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Chapter 5. Electron emission from solids
trons are approximately free to diffuse throughout the bulk material. Electrons in the conduction band occupy energy states. The
Pauli exclusion principle dictates that no more than one electron
can occupy any given state. The average occupation number for a
state obeys Fermi–Dirac statistics, and is between zero and one.
In the limit where the absolute temperature T approaches zero,
all states with energy ε in the range 0 ≤ ε ≤ ζ are occupied by
one electron, where ζ is called the Fermi energy. In this limit all
states with energy higher than the Fermi energy are unoccupied.
In the following we assume that the emission surface is planar,
and infinite in lateral extent. In this approximation the problem
can be regarded as spatially one-dimensional, with the x-axis perpendicular to the emission surface. Some fraction of the conduction
electrons drift to the surface, where they can be emitted into the
vacuum to form a beam. Once emitted, an electron experiences a
Coulomb force which tends to attract it back toward the emission
surface. This is called an image force, and is described in detail
in the following section. It gives rise to a potential energy barrier
which must be overcome in order for the electron to be emitted
into the vacuum.
In this one-dimensional model we consider the potential energy of
an electron to be zero everywhere inside the bulk material. Electrons are free to drift throughout the bulk material, with a net
flux incident on the emission surface from within the material. For
electrons with a specific total energy W within the bulk material,
we assume a current density J(W ) incident on the emission surface from within. Here J(W ) has dimensions of charge per unit
transverse area per unit time per unit energy W . We further assume a single electron with energy W has a probability D(W ) of
overcoming the potential barrier, to be emitted into the vacuum.
The total emission current density j is then given by
∞
j =
dW J(W ) D(W ),
(5.1)
0
where we have integrated over all possible values of the energy W .
Chapter 5. Electron emission from solids
trons are approximately free to diffuse throughout the bulk material. Electrons in the conduction band occupy energy states. The
Pauli exclusion principle dictates that no more than one electron
can occupy any given state. The average occupation number for a
state obeys Fermi–Dirac statistics, and is between zero and one.
In the limit where the absolute temperature T approaches zero,
all states with energy ε in the range 0 ≤ ε ≤ ζ are occupied by
one electron, where ζ is called the Fermi energy. In this limit all
states with energy higher than the Fermi energy are unoccupied.
In the following we assume that the emission surface is planar,
and infinite in lateral extent. In this approximation the problem
can be regarded as spatially one-dimensional, with the x-axis perpendicular to the emission surface. Some fraction of the conduction
electrons drift to the surface, where they can be emitted into the
vacuum to form a beam. Once emitted, an electron experiences a
Coulomb force which tends to attract it back toward the emission
surface. This is called an image force, and is described in detail
in the following section. It gives rise to a potential energy barrier
which must be overcome in order for the electron to be emitted
into the vacuum.
In this one-dimensional model we consider the potential energy of
an electron to be zero everywhere inside the bulk material. Electrons are free to drift throughout the bulk material, with a net
flux incident on the emission surface from within the material. For
electrons with a specific total energy W within the bulk material,
we assume a current density J(W ) incident on the emission surface from within. Here J(W ) has dimensions of charge per unit
transverse area per unit time per unit energy W . We further assume a single electron with energy W has a probability D(W ) of
overcoming the potential barrier, to be emitted into the vacuum.
The total emission current density j is then given by
∞
j =
dW J(W ) D(W ),
(5.1)
0
where we have integrated over all possible values of the energy W .