Charge‐Carrier Density Independent Mobility in Amorphous Fluorene‐Triarylamine Copolymers

Abstract

3720 wileyonlinelibrary.com (OPVs), and organic fi eld-effect transistors (OFETs). A crucial parameter in the development of these technologies is the OSC charge-carrier mobility, and how it is related to the different OSC materials, processing, device architectures, and device operating conditions. Many semiconducting polymers and small molecules are amorphous, and such disorder in the physical morphology is expected to refl ect itself in disorder of the energy levels of the hole and electron transport states ( Figure 1 a). Such energetic disorder will directly impact charge transport and mobility. [1][2][3][4][5][6][7][8][9][10][11][12] For such energetically disordered OSCs, one feature predicted by many charge transport models is a charge-carrier density dependent mobility. The original Gaussian disorder model (GDM) developed by Bässler for hopping transport in a Gaussian density of states (DOS) distribution was a single carrier approach, [ 1 ] as were the models based on it which considered both correlated energetic disorder, [ 2 ] with a smoothly varying energy landscape (see Figure 1 a), and the effect of polaronic relaxation. [ 3 ] The percolation model developed by Vissenberg and Matters for transport involving an exponential DOS instead considered multiple carriers, [ 4 ] and this predicted a mobility which has a power-law dependency on the charge-carrier density. The measured transistor mobility falls two to three orders of magnitude below that predicted from the charge-carrier density dependent model, and does not follow the expected power-law relationship. The experimental results for these two amorphous polymers are therefore consistent with a charge-carrier density independent mobility, and this is discussed in terms of polaron-dominated hopping and interchain correlated disorder.

Thickness Dependence of Space-Charge-Limited Current in Spatially Disordered Organic Semiconductors

“…For such materials, our proposed model here would be a better choice to extract the mobility for spatially disordered organic materials as we have shown that the traditional thickness scaling is not valid anymore. By applying our model with field-dependent mobility, we are able to reproduce the experimental results of SCLC transport in PPV derivative based device without using the carrier-density dependent mobility [1], agreeable with a recent report for amorphous polymers [3].…”

“…We first analyze various experimental results to study the thickness (or L) dependence to show that the traditional L scalings from the traditional models are not valid for spatially disordered semiconducting materials. By using our proposed models, we are able to reproduce the experimental currentvoltage measurements in [1] without using the carrier-density dependent model, and thus solving the issues raised by recent paper [3].…”

“…are determined by two kinds of microscopic disorders, namely the energetic disorder characterized by a broad distribution of localized states and the spatial disorder related to the morphological features of the material [3]. The space-chargelimited current (SCLC) is an important classical transport phenomenon in organic semiconductors where the quantum effects can be ignored at microscale and above [1]- [17].…”

“…However, assuming Gaussian density of states (DOS), it is known that in low carrierdensity regime the mobility should be carrier-density independent [14]. Another recent experiment [3] has also reported that the charge transport in amorphous semiconductors is not charge density dependent but instead follows a field-dependent mobility model. In such scenarios, a new model of spacecharge-limited transport is required to capture the correct thickness scaling of measured SCLC.…”

Relativistic space-charge-limited current for massive Dirac fermions

“…For organic semiconductors, field-dependent [12][13][14][15] and density-dependent mobility SCLC models 16,17 are commonly employed to characterize the SCLC carried by the holes. Similarly, SCLC of electrons was found to be universally described by a trap model with Gaussian energy distribution in a large class of organic semiconductors 18,19 .…”