Page 257 - A Comprehensive Guide to Solar Energy Systems

260 A COmPreHenSIVe GuIde TO SOlAr enerGy SySTemS

For this reason, organic semiconductors are often described as van der Waals solids, and
the energy levels that transport charge are highly localized on individual molecules. Con-
sequently, the properties of organic semiconductors are typically understood in terms of
an array of weakly interacting potential wells, as depicted in Fig. 12.3. Since the integrity of
the molecule is preserved in organic semiconductors, a molecular description of the orbit-
als involved in charge transport is most widely used, in which the HOmO is equivalent to
the valence band and the lumO to the conduction band in a crystalline inorganic semi-
conductor. In some circumstances, such as at low temperature, a band model can be used
to explain the behavior of some highly ordered organic semiconductors (e.g., pentacene),
although even at low temperature the bandwidth is very narrow (<0.1 eV) due to the very
weak interaction between adjacent molecules.
upon photon absorption, the photo-excited electron is localized in the lumO of the
same molecule as the hole, which for small molecule organic semiconductors corresponds
to a separation of the order of <1 nm. While semiconducting polymers can have dimen-
sions hundreds of times greater than this, the electronic and optical properties are domi-
nated by that of much smaller segments of the polymer chain known as the conjugation
length. This is because, in real polymer films, twists and kinks in the polymer chain disrupt
the strong coupling of the p-atomic orbitals that gives rise to the HOmO and lumO [18].
As a result, a photo-excited electron in the lumO and the hole formed in the HOmO are
spatially confined to the same small segment of the polymer chain. This very close prox-
imity of oppositely charged charge carriers, combined with the relatively low dielectric
constant of typical of organic semiconductors, results in a strong coulombic interaction
between the photo-generated electron and hole. Consequently light absorption in organic
semiconductors does not result in direct formation of free charge carriers, but of tightly
bound electron-hole pairs, which can be described in terms of a charge neutral quazi-par-
ticle called a Frenkel exciton (Fig. 12.4 process 1) [24,26]. Since excitons have no net charge

FIGURE 12.3 Schematic diagram illustrating the potential well for an isolated molecule (left) and an aggregation of
molecules (right) held together by van der Waals interactions (i.e., a molecular solid). The electron affinity (E a ) and
ionization potential (I p ) are also shown.