Perspectives

Avoid the kinks when measuring mobility

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Science  24 Jun 2016:
Vol. 352, Issue 6293, pp. 1521-1522
DOI: 10.1126/science.aaf9062

The ability to make flexible electronics enables us to envision new types of devices such as durable displays, implantable bioelectronics, and sensors seamlessly integrated in everyday items (1). Furthermore, the power and flexibility of organic chemistry to design new semiconductors has been a strong driver for an unprecedented effort in materials development worldwide (2). A key materials parameter is the mobility of charge carriers, which is often determined by building a field-effect transistor (FET) with the material. We outline why such measurements, which are indirect and depend on the appropriate use of device models, only provide apparent mobilities that can, in some cases, overstate the real values by more than an order of magnitude.

Electronic devices operate by controlling how charge carriers—electrons and holes—move through semiconductors, and higher carrier mobilities lead to faster circuitry. Carrier mobility is the first materials property measured to benchmark improved performance of new organic semiconductors. Targeted mobility values in FETs, often considered the building blocks of electronic circuits, are on the order of 10 cm2 V−1 s−1 or larger. Accurate mobility values are needed by synthetic chemists to validate molecular design concepts aimed at improving charge transport and by circuit designers to ensure that devices can perform their functions.

Nonetheless, a correct measurement of carrier mobility in organic semiconductors has proven challenging (3, 4). Organic semiconductors are van der Waals solids with weak intermolecular interactions and strong structural anisotropy, so their properties are at the edge of the applicability of well-known transport models developed for inorganic semiconductors (5). Furthermore, the presence of disorder and nonconventional transport mechanisms has severely limited the use of common techniques such as the measurement of the Hall voltage. Finally, the strong dependence of mobility on thin-film microstructure, originating from specific fabrication conditions, compels experimentalists to measure these electronic properties in the actual devices of interest rather than in idealized model structures.

A misleading kink.

(A) An example of the “kink-down” feature exhibited in the nonideal transfer characteristics of a rubrene small-molecule semiconductor device [reproduced from (9)]. The difference in the extracted apparent mobility of the two regions of the plot is shown as red and blue extrapolations. The true mobility of the semiconductor is closer to the value in blue. (B) Illustration of a FET architecture, with bottom gate, top contacts (light gray), dielectric (red), semiconductor (blue), and substrate (dark gray).

GRAPHIC: C. BICKEL/SCIENCE

As a result, carrier mobility is often measured in FETs. However, transistor characteristics only provide a current-voltage relation that aggregates contributions from many factors present in a device, including charge injection and carrier concentration effects, and do not directly measure carrier mobility. In principle, detailed modeling is needed to extract the mobility rigorously, but the most popular transistor model used in organic electronics relies on the gradual-channel approximation, which posits a simple carrier distribution comprising only one type of carrier in the channel and neglects contact effects. The characterization of an FET based on a fit to a particular model provides an “apparent mobility of carriers in a device,” and the numbers are meaningful only if device operation conforms to the model's assumptions.

The carrier mobility is frequently derived from transfer characteristics, which describe the dependence of the device current on charge density, which is in turn controlled by the voltage on the gate electrode. Mobility is calculated by making use of the ideal gradual-channel approximation, which was sufficient in the early development of organic electronics when the current was limited by the organic semiconductor. For newer, high-performance materials, the organic semiconductor, in many cases, is not the limiting factor. The emergence of this new condition is apparent in many recent reports (68), where substantial nonidealities in the characteristics of FETs are observed. The typical manifestation of this nonideality is the existence of a downward kink in the transfer characteristics of the FET, as shown in the figure, as well as a pronounced dependence on the history of electrical biasing of the device.

Recently, several groups have taken a closer look at some irregularities in the characteristics of previously reported high-performance organic FETs, drawing the common conclusion that the conventional methods to extract carrier mobility cannot be used when devices exhibit nonideal characteristics (911). For example, deviations from ideal behavior have been observed with polymers where both electrons and holes can be injected into the channel of the device. Localized electron trapping near one contact invalidated a key assumption of the gradual-channel approximation. The use of the simple transistor equations resulted in an overestimation of the hole mobility by a factor exceeding 20, 14 cm2 V−1 s−1, rather than a more likely value of 0.6 cm2 V−1 s−1 (10). Another type of nonideality occurs when non-ohmic injection from the electrodes generates a gate-bias dependence of the contact resistance. Single-crystal rubrene FETs with severely non-ohmic contacts also led to an overestimation of the mobility by more than an order of magnitude (9).

Without a robust and reliable method to determine carrier mobility as an intrinsic materials property, chemists dedicated to the synthesis of improved organic semiconductors can easily pursue erroneous design principles based on inaccurate literature values of mobility. For example, notable instances of these nonidealities are observed in the characteristics of recent polymers synthesized from a highly polar, electron-deficient diketopyrrolopyrrole (DPP) conjugated monomer (12). This repeat unit generates a high electron affinity that can facilitate electron injection in hole-based devices, thereby invalidating the use of formulas derived from the gradual-channel approximation to extract mobility. Molecular design principles for this class of polymers developed from these mobility values may thus be unsubstantiated and, in fact, impede an understanding of the fundamental structure-property relations. Furthermore, high mobilities obtained from nonideal characteristics may set erroneous benchmarks for device design. Until better models and solutions to eliminate nonidealities are found, the best prescription is conservatism on absolute metrics and trends, particularly with small differences in electrical properties, as suggested in a number of recent commentaries (13).

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