A very general rate expression for charge hopping in semiconducting polymers

Area of Science:

• Materials Science
• Condensed Matter Physics
• Polymer Science

Background:

• Charge transport in semiconducting polymers is crucial for organic electronics.
• Existing models for hopping rates, like Miller-Abrahams, have limitations in disordered systems.
• Disorder-induced localization prevents direct application of standard electron transfer theories.

Purpose of the Study:

• To develop a general expression for hopping rates in disordered polymers.
• To unify existing rate expressions (single-phonon, Miller-Abrahams, multi-phonon) into a single framework.
• To accurately model charge transport, particularly under conditions deviating from standard assumptions.

Main Methods:

• Defining distinct classes of nuclear modes (accepting and inducing).
• Deriving a general expression for the hopping rate based on these modes.
• Analyzing the limits of the general expression to recover known rate forms.
• Validating the model with realistic parameters and comparing with the Miller-Abrahams rate.

Main Results:

• A unified expression for hopping rates in disordered semiconducting polymers is proposed.
• The general expression encompasses single-phonon, Miller-Abrahams, and multi-phonon rates as special cases.
• Significant deviations from the Miller-Abrahams rate are observed, especially for hopping to lower energy states.
• The energy gap law significantly influences hopping rates towards lower energy states.

Conclusions:

• The proposed general hopping rate expression provides a more comprehensive description of charge transport in disordered polymers.
• This unified approach allows for interpolation and validation of simplified models.
• The findings highlight the importance of considering nuclear modes and energy gap effects for accurate charge transport modeling in organic materials.