Modeling of bias-induced changes of organic field-effect transistor characteristics

Abstract

Organic semiconductors offer exciting possibilities in developing new types of solar cells, photodetectors, light emitting diodes and field-effect transistors. Important advantages of organic semiconducting materials over their inorganic counterparts are their chemical tunability, their low weight, their relative low cost and the ease in which they can be processed. Many organic semiconductors can be processed from solution by using relatively cheap techniques like ink-jet printing or spin-coating, whereas ultra-clean high-vacuum conditions and high temperatures are required for inorganic semiconductors. Organic-based semiconductors in thin-film form are projected to be active elements in plastic-based circuits. In particular, using organic field-effect transistors as switching or logic elements opens up a wide range of possibilities into developing applications. However, organic field-effect transistors exhibit an operational instability. On applying a gate bias to a transistor, the on-current slowly decreases with time eventually going to zero, which is caused by a shift of the threshold voltage. This phenomenon is known as the bias-stress effect and severely hampers the application of organic transistors. For example, in an active matrix display, where light emission from each pixel is proportional to the current supplied by the driving transistor, any change in source-drain current with time is going to impact the brightness of the pixel. The main goal of the work described in this thesis has been to understand and model bias-induced changes of the electrical characteristics of organic field-effect transistors. The work described is the theoretical part of a joint experimental-theoretical effort. In Chapter 2, the bias-stress effect is presented and its main aspects are highlighted. Some of the previously reported mechanisms for the bias-stress effect are briefly discussed, namely trapping mechanisms, a mechanism based on bipolarons, a mechanism based on water-induced polaron formation, and a contact degradation mechanism. However, there are many aspects of the bias-stress effect that cannot be consistently explained within the framework of these mechanisms. In particular, the fact that the bias-stress effect is thermally activated with an activation energy of about 0.6 eV, independent of the organic semiconductor used, cannot be explained by any of the mechanisms listed above. Experimental studies have established that water is the primary agent causing the bias-stress effect. An increase in humidity accelerates the bias-stress effect, whereas operating the device in vacuum practically eliminates the effect. In Chapter 3, a new mechanism for the bias-stress effect is presented. Reversible proton migration into the gate oxide is proposed as the main cause of the bias-stress effect in p-type organic transistors with silicon-dioxide (SiO2) as the gate dielectric. Protons are produced in an electrolytic redox reaction between holes and water in the accumulation layer of the transistor. In this reaction, water is oxidized by holes producing protons and oxygen. This reaction essentially establishes an equilibrium between holes and protons in the accumulation layer. The protons produced in the accumulation layer subsequently migrate into the SiO2. It is assumed that, independent of the organic semiconductor, the dynamics of the bias-stress effect is determined solely by the motion of protons in SiO2The model is called the proton-migration model. The motion of protons away from the accumulation layer into the SiO2has two consequences: (i) more holes are converted into protons in the accumulation layer, and (ii) the protons in the SiO2 screen the gate field, giving rise to the observed threshold-voltage shift. Taking only diffusion into account a model is developed that has only one parameter: a characteristic time. The predicted threshold-voltage shift is very close to a stretched-exponential function, which has often been used as an empirical fit. The model explains the role of water as the source of protons. Since the time scale of the bias-stress effect is determined by the motion of protons in the SiO2 the activation energy of the bias-stress effect is independent of the organic semiconductor. The activation energy of the effect indeed corresponds to that for transport of protons in the silicon-dioxide. In Chapter 4 the recovery of a transistor that has been exposed to bias stress is described within the proton-migration model. Recovery is associated with the backward shift of the threshold voltage of an organic transistor that has been exposed to stressing. During stressing protons migrate into the SiO2.The depth of penetration depends on the extent of stressing. At the end of stressing, the threshold voltage has shifted to the applied gate voltage and the transistor is in the off state. Applying zero gate bias to the transistor results in a backward shift of the threshold-voltage. Protons that have migrated into the oxide during stressing diffuse back to the semiconductor, where they are converted back into holes. Since the applied gate bias is zero, these holes are carried away by the source and drain electrodes. Recovery is modeled quantitatively within the proton-migration mechanism. The model predicts that the extent of stressing has a large influence on the dynamics of the recovery, which is in agreement with experiments. Experimentally obtained threshold-voltage shifts during recovery for different values of stressing periods clearly show that the dynamics of recovery is not governed by a single relaxation time. The measured time dependence of the threshold voltage during recovery quite accurately follows the model predictions, obtained using parameters from the modeling of the threshold-voltage shift for stress. In Chapter 5, the predictions of the proton-migration model for a dynamic, time dependent, gate bias are tested. The model makes the following prediction: stressing the transistor with a highly negative gate voltage for a certain period of time and thereafter switching the gate voltage to a less negative value leads to a temporary recovery of the transistor, despite the fact that the transistor is under monotonous stressing. This temporary recovery is experimentally observed as an anomalous increase in the current. The occurrence of the resulting non-monotonic current transients was verified experimentally. The measured current transients accurately follow the model predictions, obtained using parameters from the modeling of the bias-stress effect in Chapter 3 In Chapter 6, the effect of Coulomb scattering on the mobility of the charge carriers in the channel of the transistor is investigated. It is shown that Coulomb scattering from charges trapped in the channel of the transistor has a major effect on the mobility of the mobile charges in the transistor channel. The number of trapped charges is tuned by a prolonged application of the gate bias. Two cases are considered: (i) charges trapped in the channel, and (ii) charges trapped in the gate dielectric beneath the organic semiconductor. The distance over which the trapped charges are spread out in the gate dielectric is varied from 1 nm to 100 nm. Two-dimensional Monte-Carlo simulations of the charge transport in this transistor are performed in which the static random Coulomb field of the trapped charges is taken into account. The simulations show that the change in mobility of charge carriers in the channel of the transistor is substantially reduced if the trapped charges are assumed to be located in or very close to the transistor channel. The experimentally observed decrease in mobility is much smaller than that obtained from these simulations. The decrease in mobility is accurately obtained if in the simulations the trapped charges are assumed to be distributed in a layer with a thickness of a few tens of nanometer underneath the monolayer. This finding provides strong evidence for the proton migration mechanism. In Chapter 7, the dependence of the time scale of the bias-stress effect on the organic semiconductor is investigated. The model predicts that this time scale should decrease exponentially with increasing energy of the highest occupied molecular orbital of the organic semiconductor. This was tested by comparing the relaxation times of organic field-effect transistors of organic semiconductors with different HOMO energies. The observed trend is correct, but the exponential dependence could not be quantitatively verified, because of uncertainties in the water and oxygen uptake of the semiconductors. In summary, we can say that the proton-migration model has been able to describe all the main features of bias-induced changes of p-type organic field-effect transistors with silicon-dioxide as gate dielectric. The model has even triggered new experiments, which have verified the theoretical predictions. We conclude that the objective of this thesis work, to understand and model the electrical characteristics of organic field-effect transistors and identify the mechanism of the bias-stress effect, has been fully achieved.