5. Organic Electronics and Optoelectronics

5. Organic Electronics and Optoelectronics

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5. Organic Electronics and Optoelectronics
Sources:
W. Brütting, Physics of Organic Semiconductors, Wiley-VCH
M. Schwoerer / H. C. Wolf, Organic Molecular Solids, Wiley-VCH
Atkins / Friedman, Molecular Quantum Mechanics, Oxford
Complementary to devices based on more conventional (inorganic) materials such as
Si, GaAs, or others, in recent years devices based on organic (molecular) materials
have become more and more popular and successful. Before we will discuss their
technology and potential advantages (superior colour, light weight, cost efficiency,
spin coherence etc.) in Sec.5.2, we will first briefly review the fundamental physics
underlying their electronic and optical properties relevant for device applications.
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5.1 Organic Materials:
Concepts for Optical and Electronic Properties
5.1.1 Molecular Orbitals, π-Electrons, the Benzene Molecule, and Aromaticity
Fig.XXX: An orbital picture of the carbon-carbon double bond. Both σ and π bonding
molecular orbitals are filled. The antibonding combinations are unfilled (from McMurry
“Organic Chemistry”, Fig. 6.2, p.178).
Fig.XXX: Cross sections cut through carbon-carbon single and double bonds. Free rotation is
possible around a single bond but not around a double bond (from McMurry “Organic
Chemistry”, Fig. 6.3, p.179).
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Atoms
--- Spherically symmetric field
--- Use orbital quantum number l as a label
Diatomic molecules
--- Cylindrically symmetric field
--- Use magnitude of the component of the angular momentum
along the internuclear axis, λħ
Thus if we look down the symmetry axis
Fig. XXX
As is more thoroughly discussed in other lecture courses (such as “Atoms, Molecules,
and Light”), the interaction of atomic orbitals leads to molecular orbitals characterized
by σ, π, etc.
The σ orbitals of a diatomic molecule exhibit rotational symmetry about the
molecular axis and typically have stronger binding energies. As a rough gide, an
isolated single σ bond absorbs light (σ* σ) at 120 nm (10.3 eV), i.e. well above
photon energies of the visible light.
The π orbitals characteristically exhibit electron density “standing away” from the
axis. They are less strongly bound and more delocalised, which is why they are most
relevant for optical absorption in the visible and for charge carrier transport.
The next few pages feature a summary of molecular orbital theory from the course
“Atoms, Molecules, and Light”.
We will conclude with a simple theory for benzene and its “delocalized π orbitals”.
Benzene is a prototype for aromatic molecules, which play a key role in organic
electronics.
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5.1.2 Linear combination of atomic orbitals (LCAO), applications of the
variation principle and secular equation
Eq. Feh
Eq. Feh
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5.1.3 Hückel theory --- π electrons --- aromaticity
Eq. Feh
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Example 1: Ethylene H3C=CH3
We optimize the orbital coefficients as before using the variation principle.
We know already that this leads to secular equations as follows.
Eq. Feh
Eq. Feh
Eq. Feh
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Example 2: Aromaticity and the benzene ring
σ bonds
π bonds
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Consider π molecular orbitals of a cyclic polyene (N carbon atoms, not necessarily
exactly 6 as in benzene), following the same formalism as above
Eq. Feh
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(i) For even membered rings (N=2l, where l is an integer)
Eq. Feh
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(ii) For odd membered rings (N=2l-1, where l is an integer)
Eq. Feh
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5.1.4 The spectrum of benzene and larger acenes
Analogy benzene – band structure
Note that the dependence of the energy levels on k (the “wavevector index”) in one
single benzene molecular (which is considered here as a (1d) periodic system, i.e. a
ring with periodic boundary conditions !) is conceptually similar to the band structure
of a crystalline (i.e., periodic) solid.
Note also that for larger aromatic molecules the energy levels are typically more
closely spaced (i.e. “more k points”, with again some analogy to crystals).
The gap and HOMO-LUMO difference
Also, as one would expect, the lowest-energy transition (HOMO-LUMO, i.e. highest
occupied molecular orbital to lowest unoccupied molecular orbital) is also at lower
(red-shifted) for larger molecules compared to smaller ones.
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Larger acenes
Although the complete spectrum is certainly more complicated, also for the larger
acenes, we can find indications of the k dependence of the orbitals as we virtually go
in a circle around the molecule.
Abbildung 1.3: Oben: Gesamte Verteilung der π-Elektronen im elektronischen Grundzustand des AnthracenMoleküls, C14H1O. Der Rand wurde so gewählt, dass etwa 90 % der gesamten Elektronendichte erfasst sind.
Mitte: Verteilung eines π-Elektrons im höchsten besetzten Molekülorbital (HOMO). Unten: Verteilung eines πElektrons im tiefsten nicht besetzten Molekülorbital (LUMO). (after Schwoerer /Wolf, p.3, Fig.1.3)
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Real absorption spectra: Size dependence in the series of the acenes
The wavelength of the absorption edges of the acenes as a function of length follows
at least qualitatively the predicted increase with conjugation.
Fig.XXX. Absorption spectra of the acenes in solution.
(from Haken / Wolf II, p. 291, Fig.14.19 and Fig.14.20).
Of course, for a quantitative agreement with the experiment a less approximate theory
has to be employed.
In the present context, it is sufficient to note that aromatic compounds
--- typically exhibit excitations in the visible (e.g., red or blue light)
--- feature delocalised electrons
The latter are relevant for the excitations and charge carrier transport, which we shall
discuss in the following sections.