Growth and physical properties of crystalline rubrene - BOA Bicocca ...

1.3 Small-molecule organic semiconductors 7
Figure 1.3: Classification of excitons on the basis of the electron-hole pair radius.
From [36].
moment µ given by:
M ∝ |µ|2
∝
r3 f
(e ∗ − e0)
(1.8)
where e ∗ − e0 is the energy difference corresponding to the molecular transi-
tion ϕ 0 → ϕ ∗ , r is the intermolecular distance, and f is the oscillator strength
for the single molecule transition. Even for more complex crystals the pro-
portionality between the two momenta still holds, indicating the close link
between crystal and molecular properties typical of organic crystals.
As already noted, the result of the coherent excitation of molecules in the
crystal is called molecular exciton. Excitons are usually classified on the basis
of the radius of the electron-hole pair, as exemplified in figure 1.3. Frenkel
excitons, which are the most common type of exciton found in molecular
solids, are formed by an electron-hole pair residing on the same molecule
and which is able to move around the crystal by jumping between adjacent
molecules. The other limiting case, common for inorganic semiconductors
and not found in molecular crystals, is that of the Wannier exciton, with
a radius of the electron-hole pair corresponding to several primitive lattice
vectors. The intermediate case, called charge transfer exciton, can also be
found in aromatic molecular crystals, and is formed when an electron or hole
is transferred between two adjacent molecules, giving rise to an ion pair.
The importance of molecular excitons lies in their ability to conduct
electronic excitation energy within molecular crystals, a process which is also
extremely relevant for their electric transport properties and in particular for
the development of photovoltaic devices based on these materials.