Charge-Carrier Mobility in Organic Crystals
Organic crystals are usually lacking main valence bonds between their constituent molecular repeat units. Therefore, in organic crystals there is usually no substantial electronic overlap between the molecules1; interactions are based on mere van der Waal
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8.1
Introduction
Organic crystals are usually lacking main valence bonds between their constituent molecular repeat units. Therefore, in organic crystals there is usually no substantial electronic overlap between the molecules 1 ; interactions are based on mere van der Waals forces in the very large class of neutral molecular crystals (or on a combination of van der Waals and local [closed shell] Coulombic interactions in the barely studied class of ionic organic crystals). As a consequence, exchange of a possibly present conduction electron or hole between neighboring molecules is not a very efficient process and, hence, electronic transport is generally slow in organic solids. Charge carriers are to be considered as rather localized (on individual molecules), with the consequence, specific for this class of materials, of considerable local changes of nuclear positions, vibrational frequencies, and electronic wavefunctions by polarization interactions (see, e.g., [1-3]). This situation is usually described by introducing the concept of a polaron [1,4] as an appropriate quasiparticle, comprising the electronic charge and the induced surrounding polarization based on electronic, vibronic and phononic relaxation. Due to strong intraand intermolecular vibrational fluctuations, no coherent propagation of this quasiparticle is usually possible around room temperature and above, not even in a pure and structurally perfect crystal. The strong localization is reflected macroscopically by strong inertial resistance against acceleration (e.g. by an applied electric field), which can formally be ascribed to a high "effective" mass of the "polaronic" charge carrier [4]. As we will see below, however, gradual freezing out of uncorrelated vibrations upon cooling allows the charge carriers to move faster at lower temperatures, with the consequence of a reduction of the local interaction times with the polarizable environment, which in turn leads to a gradual reduction of the effective masses in addition. It is therefore not too much of a surprise to find that charge-carrier transport in extremely purified and highly perfect organic crystals at sufficiently low temperature can be nearly as fast as, for example, in silicon at room temperature [5,6]. A description of 1
Except for a few well-defined polymer crystals with a one-dimensionally extended system of main valence bonds-mainly from the class of the polydiacetylenes.
R. Farchioni et al. (eds.), Organic Electronic Materials © Springer-Verlag Berlin Heidelberg 2001
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transport by coherent Bloch waves - instead of stochastic polaron hopping can therefore be more adequate at the lowest temperatures (e.g., at 4 K) [5]. The fundamental theoretical concepts of possible competition and apparent transition between band and hopping transfer in this class of materials have been elaborated long ago (see [1]; see also [7]). More recent investigations have treated the different basic theoretical concepts in a rather exhaustive, albeit general, manner [2, 3, 8]. A more deta
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