5.5. Emission with elevated temperature and field
319
Problems
1. Complete the details of the derivation of (5.81).
2. The work function for tungsten is 4.5 electron-Volts. Estimate
the field F required for the onset of field emission from tungsten.
Describe the functional dependence of the current density j on F
for F higher and lower than this onset value.
5.5 Emission with elevated temperature and field
In the preceding sections we explored thermionic emission, and
separately cold field emission. In this section we generalize the
preceding concepts to calculate the emission current density as a
function of temperature and applied electric field. We follow the
general approach of Murphy and Good [64], which is based on earlier work by Kemble [52].
Again we make use of (5.1) for the emission current density j,
and (5.18) for the incident current density per unit energy J(W ).
The present task is to calculate the transmission probability D(W )
that an electron with total energy W in one dimension will tunnel
through the potential barrier.
The potential energy U (x) is given by (5.38), and is plotted as
a function of x in Figure 5.3. We intentionally include the image
potential term in the following. The potential energy U (x) is assumed to join smoothly on both sides of the emission surface at
x = 0. In the vacuum (x > 0), the potential energy (5.38) has a
319
Problems
1. Complete the details of the derivation of (5.81).
2. The work function for tungsten is 4.5 electron-Volts. Estimate
the field F required for the onset of field emission from tungsten.
Describe the functional dependence of the current density j on F
for F higher and lower than this onset value.
5.5 Emission with elevated temperature and field
In the preceding sections we explored thermionic emission, and
separately cold field emission. In this section we generalize the
preceding concepts to calculate the emission current density as a
function of temperature and applied electric field. We follow the
general approach of Murphy and Good [64], which is based on earlier work by Kemble [52].
Again we make use of (5.1) for the emission current density j,
and (5.18) for the incident current density per unit energy J(W ).
The present task is to calculate the transmission probability D(W )
that an electron with total energy W in one dimension will tunnel
through the potential barrier.
The potential energy U (x) is given by (5.38), and is plotted as
a function of x in Figure 5.3. We intentionally include the image
potential term in the following. The potential energy U (x) is assumed to join smoothly on both sides of the emission surface at
x = 0. In the vacuum (x > 0), the potential energy (5.38) has a