Transport and reactions in doped conjugated polymers: Electrochemical processes and organic devices

Abstract

Abstract For analyzing the electrochemical impedance spectra, the small-signal ac transport properties of hole polarons ( P + ) and counter ions ( C − ) are often modelled by transmission line equivalent circuits. Recently, this description has been extended to include steady-state effects, traps, the direct P + -bipolaron ( BP 2+ ) reaction, and the formation of complexes from a polaron and a counter ion. Here, besides the direct P + – BP 2+ reaction the formation of three different complexes P + – C − , BP 2+ – C − , BP 2+ –2 C − is taken into account as suggested by Kirova and Brazovskii [Synth. Metals 76 (1996) 229]. Making use of the connections between the apparently different theoretical descriptions common in electrochemistry and in solid-state electronics, the mathematical description of these reactions and of the transport processes is presented. The resulting system of equations is rather complicated and should be solved preferably numerically. However, the ac small-signal analysis is advantageous for special cases. It is derived for the case that two processes are slow, the direct bipolaron formation and the formation of the complex BP 2+ –2 C − . Due to the coupling between the processes, the polaron and displacement currents in the transmission line are shunted by a resistive-capacitive series connection in parallel with a current generator. Applying the analysis to hysteresis in metal-oxide-semiconductor capacitors with conjugated polymers as organic semiconductor, it is shown that different time constants for formation and dissociation of the bipolarons can cause basically this effect. Thereby the rate constant has been used as obtained recently from bias stress investigations [Phys. Rev. B 70 (2004) 235324]. On the other hand, the slow complex formation can modify this general run of the hysteresis, which depends indeed also on polymer purification and surface treatment.