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Underlying all tube operation is the fact that any metal is continuously emitting electrons. Both the number and the speed with which they are emitted increases very strongly with temperature, although emission takes place at anything above absolute zero (-273°C). To understood emission, we have to look at what is going on inside the body of the metal.
In any metal, there are one or two electrons that can easily be detached from an atom, so that inside the solid metal there is a kind of sea of electrons floating around independently of any particular atom. The latter are fixed in place inside the crystal structure and do not move about at all, although they vibrate in place. This sea of electrons is common to all metals, and indeed is really the defining characteristic of a metal and explains many of their familiar properties such as electrical conductivity and the fact that they are shiny.
Since the electrons are not attached to any particular atom, they move about constantly, very much like the molecules in a gas. The average speed of the electrons increases with temperature, but because they are constantly bouncing off of the atoms and each other they do not all have the same speed but rather obey a statistical distribution law.
If an electron happens to be going towards the surface of the metal, then it will naturally tend to fly right out through the surface. However there are powerful forces trying to stop it, for the simple reason that there are positively charged metal atoms inside (because they have lost one or two electrons to the electron sea) and none outside. Thus an electron approaching the surface is slowed down, and only those having enough energy can escape. The amount of energy required is called the work function, and varies for different metals.
This is a convenient point to say how electron energy is measured. First of all, the energy of an electron corresponds directly to its speed. This follows the same law for kinetic energy as anything else, such as a car:
| $E=\tfrac{1}{2}mv^{2}$ | where: | $E$ = energy $m$ = mass $V$ = velocity |
In this case, $m$ is the mass of an electron, which is about 10-30 kg. Energy is normally measured in Joules, but for electrons this is impracticably huge. Instead we use electron Volts (eV). One eV is the energy that an electron acquires when it is accelerated through a potential field of one Volt. It is about 10-19 Joules, and corresponds to a speed of about 800,000 meters/sec.
The work function of a metal is expressed in eV. For tungsten, it is about 4.5eV. Any electron having less energy than this will not manage to escape, but will be turned around by the electric field close to the surface and will return into the body of the metal.
The electrons escaping from the metal correspond to an electric current, and this current is given by Dushmanns Equation:
| $I_{0}=AT^{2}e^{-\frac{11600w}{T}}$ | where: | $I_{0}$ = emitted current $A$ = a constant, 120.4 A/cm2 $T$ = temperature in °K (i.e. °C + 273) $w$ = work function of emitted metal in eV |
The striking thing about this equation is the exponential element, which means that emission increases very rapidly with temperature. Figure 3 shows the emission of a tungsten filament as a function of temperature. Even a small percentage change in temperature results in a big change in the emitted current. For an oxide-coated cathode under typical operating conditions, a 10% increase in temperature increases emission by about a factor of 3.
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| Figure 3: Electron emission as a function of temperature |
The electrons that do manage to escape have the same distribution of energy as they did inside the body of the metal. Some of them flop exhaustedly from the surface, while others still have considerable velocity. This becomes important when examining the behavior of the tube. The distribution of energy (and hence speed) obeys the equation:
| $p=e^{-\frac{Vq_{\epsilon}}{kT}}$ | where: | $p$ = proportion of all electrons having energy greater than $V$ $q_{\epsilon}$ = electron charge, 1.602·10-19 Coulomb $k$ = Boltzmanns constant, 1.38·10-23 Joules/degree $T$ = temperature in °K (i.e. °C + 273) |
It is not a coincidence that the exponential element here closely resembles that in Dushmanns equation. Figure 4 shows this distribution graphically. The great majority of electrons have low energy levels, and the average for an oxide cathode is only about 0.1eV, but there is no upper limit on the energy that a single electron may have. For example, about one electron in a billion is emitted with an energy greater than 1eV.
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| Figure 4: Electron velocity distribution: proportion of emitted electrons having given energy |
Early tubes used solid tungsten filaments. Tungsten has a high work function, and there are other metals which are much more suitable in this respect (for example caesium, whose work function is only 1.6eV). However tungsten has the great advantage of a high melting point - other metals would melt long before they gave adequate emission. A tungsten filament has to be operated at about 2700°C, which is the same as a light bulb. The amount of heat thrown out by any hot object increases with the fourth power of its temperature, which means that a great deal of power (i.e. filament current) is required to replace this lost heat and remain at this temperature.
It was fairly soon discovered that the addition of a small amount of the element thorium (about 1%) to tungsten greatly reduces its work function, to about 2.6eV, allowing filament operation at around 1900°C. This reduces the required power by about a factor of four. Such tubes were called dull emitters, because compared to a tungsten filament (or a light bulb) they were much less bright.
Later it was found that a surface coating of barium oxide (or a mixture of barium and strontium oxides) gave even better results. This is because the oxide is no longer a metal, and the energetic electrons within the body of the filament can escape through the oxide layer at much lower velocity. In fact, the oxide layer is a n-type semiconductor, i.e. one having an excess of electrons, and its behavior is due to this. Oxide filaments have a work function of about 1.1eV, and can be operated at around 700°C. It is this oxide coating which makes filaments and cathodes appear white. There are however disadvantages. The oxide coating is mechanically fragile, and can be damaged as a result of gas in the tube or by vibration or shock. This is why high voltage tubes (such as the 211 and 845) still use thoriated tungsten. It is also relatively volatile, and slowly evaporates from the surface of the filament from where it is deposited in undesirable places such as the grid wires. Emission from an oxide surface is much more complex, in physical terms, than from a pure metal, although it does still essentially follow Dushmanns equation. Overall, though, the advantages of oxide-coated filaments and cathodes for small-signal tubes are overwhelming, and no other materials have been used since the 1930s.
Electrons within the body of the cathode are travelling in all directions, and in consequence so are the ones that are emitted. It turns out that the average lateral (sideways) velocity of the electrons is about the same as their average forward velocity. It is therefore wrong to think of them all travelling along the shortest straight line from the cathode towards the plate.
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