310
Chapter 5. Electron emission from solids
y =
W
]
I
C
x
U x
x =
Figure 5.2: Approximate energy diagram for cold field emission.
we will include this image force term to improve the accuracy and
generality of the calculation.
In the limit of zero absolute temperature T , conduction electrons
within the bulk material occupy all energy states up to the maximum energy ζ, which is the Fermi energy. No states above this
energy are occupied. Classically no emission can occur, because
the topmost filled energy level is below the top of the potential
energy barrier. Quantum mechanically a conduction electron incident on the barrier from within the buk can tunnel through the
barrier, and be emitted into the vacuum.
We designate D(W ) as the probability that an electron with energy W inside the material will tunnel through the potential barrier. Again we designate the incident current density per unit energy from within the material as J(W ). We seek the emission
current density, which is the incident current density J(W ) times
the transmission probability D(W ), integrated over all possible
Chapter 5. Electron emission from solids
y =
W
]
I
C
x
U x
x =
Figure 5.2: Approximate energy diagram for cold field emission.
we will include this image force term to improve the accuracy and
generality of the calculation.
In the limit of zero absolute temperature T , conduction electrons
within the bulk material occupy all energy states up to the maximum energy ζ, which is the Fermi energy. No states above this
energy are occupied. Classically no emission can occur, because
the topmost filled energy level is below the top of the potential
energy barrier. Quantum mechanically a conduction electron incident on the barrier from within the buk can tunnel through the
barrier, and be emitted into the vacuum.
We designate D(W ) as the probability that an electron with energy W inside the material will tunnel through the potential barrier. Again we designate the incident current density per unit energy from within the material as J(W ). We seek the emission
current density, which is the incident current density J(W ) times
the transmission probability D(W ), integrated over all possible