Environmental Engineering Reference
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Fig. 6.5 An equivalent circuit accounting for the diffusion-recombination mechanism used for
fitting. Modulation of stored excess minority carriers gives rise to distributed chemical
capacitance c
n
. Bimolecular recombination of conduction band electrons and valence band holes
are modeled by resistive elements r
rec
. Transport of electrons is represented by means of r
t
.An
additional series resistance is needed to model contact and wire effects, R
s
. Finally, a capacitor
C
g
& ee
0
A/L represents dielectric contribution of the diode [
53
]. (Reprinted from [
53
], with
permission from Elsevier) (
http://www.sciencedirect.com/science/journal/15661199
)
There has been a very detailed review on application of IS technique in
dye-sensitized solar cells (DSSCs), quantum dot based dye-sensitized solar cells
(QD-DSSCs), and OPVs [
55
]. Fabregat-Santiago et al. speculated the under-
standings of measured capacitance as a function of voltage and IS spectra [
55
].
First, they summarized a characteristic measurement as shown in Fig.
6.6
a and the
subsequent four feature regions that can be distinguished as follows:
(I) at a large reverse bias (V
app
« V
fb
), the sample is considered as a dielectric
capacitor with a constant capacitance, giving rise to a geometrical value C
g
;
(II) at a moderate reverse and low forward bias (V
app
\ V
fb
), the C-V characteristic
is close to a Mott-Schottky model (C
sc
= Ae
r
e
0
/W = Ae
r
e
0
/W
0
V
sc
1/2
), as
shown in Fig.
6.6
b, where C
sc
is determined by the depletion layer modulation.
(III) at a proper forward voltage (V
app
C V
fb
), the capacitance (C
l
) is controlled
by a chemical capacitance due to the excess carriers, which results in the
collapsed depletion zone.
(IV) at a larger forward bias (V
app
» V
fb
), the capacitance goes saturated and
finally decreases exhibiting negative limitation mechanisms.
Secondly, the authors present their interpretation on typical IS spectra, recorded
under open-circuit conditions by varying the illumination level and characterized
by a major RC arc plus additional minor features at high frequency [
55
,
56
].
Generally, the information of charge transport, series resistance, and dielectric
contributions might be reflected by the high-frequency arc of the spectra [
53
]; on
the other hand, the recombination in the active layer will lead to the low-frequency
arc of the spectra [
57
]. The values of the capacitance, resistance, and lifetime can
be plotted as a function of V
oc
.
Glatthaar et al. studied the effect of post-treatment on P3HT:PCBM BHJ OPVs
by using IS [
58
]. The results indicate that a reduced doping level at the Al interface
is observed as a depletion region evidenced by the bias dependence of IS
(Fig.
6.7
), leading to an improved rectification behavior at the organic/metal
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