299
5.1. The image force
In practice many sources are not planar. Furthermore, the energy
bands of the solid emitter material tend to bend at the interface
with the vacuum. This band-bending can be enhanced by preparing the emitter surface with an additional surface layer. These
factors affect the actual emission, and the resulting macroscopic
source properties. We define the electron affinity as the energy
needed in practice to remove a single electron from the emitter.
Because of these factors, the following analysis must be regarded
as approximate. As is often the case, one replaces an intractable
problem by a related problem which can be solved, producing an
approximate result.
To summarize, the emission current density depends on the temperature and the applied electric field. In the limit of zero applied
electric field F and elevated temperature T , the current is called
thermionic emission. In the limit of zero temperature T and elevated electric field F , the current is called f ield emission. The
central problem of this chapter is to determine the emitted current density j as a general function of temperature T and applied
electric field F .
5.1 The image force
An electron which has been emitted into the vacuum experiences
an electrostatic force which attracts it back toward the emission
surface. This can be understood by examining the Coulomb force
on an electron with charge −e located in the vacuum a distance x
from a planar conductive surface at ground potential. This situation is completely equivalent to a configuration where the planar
surface is replaced by a charge +e located behind the emission
surface at a distance 2x from the electron. This fictitious charge
5.1. The image force
In practice many sources are not planar. Furthermore, the energy
bands of the solid emitter material tend to bend at the interface
with the vacuum. This band-bending can be enhanced by preparing the emitter surface with an additional surface layer. These
factors affect the actual emission, and the resulting macroscopic
source properties. We define the electron affinity as the energy
needed in practice to remove a single electron from the emitter.
Because of these factors, the following analysis must be regarded
as approximate. As is often the case, one replaces an intractable
problem by a related problem which can be solved, producing an
approximate result.
To summarize, the emission current density depends on the temperature and the applied electric field. In the limit of zero applied
electric field F and elevated temperature T , the current is called
thermionic emission. In the limit of zero temperature T and elevated electric field F , the current is called f ield emission. The
central problem of this chapter is to determine the emitted current density j as a general function of temperature T and applied
electric field F .
5.1 The image force
An electron which has been emitted into the vacuum experiences
an electrostatic force which attracts it back toward the emission
surface. This can be understood by examining the Coulomb force
on an electron with charge −e located in the vacuum a distance x
from a planar conductive surface at ground potential. This situation is completely equivalent to a configuration where the planar
surface is replaced by a charge +e located behind the emission
surface at a distance 2x from the electron. This fictitious charge