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

60 Chapter 3
The rate of electron emission can be represented as a current density Je
(in A/m 2 ) at the cathode surface, which is given by the Richardson law:
Je = A T 2 exp(� �/kT) (3.1)
In Eq. (3.1), T is the absolute temperature (in K) of the cathode and A is the
Richardson constant (� 10 6 Am -2 K -2 ), which depends to some degree on the
cathode material but not on its temperature; k is the Boltzmann constant
(1.38 � 10 -23 J/K), and kT is approximately the mean thermal energy of an
atom (or of a conduction electron, if measured relative to the Fermi level).
The work function � is conveniently expressed in electron volts (eV) of
energy and must be converted to Joules by multiplying by e =1.6 � 10 -19 for
use in Eq. (3.1). Despite the T 2 factor, the main temperature dependence in
this equation comes from the exponential function. As T is increased, Je
remains very low until kT approaches a few percent of the work function.
The temperature is highest at the tip of the V-shaped filament (farthest from
the leads, which act as heat sinks), so most of the emission occurs in the
immediate vicinity of the tip.
Tungsten has a high cohesive energy and therefore a high melting point
(� 3650 K) and also a low vapor pressure, allowing it to be maintained at a
temperature of 2500 � 3000 K in vacuum. Despite its rather high work
function (� = 4.5 eV), �/kT can be sufficiently low to provide adequate
electron emission. Being an electrically conducting metal, tungsten can be
made into a thin wire that can be heated by passing a current through it. In
addition, tungsten is chemically stable at high temperatures: it does not
combine with the residual gases that are present in the relatively poor
vacuum (pressure > 10 -3 Pa) sometimes found in a thermionic electron gun.
Chemical reaction would lead to contamination (“poisoning”) of the
emission surface, causing a change in work function and emission current.
An alternative strategy is to employ a material with a low work function,
which does not need to be heated to such a high temperature. The preferred
material is lanthanum hexaboride (LaB6; � = 2.7 eV), fabricated in the form
of a short rod (about 2 mm long and less than 1 mm in diameter) sharpened
to a tip, from which the electrons are emitted. The LaB6 crystal is heated (to
1400 � 2000 K) by mounting it between wires or onto a carbon strip through
which a current is passed. These conducting leads are mounted on pins set
into an insulating base whose geometry is identical with that used for a
tungsten-filament source, so that the two types of electron source are
mechanically interchangeable. Unfortunately, lanthanum hexaboride
becomes poisoned if it combines with traces of oxygen, so a better vacuum
(pressure < 10 -4 Pa) is required in the electron gun. Oxide cathode materials