Optical Excited States in Crystals

Since these early works, the field of the spectroscopic properties of molecular solids has grown enormously. In the following sections, we shall present the most important phenomena and discoveries from this field. 

The electronic excited states of organic molecular crystals are clearly and in a readily understandable way derived from those of the free molecules (or of molecules in liquid solutions). This follows, as was already discussed in Chap. 2, from the fact that the intermolecular forces in crystals are relatively weak in comparison to the binding forces within the molecules. The excited states and the transitions between them are studied by means of optical spectroscopy, particularly in the visible and the ultraviolet spectral ranges. Here, we will explain the essential facts using 

Light can be absorbed by organic molecular crystals in their singlet or in their triplet term systems (Fig. 6.2). The term diagram shown here is equally vahd for free molecules and for molecular crystals. In an ideal crystal, the excited states 

The lowest excited states Si and Ti have, in contrast, long lifetimes, usually between 10 and 10 s for Si and 10to 20 s for Ti in typical crystals. The radiative transitions Si So are termed fluorescence and the Ti — So radiative transitions are called phosphorescence. Transitions between the pure singlet and the pure triplet systems, so called intersystem crossings (ISC), are forbidden. 

As shown in Fig. 6.2, within the purely electronic terms S (u 0) and T (u l) there are superposed vibronic terms, that is terms with excited molecular vibrations. In the crystal, the intramolecular vibrations are only slightly different from those in the free molecules (cf. Chap. 5). Electronic transitions between levels with zero vibrational quantum numbers are called 0,0 transitions. 

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The lowest excited states in molecular crystals are singlet and triplet excitons [3]. Since it costs coulombic energy to transfer an electron that has been excited optically from the HOMO (highest occupied molecular orbital) to the LUMC)... 

By making use of classical or quantum-mechanical interferences, one can use light to control the temporal evolution of nuclear wavepackets in crystals. An appropriately timed sequence of femtosecond light pulses can selectively excite a vibrational mode. The ultimate goal of such optical control is to prepare an extremely nonequilibrium vibrational state in crystals and to drive it into a novel structural and electromagnetic phase. 

The resemblance of the photocurrent to the optical adsorption spectrum has suggested the involvement of molecular excited states in the creation of charge carriers. While this resemblance is by no means universally observed, the concept of carrier creation via exciton interactions at or very near the illuminated electrode has become increasingly favored. Many of the data leading to these conclusions have been obtained by the use of pulsed light techniques (6, 7,3). These methods are virtually independent of electrode effects and the subsequent analysis of the transient current has led to considerable advances in the theory of charge transfer in molecular crystals. 

Several kinetic schemes have been put forward (4, 13, 24) to explain the kinetics of excited states in solid solutions and pure and mixed crystals following optical and ionizing-particle excitation. These schemes, as well as the direct quenching reactions for singlets and triplets, include triplet-triplet annihilation reactions... 

The class which has been most intensively investigated in solid-state physics includes the crystals of simple aromatic hydrocarbons such as anthracene or naphthalene. Various usual versions of the structural formula of anthracene are given in Fig. 1.5. For the aliphatic compounds, we take n-octane as model substance. Here, the optically-excitable states lie at considerably higher quantum energies than in the case of the aromatic compounds, since here there are no n electrons. We will not treat them at any length in this book. 

In a first step, we consider a physical dimer. This is a pair of equivalent molecules, denoted by 1 and 2, whose distance and relative orientation are the same as in the crystal lattice. In the case of anthracene, let these be the two molecules in a unit cell. Such a configuration gives a mini-exciton [17] in an optically-excited state. This model is explained in Fig. 6.7. Later, we will expand it to include the whole crystal lattice, and will thus obtain the Frenkel excitons. 

In Chap. 6, we discussed low-energy optical excitation states, the singlet and triplet excitons and energy transfer. The primary experimental method applied there was optical spectroscopy in the visible, in the near IR and in the UV spectral ranges. In the present chapter, we treat the structure and the dynamics of localised triplet states, of triplet mini-excitons, and of triplet excitons in molecular crystals. The primary experimental method for the investigation of the lowest-energy triplet level Ti is electron-spin resonance (ESR) (Fig. 7.1). 

Fig. 7.24 The ESR spectrum of the T- state of a naphthalene-dg 0.2% naphthalene-hg mixed crystal at T=4.2K,v = 9.4 GHz. The ESR signal is as usual the first derivative of the microwave absorption spectrum. In the centre of the signal UHU, which is due to free radicals in the sample holder and not to an optically-excited state, the first derivative is...

