Charge Transport in Organic Semiconductors
An in depth understanding of how charge carriers travel through organic polymers and small molecules is the first step towards building advanced functional devices based on these versatile van der Walls bonded materials. Traditionally, one of the ways to study the physics of charge transport in organic semiconductors has been by measuring the mobility of charge carriers in thin film organic field-effect transistors and by charting its variation as a function of temperature and gate voltage.  Empirical models that simulate the dominant trends in the modulation of carrier mobility are then fit to the observations to make reasonable predictions about fundamental properties of these charge carriers such as how localised they are and how strongly they are influenced by the dispersion of the energy bands within which they move. 
Temperature dependent studies of mobility in organic semiconductors have invariably pointed at the existence of disorder within them. Such disorder has multiple origins and is conventionally believed to arise from the lack of long-range structural order within organic semiconductor films, thus manifesting as a broadening in the material’s density of states (DOS). Simply put, Structural disorder in the Cartesian domain results in an energetic disorder within the energy domain of the material. While structural disorder can be investigated using morphology and surface topography techniques such as X-ray diffraction and atomic force microscopy, energetic disorder has been investigated through electrical conductivity and optical excitation techniques. Large energetic disorder is the primary reason why the mobility of organic polymers is normally low and only on the order of 1 cm2/Vs. The magnitude of the mobility in organic polymers is several orders lower than conventional inorganic materials such as silicon and GaAs, and currently poses the biggest roadblock in using organic polymers in fast logic devices.
In the recent past, disorder arising from torsion within the backbone of a polymer [Figure 1 (a)] has also been identified as a cause of a broadened density of states, and the attempt at using torsion-free polymers in organic electronics has been identified as a viable route to achieving higher carrier mobilities. Disorder can be studied using a technique based on carrier concentration modulated thermoelectric or Seebeck coefficients [Figure 1 (b)], and it has been found that polymers with smaller backbone torsional disorder show thermoelectric properties that approach ideal materials free from disorder [Figure 1 (c)].
Figure 1 (a) Torsional Simulations. Molecular Dynamics Simulations of backbone torsion in two different organic polymers IDTBT and PBTTT showing how PBTTT has greater backbone torsion compared with IDTBT.
Figure 1 (b) Device Architecture. A microfabricated device to measure field effect mobility and carrier induced modulated Thermoelectric (Seebeck) coefficients.
Figure 1 (c). Field-effect modulated or carrier induced Seebeck coefficients (α) in organic semiconducting polymers. The slope of the Seebeck coefficient on this plot indicates the extent of disorder in the polymer. The solid lines represent the ideal, i.e., transport under the influence of no disorder induced traps. n is the induced carrier concentration, while N is the total number of available states.
[For more information: D. Venkateshvaran, M. Nikolka et al., Nature 515, 384 (2014)]
In the presence of disorder, charge transport takes place via a hopping mechanism where charge carriers jump from one discrete energy level to another within the broadened density of states, under the influence of a driving force such as an applied voltage. In polymers with a substantial degree of energetic disorder, hopping remains the dominant mechanism for transport. In organic small molecules however, the degree of energetic disorder tends to be smaller, and it remains unclear as to whether hopping is the dominant transport mechanism or whether diminishing disorder leaves open the possibility of a transport mechanism where the quantum mechanical wave function of an electron is “sufficiently extended” to mimic a wave packet. A powerful technique to measure this “band-like” transport behaviour in organic semiconductors is the Hall effect where the k-wave vector of the extended electron wave packet can couple with an externally applied magnetic field to generate a transverse Hall voltage.  Such a Hall voltage was recently measured in two small molecules [Figure 2], and supports the claim that electrons in organic small molecules may indeed have a quasi-delocalised character.
Figure 2. Hall Effect measurements in organic semiconductors (organic small molecules)
(a) Chemical structures of the two small molecules investigated. (b) Field effect transistor transfer characteristics of devices fabricated from the two organic molecules. (c) Gate voltage modulated Hall coefficients. (d) Hall mobility versus temperature.
[For more information: J.-F. Chang et al., Physical Review Letters 107, 066601 (2011)]
Another recent study of the structure of small molecule organic semiconductors through electron diffraction shows that these materials display diffusive streaks not normally seen in inorganic electron diffraction patterns on materials such as gold.  Such diffusive streaks [Figure 3] arise on account of there being intermolecular movement between the different molecules in the crystal lattice on account of van der Walls interactions being weak.
Figure 3. Electron diffraction patterns of an inorganic material compared with that of an organic semiconducting small molecule. Intermolecular motion between organic semiconducting small molecules are observed as diffuse streaks in the electron diffraction pattern.
[For more information: A. S. Eggeman, S. Illig et al., Nature Materials 12, 1045 (2013)]
Disorder continues to be a central topic of research on organic semiconductors and the search for both better materials with structural paradigms that overcome disorder, as well as better techniques to probe this disorder constitutes the theme of research engaged in by the Optoelectronics Group. Only the future shall tell us whether there are fundamental limits on performance of organic semiconductors on account of intrinsic disorder, or whether we will indeed find organic semiconductors that perform better than conventional inorganic semiconductors such as Silicon.
 H. Sirringhaus, Advanced Materials 26, 1319 (2014)
 M. C. J. M. Vissenberg and M. Matters, Phys. Rev. B 57, 12964 (1998)
 D. Venkateshvaran, M. Nikolka et al., Nature 515, 384 (2014)
 J.-F. Chang et al., Physical Review Letters 107, 066601 (2011)
 A. S. Eggeman, S. Illig et al., Nature Materials 12, 1045 (2013)