Charge transport in organic semiconductors is a fundamental aspect that governs their performance in electronic and optoelectronic applications. Unlike inorganic semiconductors, where charge transport is often described by band theory, organic semiconductors exhibit more complex mechanisms due to their molecular nature, weak intermolecular interactions, and inherent disorder. The primary charge transport mechanisms in these materials are hopping conduction and band-like transport, each influenced by factors such as molecular packing, crystallinity, and defects. Understanding these mechanisms is critical for optimizing material design and device performance.

Hopping conduction is the dominant transport mechanism in most organic semiconductors, particularly in disordered systems. In this model, charge carriers move by thermally activated jumps between localized states. The hopping rate depends on the overlap of electronic wavefunctions between adjacent molecules, which is influenced by the intermolecular distance and orientation. The Miller-Abrahams formalism describes the hopping probability, which decreases exponentially with the spatial separation between sites and the energy difference between them. Energetic disorder, caused by variations in molecular environments, further complicates hopping transport by creating a distribution of localized states. This disorder leads to a dependence of mobility on temperature and electric field, often characterized by the Gaussian disorder model. For example, in amorphous organic films, charge carrier mobility typically ranges from 10^-6 to 10^-3 cm^2/Vs, reflecting the limitations imposed by disorder.

Band-like transport, on the other hand, occurs in highly ordered organic semiconductors with strong electronic coupling between molecules. In these systems, delocalized states form, allowing charge carriers to move with lower scattering rates. Band-like transport is characterized by a decrease in mobility with increasing temperature, a hallmark of coherent motion. This behavior is observed in single crystals of small-molecule organic semiconductors, such as rubrene, where mobilities can exceed 10 cm^2/Vs. The degree of band-like transport depends on the quality of the crystal lattice and the absence of defects that disrupt electronic coupling. However, even in these systems, thermal vibrations and dynamic disorder can lead to a transition to hopping-like behavior at higher temperatures.

The role of disorder in organic semiconductors cannot be overstated. Structural disorder, such as variations in molecular packing and grain boundaries, creates trapping sites that impede charge transport. Energetic disorder, arising from variations in polarization energies and molecular conformations, further localizes charge carriers. The interplay between these disorders determines the overall transport properties. For instance, in polycrystalline films, grain boundaries act as barriers to charge transport, reducing mobility compared to single-crystalline domains. Defects, whether chemical impurities or physical imperfections, also introduce trap states that capture charge carriers, leading to reduced conductivity and non-ideal current-voltage characteristics.

Molecular packing and crystallinity are critical factors influencing charge transport. Close-packed, well-ordered molecular arrangements enhance electronic coupling, facilitating higher mobility. Small-molecule organic semiconductors, such as pentacene and C60, often exhibit higher crystallinity and more uniform packing compared to polymers, resulting in superior charge transport properties. In contrast, polymer semiconductors, such as P3HT and PBTTT, typically exhibit more disorder due to their chain-like structure and conformational flexibility. However, advances in polymer design, such as side-chain engineering and backbone rigidity, have led to improved molecular order and mobilities approaching those of small molecules. The choice between small-molecule and polymer-based systems depends on the application, with small molecules favored for high-performance devices and polymers preferred for solution-processable, flexible electronics.

Experimental techniques for characterizing charge transport in organic semiconductors provide insights into the underlying mechanisms. Field-effect transistor (FET) measurements are widely used to extract charge carrier mobility by analyzing the transfer characteristics in the linear and saturation regimes. FET measurements also reveal the influence of interface traps and contact resistance on transport. Time-of-flight (TOF) measurements are another key technique, particularly for studying bulk transport properties. In TOF, a pulsed laser generates charge carriers, and their transit time across the material is measured, allowing the calculation of mobility. TOF is especially useful for probing disorder effects, as the dispersive or non-dispersive nature of the photocurrent transient provides information about the energy distribution of trap states. Other techniques include space-charge-limited current (SCLC) measurements, which analyze the current-voltage characteristics in trap-free and trap-limited regimes, and Hall effect measurements, which provide information about carrier density and type.

The temperature dependence of mobility is a key indicator of the dominant transport mechanism. In hopping-dominated systems, mobility typically follows an Arrhenius-like behavior, increasing with temperature as thermal energy helps carriers overcome barriers between localized states. In band-like systems, mobility decreases with temperature due to increased electron-phonon scattering. Intermediate cases, where both mechanisms contribute, exhibit more complex temperature dependencies. For example, in some high-mobility polymers, a transition from band-like to hopping-like transport is observed as temperature increases, reflecting the competition between coherent and incoherent motion.

The impact of molecular structure on charge transport is evident in the design of high-performance organic semiconductors. Conjugated cores with extended pi-electron systems enhance electronic coupling, while side chains can be tailored to improve solubility and packing. For instance, the introduction of alkyl side chains in polythiophenes promotes lamellar stacking, improving interchain charge transport. Similarly, the use of fused-ring systems in small molecules increases rigidity and reduces energetic disorder. Chemical doping is another strategy to enhance conductivity by introducing additional charge carriers, though it must be carefully controlled to avoid introducing traps.

In summary, charge transport in organic semiconductors is governed by a delicate balance between hopping conduction and band-like transport, shaped by molecular packing, crystallinity, and disorder. Small-molecule systems generally exhibit higher mobilities due to their superior order, while polymers offer processing advantages at the cost of increased disorder. Advanced experimental techniques provide critical insights into these mechanisms, guiding the development of next-generation organic electronic materials. Continued progress in understanding and controlling charge transport will enable new applications in flexible electronics, energy harvesting, and beyond.