In Chap. 8, we treated organic crystals which are composed of a single type of molecules. As we expect of organic substances, these crystals are semiconductors or insulators. The LUMOs of the molecules form the conduction band, the HO-MOs form the valence band, and the energy gap is large compared to ksT. At room temperature, typical values of the conductivity are less than about lO" (S2 cm) , and values of the mobilities are less than around 1 cm /Vs. The lowest-lying optical excitation states of these substances are Frenkel excitons. 

Both solitons and polarons have their characteristic absorption bands below the band gap energy. Then, for the identification of the nonlinear excited states, the optical absorption and the electron spin resonance spectra must be studied, to get information about the midgap states and the spin, respectively. Studies of the electrical properties are also needed to get information about the charge. In this report, the excited states in single crystals of (Pt(en)2][Pt(en) ] 2 4 are studied by the experimental methods mentioned above, and the photo-induced excited state in this material is shown to be polarons, which are also produced by halogen-doping. 

The X-ray excitation process frequently is analyzed in terms of an excitonic electron hole pair (e.g. Cauchois and Mott 1949). The excitonic approach to X-ray absorption spectra accounts for the fact that the excited state is a hydrogen-like bound state. The X-ray exciton is different from the well-known optical excitons. In the latter cases the ejected electron polarizes a macroscopic fraction of the crystal-fine volume because the lifetime of optical excitations is in the order of lO s. The lifetime of the excited deep core level state, however, is in the order of 10 — 10 s, much too short to p-obe more than the direct vicinity of excited atom. Following Haken and Schottky (1958) the distance r between the ejected electron and core hole of an excited atom for E = 1 turns out to be r oc [h/(2m 0))] Here m denotes the effective mass of the ejected electron, to is the phonon frequency and is the dielectric constant. A numerical estimate yields r 10 A. Thus the information obtainable in an L, spectrum of the solid is very local the measurement probes essentially the 5d state of the absorbing atom as modified from the atomic 5d states by its immediate neighbors only. It is not suited to give information about extended Bloch states. On the other hand it is well suited to extract information about local correlations within the 5d conduction electrons, whose proper treatment is at the heart of the difficulty of the theory of narrow band materials and about chemical binding effects. 

The term solid-state laser refers to lasers that use solids as their active medium. However, two kinds of materials are required a host crystal and an impurity dopant. The dopant is selected for its ability to form a population inversion. The Nd YAG laser, for example, uses a small number of neodymium ions as a dopant in the solid YAG (yttrium-aluminum-gar-net) crystal. Solid-state lasers are pumped with an outside source such as a flash lamp, arc lamp, or another laser. This energy is then absorbed by the dopant, raising the atoms to an excited state. Solid-state lasers are sought after because the active medium is relatively easy to handle and store. Also, because the wavelength they produce is within the transmission range of glass, they can be used with fiber optics. 

Germanium crystals that contain the substitutional triple acceptor copper (Hall and Racette, 1964), as well as hydrogen, exhibit in PTIS a series of broad lines that belong to an acceptor with a ground state at 17.81 meV above the top of the valence band (Haller et al., 1977a). PTIS studies over a range of temperatures have shown that this acceptor has a ls-state that is split into a large number of components that are closely spaced (Kahn et al., 1987). When thermally populated, each of the components of the ls-state manifold acts as an initial state for optical trasitions of the bound hole to one of the effective mass-like excited states. This in turn explains why the lines of this center appear broad. 

In ideal situations, optical spectroscopy as a function of temperature for single crystals is employed to obtain the electronic spectrum of a SCO compound. Knowledge of positions and intensities of optical transitions is desirable and sometimes essential for LIESST experiments, particularly if optical measurements are applied to obtain relaxation kinetics (see Chap. 17). In many instances, however, it has been demonstrated that measurement of optical reflectivity suffices to study photo-excitation and relaxation of LIESST states in polycrystalline SCO compounds (cf. Chap. 18). 

For excited state calculations, significant progress has been made based on the GW method first introduced by Hybertsen and Louie. [29] By considering quasi-partide and local field effects, this scheme has allowed accurate calculations of band gaps, which are usually underestimated when using the LDA. This GW approach has been applied to a variety of crystals, and it yields optical spectra in good agreement with experiment. 

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