Discrete modeling of ionic space charge zones in solids

Area of Science:

• Solid-state physics
• Materials science
• Physical chemistry

Background:

• Continuous models like the Gouy-Chapman solution face limitations with high space charge potentials.
• Steep charge carrier profiles near interfaces in continuous models raise questions of internal consistency.
• Discrete modeling offers a more robust approach for pronounced space charge effects.

Purpose of the Study:

• To present a discrete model for space charge zones in solids that overcomes issues with continuous models.
• To demonstrate the advantages of discrete modeling, particularly for significant space charge potentials.
• To integrate crystallographic details and interface non-idealities into space charge modeling.

Main Methods:

• Development of a quasi-1D discrete model for space charge zones.
• Combination of discrete modeling with continuum descriptions.
• Incorporation of crystallographic details, elastic, structural, saturation effects, and permittivity variations.

Main Results:

• The discrete model resolves internal consistency problems of continuous solutions.
• It accurately describes steep charge carrier profiles near interfaces.
• The model enables realistic consideration of interface properties and their impact on space charge capacitance and resistance.

Conclusions:

• Discrete modeling is a sensible and advantageous approach for significant space charge effects in solids.
• This model can be effectively combined with continuum methods.
• The discrete model provides a realistic framework for analyzing charge carrier behavior and space charge properties, applicable to ionic carriers and small polarons.