Evidence of Lampert Triangle and Jonscher’s Double Power Law in Doped Poly(3,4-ethylenedioxythiophene) Devices

Abstract

The Lampert triangle model can be an interesting method for investigating the conduction mechanism in semiconducting polymers. A complete Lampert triangle is observed in PF6− doped poly(3,4-ethylenedioxythiophene) [PEDOT:PF6] devices, fabricated in a stainless steel/PEDOT/Ag structure and synthesized by electro-polymerization at three different doping levels (high-S1, medium-S2, and low-S3). The temperature-dependent current–voltage characteristics show three distinct regimes limited within a triangular region called the Lampert triangle: Ohmic, trap-limited/filling space charge-limited conduction (TFL-SCLC), and trap-free/trap-filled space charge-limited conduction (TF-SCLC). The vertices of the Lampert triangle represents the transition voltages (VT) for different conduction mechanisms, and the carrier density (p0), carrier transit time (tt), and relaxation time (td) for different doping levels are estimated through the analysis of the triangle. The mobility of carriers shows significant temperature dependence (Arrhenius type). The Jonscher’s double power law fit to AC conductivity data shows that the exponent (in the range 0–1) varies with carrier density and has different trends in bulk and interface. The impedance data and Nyquist plots are analyzed with two parallel RQ circuits (R: resistance; Q: constant phase element) connected in series. The values of onset frequency (ωo) in the conductivity plot of the different samples (S1, S2, and S3) give insights into their relative disorder. Raman spectroscopy studies have attempted to corroborate the changes in bond deformation with carrier density in correlation with the structure and disorder.