Transient Response and Charge Transport in Organic and Polymer Thin-Film Transistors
Authors: Krutko Oleksiy , Dodabalapur Ananth 
Published: February 2020

Organic thin-film transistors (TFTs) are very promising for several large-area applications particularly when mechanical flexibility is important. A detailed model that directly correlates the TFT time-domain transient response with charge transport and material properties is very desirable for circuit applications. Temperature-dependent measurements of the field effect transistor (FET) mobility have provided numerous insights on the characteristics of the charge carriers and nature of transport phenomena. However, in disordered semiconductors such as organics and polymers, the FET mobility μFET
is very different from the trap-free mobility μ as most of the carriers remain trapped in the band-tail states. In such systems, determining the drift mobility becomes very important. To study this drift mobility, we analyze the time-domain response of the transistor. The time-domain response of transistors can be obtained through channel formation time measurements. In such measurements, carriers are injected at the source of the transistor using a voltage pulse and extracted at the drain. A large-signal time domain analysis of these electronic time-of-flight measurements was first done by J.R. Burns [1] nearly 50 years ago for metal-oxide-semiconductor (MOS) transistors and was later extended to organic thin-film transistors by D. Basu et al. [2]. However, the mathematical models used in both works assumed that mobility is insensitive to the variance in carrier density and temperature. Therefore, these models cannot accurately predict complex time-domain response in organic and polymer FETs, hence there exists the need for more comprehensive models that account for mobility dependence on carrier concentration and temperature. Indeed, the main mechanisms of charge transport in organic and polymer semiconductors are commonly accepted to be variable-range hopping (VRH) and multiple-trap and release (MTR). In MTR, trapped carriers are thermally excited into the band, where charge transport takes place. Both charge transport models predict a mobility that depends on the trap density of states of the material, carrier density, and lattice temperature and, thus a complete model must account for these parameters.
This paper presents an extension to the work of Burns and Basu et al. that considers the effect of the multiple trap and release charge transport model on mobility. With the underlying assumption that the trap density of states in most high-mobility organic and polymer transistors can be modeled by a single exponential function, we can write a closed form non-linear partial differential equation that describes the time and spatial evolution of current and voltage in an organic or polymer FET. In this way, we account for relevant material and device operation parameters such as trap density of states, carrier density, and temperature and therefore present a much more complete model of the time-domain response of organic and polymer thin-film transistors while retaining ease of use. Given sufficient knowledge of material parameters, we are able to accurately model electronic time-of-flight measurements in organic and polymer thin film transistors across different device operation regimes and temperatures. This model can also be used to extract material parameters from channel formation measurements. We apply this more complete time-domain dynamic response model to experimental data from high-mobility donor-acceptor polymer based thin-film transistors measured in our group.
[1] J. R. Burns, RCA Review, 30, 15, 1969.
[2] Basu, Debarshi & Dodabalapur, Ananth. (1970). Drift Velocity and Drift Mobility Measurement in Organic Semiconductors Using Pulse Voltage. 10.1007/12_2009_4.

Figure 1