The transverse structure of cold field electron emission

Area of Science:

• Quantum mechanics
• Solid-state physics
• Electron emission phenomena

Background:

• Understanding electron emission is crucial for vacuum electronics and semiconductor devices.
• Previous models often simplified the complex quantum mechanical behavior of electrons.
• Investigating electron behavior in uniform electric fields is a fundamental problem.

Purpose of the Study:

• To solve the Schrödinger equation for electron emission from a localized area between planar electrodes.
• To analyze the effect of transverse momentum on electron tunneling through potential barriers.
• To characterize the spatial distribution and intensity of the emitted electron beam.

Main Methods:

• Numerical solution of the Schrödinger equation for a multi-dimensional system.
• Analysis of electron wave function behavior in a uniform electric field.
• Modeling electron emission from a point source and a small area.

Main Results:

• Wave components with transverse momentum experience modified potential barrier height and width.
• The electron beam intensity exhibits a Gaussian decrease with increasing beam radius.
• A characteristic Gaussian radius was found to increase with the square root of the distance from the emission plane.

Conclusions:

• Transverse momentum significantly influences electron tunneling and beam characteristics.
• The spatial spread of the electron beam is dependent on the electric field configuration.
• These findings have implications for designing electron sources and understanding electron transport in vacuum devices.