Fowler-Nordheim theory for a spherical emitting surface

Area of Science:

• Physics
• Materials Science
• Surface Science

Background:

• Fowler-Nordheim (F-N) theory is a cornerstone for understanding electron field emission.
• Standard F-N theory assumes a planar emitting surface, which often deviates from real-world field emitter geometries.
• Discrepancies between planar F-N theory and experimental observations highlight the need for refined models.

Purpose of the Study:

• To develop an improved Fowler-Nordheim model that incorporates the effects of emitter surface curvature.
• To enhance the accuracy of predicting field emission current density for non-planar emitters.
• To provide a more reliable method for estimating field emitter dimensions from experimental data.

Main Methods:

• Modified Fowler-Nordheim theory to include non-linear potential variation near the curved surface.
• Accounted for changes in the exponent and pre-exponential factors within the F-N current equation due to curvature.
• Modeled current density variation across the surface using an effective solid angle approximation.

Main Results:

• The refined model demonstrated significantly better agreement with experimental field emission data compared to the standard planar F-N theory.
• The inclusion of surface curvature effects led to more accurate estimations of the emitter's apex radius.
• The developed model successfully reconciled theoretical predictions with observed current densities.

Conclusions:

• Emitter surface curvature is a critical factor that must be considered for accurate field emission modeling.
• The enhanced Fowler-Nordheim model provides a more robust framework for analyzing field emission from curved surfaces.
• This work offers improved methods for characterizing field emitters and understanding their performance in various applications.