Reformulated space-charge-limited current model and its application to disordered organic systems

Area of Science:

• Materials Science
• Condensed Matter Physics
• Organic Electronics

Background:

• Traditional models for current-voltage (I-V) dependence in low mobility materials often rely on local electric fields or charge carrier densities.
• These models may require specific assumptions about electrode contacts and do not always explicitly include material density-of-states.
• Disordered organic semiconductors present challenges due to field- and density-dependent mobility and generalized Einstein relations.

Purpose of the Study:

• To reformulate the traditional model for I-V dependence by introducing quasi-electrochemical potential as the fundamental variable.
• To develop a more generalized model applicable to various materials and contact types, explicitly incorporating density-of-states.
• To provide a unified framework that covers diffusion, space-charge limited, and injection limited current regimes.

Main Methods:

• Reformulation of the existing model using quasi-electrochemical potential instead of local electric field or carrier density.
• Inclusion of diffusion current within the new theoretical framework.
• Application of the model to non-degenerate, constant mobility materials and Gaussianly disordered organic materials.

Main Results:

• The reformulated model naturally incorporates the generalized Einstein relation and field/density-dependent mobility.
• A single dimensionless parameter was found to determine the I(V) curve for constant mobility materials.
• Integral expressions for carrier density and mobility were derived for disordered organic materials, revealing I∝V^n dependence (n>2) in the space-charge limited regime due to energetic disorder.

Conclusions:

• The quasi-electrochemical potential offers a more fundamental variable for describing I-V characteristics in low mobility materials.
• The new model provides a unified description of different current regimes and is applicable to a broader range of materials, including disordered organic semiconductors.
• Energetic disorder in organic materials can intrinsically lead to power-law I-V behavior in specific bias regimes, offering insights for device optimization.