Semiconducting conjugated polymer thin film transistors (TFT) with mobilities in the range of 0.1~20 cm2/Vs have been reported by man groups. There is a demand for higher mobility polymer TFTs; therefore, an accurate understanding of the physics of charge transport is necessary. However, a complete theoretical understanding and quantitative description of charge transport in such semiconductors has been difficult to attain. The mobilities and mean free paths are simply too low (on the order of intermolecular distance ~3 Å) for the application of conventional semiconductor transport theories. In this presentation, we will describe a very general solution based on the statistical nature of charge transport and introduction of a factor (mean free path factor) related to the probability of mean free path exceeding the minimum transport length. We are then able to apply the Boltzmann transport equation (BTE) with appropriate scattering mechanisms and obtain very good results that agree well with experiment. This approach is very well suited to thin-film transistors based on polymer and organic semiconductors, and also many amorphous oxide semiconductors with room temperature mobilities in the range 5~50 cm2/Vs. We combine the mean free path factor, BTE solutions with an extended multiple trap and release (MTR) model that takes into account traps in the device to get an overall response.
Several scattering mechanisms are considered based on the material properties. It is found that at low and intermediate temperatures, free carrier scattering by the trapped charge carriers is dominant. Carriers trapped in the semiconductor traps or at the semiconductor-dielectric interface can be considered immobile Coulomb scattering centers, and can scatter mobile carriers efficiently. At high temperatures, basically the room temperature (300K) or above, carrier-phonon scattering starts to dominate. An important phonon scattering mechanism in the polymer thin film is the optical deformation potential scattering. Due to the structure of the conjugated polymers, the backbone chain generates low frequency optical phonons, and the optical deformation potential is fairly large in these soft materials. This leads to very effective carrier scattering and decrease the mobility at high temperatures. Other scattering mechanisms including polar optical phonon scattering and acoustic phonon scattering are also considered into the evaluation of the band mobility for different temperatures and carrier concentrations.
The resulting band mobility of conjugated polymers is in the range of 20~40 cm2/Vs, corresponding to 0.1~20 cm2/Vs for the effective MTR mobility in a TFT device. In the case of low carrier concentration, the carrier free path is assumed to approximately obey the Poisson distribution with occurrence number of zero (exponential distribution) and the mean free path is the average of the Poisson distribution. Although the mean free path of the carrier can might be smaller than the intermolecular distance, there is still a fraction of free carriers that can survive travelling past that distance. This fraction of carriers is considered to participate the actual band transport. Thus, the apparent MTR mobility is further reduced by the factor of the mean free path survivor fraction. We compare results from our calculations with experimental data for donor-acceptor polymers. The agreement is very good and attests the validity of our approach. Our work also points to clear directions that TFT device structures must possess for high performance.
 T. J. Ha, et al. "Charge transport study of high mobility polymer thin-film transistors based on thiophene substituted diketopyrrolopyrrole copolymers." Physical Chemistry Chemical Physics 15.24 (2013): 9735-9741.
 X. Wang, A. Dodabalapur. " Trapped carrier scattering and charge transport in high-mobility amorphous metal oxide thin film transistors." Annalen Der Physik (2018) (accepted).