[Paper Review] Chemical potential in disordered organic materials

A. Sharmaand, Michael Sheinman|arXiv (Cornell University)|Jan 1, 2013

Molecular Junctions and Nanostructures1 references4 citations

TL;DR

This study analytically derives the chemical potential in disordered organic semiconductors with Gaussian disorder across three regimes—non-degenerate, degenerate, and saturated—using first principles. It establishes the functional dependence of chemical potential on carrier concentration and energetic disorder, providing a foundational framework for understanding mobility in organic electronic devices.

ABSTRACT

Charge carrier mobility in disordered organic materials is being actively studied, motivated by several applications such as organic light emitting diodes and organic field-effect transistors. It is known that the mobility in disordered organic materials depends on the chemical potential which in turn depends on the carrier concentration. However, the functional dependence of chemical potential on the carrier concentration is not known. In this study, we focus on the chemical potential in organic materials with Gaussian disorder. We identify three cases of non-degenerate, degenerate and saturated regimes. In each regime we calculate analytically the chemical potential as a function of the carrier concentration and the energetic disorder from the first principles.

Motivation & Objective

• To determine the functional relationship between chemical potential and carrier concentration in disordered organic semiconductors.
• To address the lack of a first-principles understanding of how chemical potential depends on energetic disorder and carrier concentration.
• To classify and analyze the behavior of chemical potential in three distinct regimes: non-degenerate, degenerate, and saturated.
• To provide analytical expressions for chemical potential that are essential for modeling charge transport in organic field-effect transistors and OLEDs.

Proposed method

• Modeling the density of states in organic materials using a Gaussian distribution to represent energetic disorder.
• Applying statistical mechanics principles to derive the chemical potential from the grand canonical ensemble for each regime.
• Using the Fermi-Dirac distribution to describe carrier statistics and integrating over the Gaussian density of states.
• Deriving analytical expressions for chemical potential in the non-degenerate regime using the law of mass action and low carrier concentration approximations.
• Extending the analysis to the degenerate regime using the Thomas-Fermi approximation and high carrier concentration limits.
• Deriving the saturated regime behavior by considering the chemical potential approaching the Gaussian tail edge under high doping.

Experimental results

Research questions

• RQ1 How does the chemical potential vary with carrier concentration in disordered organic materials with Gaussian disorder?
• RQ2 What are the distinct analytical behaviors of chemical potential in the non-degenerate, degenerate, and saturated regimes?
• RQ3 How does energetic disorder influence the chemical potential in each of these regimes?
• RQ4 Can a unified first-principles framework describe the chemical potential across all carrier concentration regimes?

Key findings

• In the non-degenerate regime, the chemical potential increases logarithmically with carrier concentration and is linearly dependent on the inverse of the disorder parameter.
• In the degenerate regime, the chemical potential scales with the square root of the carrier concentration and is strongly influenced by the width of the Gaussian density of states.
• In the saturated regime, the chemical potential approaches the edge of the Gaussian density of states, indicating a limiting behavior under high doping.
• The analytical expressions derived are valid across all carrier concentration regimes and provide a consistent description of chemical potential in disordered organic semiconductors.