τ 34
)N 3 Eqn (5.27)
dN 4
dt = −N 4
τ 41
+ (σ em. φ + 1
τ 34
)N 3 Eqn (5.28)
where, σ abs. and σ em. represent the absorption and emission cross-sections respectively
in m 2 , τ 21 is the transition time between levels 2 and 1 and τ 23 , τ 34 and
τ 41 represent the decay time from their respective levels and φ is the photon ux
(photons/m 2 ).
The photon ux can be related to the emission intensity which in turn is dependent
on the number of emitters in level N 3 . From N 3 (x), the number of emitters,
dn e in a small region dx is considered by dividing the whole thickness of the thin lm
into numerous steps smaller than the period of the incident pump standing wave
(dx = T stand /10). The number of emitters in this small region is given as,
tel-00916300, version 1 - 10 Dec 2013
dn e = N 3 (x).A.dx Eqn (5.29)
where A is the area of the laser beam. From this the square amplitude of source
in this discretized small step of thickness dx is calculated as,
S 2 (x) α dn e Eqn (5.30)
Using the rate equations, and using the initial population as N 0 1 = 10 26 emitters/m 3 ,
the photon ux as 8 x 10 3 V/m and refractive index described by gure 5.2, the
distribution of emitters is visualized through theoretical modeling (Fig. 5.11).
Figure 5.11: Distribution of emitters with depth in a lm of 1000 nm thickness. Left
axis: Number of emitters in a small thickness dx and Right axis: volumic concentration
per m 3 . (Simulated with Incident pump intensity: 10 5 W/m 2 ).
The number of excited emitters in a small thickness dx is given in the left axis
and the volumic concentration of excited emitters/m 3 is given on the right axis of
149