1 Basic Principles of Modern Organic Solar Cells
15
1.2.2.2 Non-radiative Recombination
Carrier recombination causing the V oc loss is an essential process that determines
the magnitude of the V oc . Figure 1.14 shows the energetic diagram of the energy loss
factors in D/A type organic solar cells (Fig. 1.7c, d). The V oc loss is defined as the
energy difference between the optical band gaps of the organic semiconductors (E g )
and eV oc (Fig. 1.14, right vertical axis). CT states are formed by the dissociation of
strongly bound (Frenkel) excitons in the single films of D and A cells (Figs. 1.6b,
1.7a) into electron–hole pairs (Fig. 1.7b) by the electron transfer from D to A at D/A
interface.
CT states are the key to understanding the recombination process. When recombination occurs before the generation of free electrons and holes by dissociating the CT
state, it is referred to as “geminate recombination” (Fig. 1.14). Recent reports have
revealed that the energy difference between the optical band gaps and the CT states,
i.e., electron transfer loss; (E g – E CT ), which drives efficient free carrier generation,
is smaller than 50 meV (Fig. 1.14, right vertical axis) [35, 36]. Thus, the main factor
of the V oc loss is the energy difference between CT states (E CT ) and eV oc caused
by the radiative recombination that dissipates the energy to emitting photons and
the non-radiative recombination dissipating the energy to thermal energy, i.e., the
molecular vibrations [37]. For the conventional organic semiconductor films, a large
Stokes shift between the absorption and emission spectra was observed (Fig. 1.15a).
Here, the vibrational coupling easily induces non-radiative recombination, which
reduces the V oc .
In addition, when the defects acting as carrier traps exist between the D/A
interface, trap-assisted recombination occurs (Fig. 1.15b) [38–41]. Since this is an
additional non-radiative recombination path, the V oc decreases even more.
Figure 1.16 shows the dependence of V oc on the CT state energy (E CT ) under
1 sun. The black solid line represents the thermodynamic theoretical limit of V oc ,
which is calculated according to the Shockley–Queisser (SQ) assumption. On this
ideal line, V oc shows its intrinsically highest values, that is, the V oc loss shows only
those smallest and inevitable values that occur due to radiative recombination [42].
For all types of organic solar cells, the reported V oc losses are always greater than
approximately 0.6 eV (Fig. 1.16, crosses) [43]. For comparison, the V oc of inorganic
GaAs solar cells has a small V oc loss of approximately 0.3 eV, which is achieved by
suppressing the non-radiative surface recombination, is shown by the closed triangle
[44]. For organic solar cells, it remains unclear how the non-radiative recombination
lowers the V oc . According to one study, the high crystallinity of the molecular layers
in the vicinity of the D/A interface, which suppresses the molecular vibrations and
lowers the defect concentration, has been reported to increase the V oc close to the
SQ limit [45]. The relationship between carrier recombination and V oc is discussed
in detail in Chap. 8.
Even after the free carrier generation, free electrons and holes are recombined by
bimolecular recombination, the details of which are discussed in Chap. 6, Sect. 6.5.1.
15
1.2.2.2 Non-radiative Recombination
Carrier recombination causing the V oc loss is an essential process that determines
the magnitude of the V oc . Figure 1.14 shows the energetic diagram of the energy loss
factors in D/A type organic solar cells (Fig. 1.7c, d). The V oc loss is defined as the
energy difference between the optical band gaps of the organic semiconductors (E g )
and eV oc (Fig. 1.14, right vertical axis). CT states are formed by the dissociation of
strongly bound (Frenkel) excitons in the single films of D and A cells (Figs. 1.6b,
1.7a) into electron–hole pairs (Fig. 1.7b) by the electron transfer from D to A at D/A
interface.
CT states are the key to understanding the recombination process. When recombination occurs before the generation of free electrons and holes by dissociating the CT
state, it is referred to as “geminate recombination” (Fig. 1.14). Recent reports have
revealed that the energy difference between the optical band gaps and the CT states,
i.e., electron transfer loss; (E g – E CT ), which drives efficient free carrier generation,
is smaller than 50 meV (Fig. 1.14, right vertical axis) [35, 36]. Thus, the main factor
of the V oc loss is the energy difference between CT states (E CT ) and eV oc caused
by the radiative recombination that dissipates the energy to emitting photons and
the non-radiative recombination dissipating the energy to thermal energy, i.e., the
molecular vibrations [37]. For the conventional organic semiconductor films, a large
Stokes shift between the absorption and emission spectra was observed (Fig. 1.15a).
Here, the vibrational coupling easily induces non-radiative recombination, which
reduces the V oc .
In addition, when the defects acting as carrier traps exist between the D/A
interface, trap-assisted recombination occurs (Fig. 1.15b) [38–41]. Since this is an
additional non-radiative recombination path, the V oc decreases even more.
Figure 1.16 shows the dependence of V oc on the CT state energy (E CT ) under
1 sun. The black solid line represents the thermodynamic theoretical limit of V oc ,
which is calculated according to the Shockley–Queisser (SQ) assumption. On this
ideal line, V oc shows its intrinsically highest values, that is, the V oc loss shows only
those smallest and inevitable values that occur due to radiative recombination [42].
For all types of organic solar cells, the reported V oc losses are always greater than
approximately 0.6 eV (Fig. 1.16, crosses) [43]. For comparison, the V oc of inorganic
GaAs solar cells has a small V oc loss of approximately 0.3 eV, which is achieved by
suppressing the non-radiative surface recombination, is shown by the closed triangle
[44]. For organic solar cells, it remains unclear how the non-radiative recombination
lowers the V oc . According to one study, the high crystallinity of the molecular layers
in the vicinity of the D/A interface, which suppresses the molecular vibrations and
lowers the defect concentration, has been reported to increase the V oc close to the
SQ limit [45]. The relationship between carrier recombination and V oc is discussed
in detail in Chap. 8.
Even after the free carrier generation, free electrons and holes are recombined by
bimolecular recombination, the details of which are discussed in Chap. 6, Sect. 6.5.1.