Effects of Disorder on Thermoelectric Properties of Semiconducting Polymers

Abstract

Organic materials have attracted recent interest as thermoelectric (TE) converters due to their low cost and ease of fabrication. We examine the effects of disorder on the TE properties of semiconducting polymers based on the Gaussian disorder model (GDM) for site energies while employing Pauli’s master equation approach to model hopping between localized sites. Our model is in good agreement with experimental results and a useful tool to study hopping transport. We show that stronger overlap between sites can improve the electrical conductivity without adversely affecting the Seebeck coefficient. We find that positional disorder aids the formation of new conduction paths with an increased probability of carriers in high energy sites, leading to an increase in electrical conductivity while leaving the Seebeck unchanged. On the other hand, energetic disorder leads to increased energy gaps between sites, hindering transport. This adversely affects conductivity while only slightly increasing Seebeck and results in lower TE power factors. Furthermore, positional correlation primarily affects conductivity, while correlation in site energies has no effect on TE properties of polymers. Our results also show that the Lorenz number increases with Seebeck coefficient, largely deviating from the Sommerfeld value, in agreement with experiments and in contrast to band conductors. We conclude that reducing energetic disorder and positional correlation, while increasing positional disorder can lead to higher TE power factors.

Non-Wiedemann-Franz behavior of the thermal conductivity of organic semiconductors

“…Furthermore, our results are in line with the results shown in Ref. [14], where the effect of disorder on the Lorenz factor in organic semiconductors is studied and with findings from the inorganic community regarding the trend of the Lorenz factor with the bandwidth of the charge-carrier dispersion. Therefore, we suggest that Eqs.…”

Tuning charge transport dynamics via clustering of doping in organic semiconductor thin films

“…6b) and cannot fully account for the significant difference in the slope of the α vs. σ plots between the P3HT and PDPP4T plots. It has been shown that long-range coulombic interaction between the ionized dopant molecules and the localized carriers further increases energetic disorder and broadens the deep tail of the DOS 58 . The physical distribution of dopant molecules within the sample and the size of the dopant clusters both further intensate the impact on the DOS.…”

“…Samples were transferred from their iodine doping chamber to a custom-built (reported elsewhere 45,58 and briefly summarized herein) thermoelectric characterization apparatus in a timely fashion since they began de-doping immediately and rapidly in the absence of iodine vapor. The sample was placed on an insulating glass slide bridging one heated copper block and one unheated copper block to establish a temperature gradient.…”

“…We use the rejection sampling technique to generate an energy distribution from the calculated DOS; and then randomly assign an energy to each site from the distribution. Details about solving the non-linear PME has been described in Supplementary Note 1 and further details of our model has been reported in an earlier work 58 .…”

Thermal Transport in Conductive Polymer–Based Materials

“…Typical methods are the continuum model, the Takayama–Liu–Maki (TLM) model, derived by Takayama et al and the tight‐binding model, the Su–Schrieffer–Heeger (SSH) model, derived by Su et al The electrical conductivity is attributed to the phonon‐assisted electron hopping between bound localized states which are located at the middle of band gap . Upadhyaya et al used the variable‐range hopping model and the Gaussian disorder model to study the dependence of thermal conductivity on the Seebeck coefficient. Wang et al adopted the Holstein small‐polaron theory and the Kubo formula to study the electrical and thermal transport with strong electron–phonon coupling in a quasi‐1D system.…”