5. Organic Electronics and Optoelectronics

Transcription

1 1 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. O R N O O N R O

2 2 5.1 Organic Materials: Concepts for Optical and Electronic Properties 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).

3 3 Atoms Diatomic molecules --- Spherically symmetric field --- Use orbital quantum number l as a label --- 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.

4 Linear combination of atomic orbitals (LCAO), applications of the variation principle and secular equation

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8 Hückel theory --- π electrons --- aromaticity

9 9 Example 1: Ethylene H 3 C=CH 3 We optimize the orbital coefficients as before using the variation principle. We know already that this leads to secular equations as follows.

10 10 Example 2: Aromaticity and the benzene ring σ bonds π bonds Fig. Fehler! Kein Text mit angegebener Formatvorlage im Dokument.-1 Consider π molecular orbitals of a cyclic polyene (N carbon atoms, not necessarily exactly 6 as in benzene), following the same formalism as above

11 11 (i) For even membered rings (N=2l, where l is an integer)

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13 13 (ii) For odd membered rings (N=2l-1, where l is an integer)

14 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.

15 15 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 Anthracen- Moleküls, 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 π- Elektrons im tiefsten nicht besetzten Molekülorbital (LUMO). (after Schwoerer /Wolf, p.3, Fig.1.3)

16 16 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 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.