Physical Principles of Electron Microscopy: An Introduction to TEM ...

The Transmission Electron Microscope 59
The process of thermionic emission can be illustrated using an electronenergy
diagram (Fig. 3-2) in which the vertical axis represents the energy E
of an electron and the horizontal axis represents distance z from the tungsten
surface. Within the tungsten, the electrons of highest energy are those at the
top of the conduction band, located at the Fermi energy EF. These
conduction electrons carry the electrical current within a metal; they
normally cannot escape from the surface because Ef is an amount � (the
work function) below the vacuum level, which represents the energy of a
stationary electron located a short distance outside the surface. As shown in
Fig. 3-2, the electron energy does not change abruptly at the metal/vacuum
interface; when an electron leaves the metal, it generates lines of electric
field that terminate on positive charge (reduced electron density) at the metal
surface (see Appendix). This charge provides an electrostatic force toward
the surface that weakens only gradually with distance. Therefore, the electric
field involved and the associated potential (and potential energy of the
electron) also fall off gradually outside the surface.
Raising the temperature of the cathode causes the nuclei of its atoms to
vibrate with an increased amplitude. Because the conduction electrons are in
thermodynamic equilibrium with the atoms, they share this thermal energy,
and a small proportion of them achieve energies above the vacuum level,
enabling them to escape across the metal/vacuum interface.
�
vacuum
level
metal
conduction
electrons
E
E F
x
vacuum
Figure 3-2. Electron energy-band diagram of a metal, for the case where no electric field is
applied to its surface. The process of thermionic emission of an electron is indicated by the
dashed line.
e -