If vacuum is an insulator, then why do charges flow inside a vacuum tube?

Question

Since vacuum or free space is used as insulators in capacitors, how is it possible for charges to flow inside a vacuum tube?

Answer 1

Good question! The answer is that the vacuum is an insulator simply because it does not contain any charges that can move to carry current. A vacuum tube really doesn't contain a vacuum. It contains a cloud of electrons that spew out from a hot wire - like the filament of a light bulb. Turn off the current that heats that wire, and no current will flow in an old-style vacuum tube.

If someone made a vacuum tube using light and the photoelectric effect to generate a cloud of electrons, current could only flow as long as the light is shining on the photocathode.

Answer 2

This is a good question. In one sense, a vacuum is a perfect conductor: an electron in an electric field in free space will move unimpeded (zero resistance). However, electrons in a material are bound to that material (i.e. they have lower energy than they would if in free space), and it takes work to remove them. The minimum amount of work required to remove an electron from a material is called the work function, and it is typically a few electron volts. It is this work function that keeps electrons in a material and allows us to treat the vacuum as an insulator.

Additional details:

1. In solid-state physics, materials are characterized by their electronic states (typically just described as configurations in energy- and momentum-space). A continuum of states is referred to as a band.
2. The bands form what's known as the band structure, from which much of the electronic properties of a material can be deduced.
3. In general, electrons will occupy the lowest energy states in a material. Similar to filling a cup with water, where the water will occupy the lowest energy states of the cup.
4. A conductor is defined by a partially filled valence band (think partially filled cup).
5. An insulator is defined by a completely filled valence band. See cartoon below.
6. For an electron in a material to move through the material, it needs unoccupied states into which it can move, and in an insulator, there are no unoccupied states in the valence band into which the electron can move. In this sense, electrons in insulators are 'frozen' in place.
7. There are unoccupied states in the insulator, but they are at much higher energies. These states form a continuum which is referred to (in semiconductor lingo) as the conduction band.
8. In an insulator, the conduction band is separated from the valence band by what's known as a bandgap, which is a range of energies that are not allowed in the material: typically about 3 to 10 electron volts.
9. For an insulator to conduct, an electron must have enough energy to overcome the bandgap and transition into the conduction band. This is what makes insulators poor conductors.
10. A semiconductor, then, is just an insulator with a very small bandgap, which allows it to conduct more easily. A typical semiconductor will have a bandgap of around one electron volt (Si, for example, is about 1.2 eV at absolute zero).
11. In a conductor, because the valence band is only partially filled, there are many accessible unoccupied states into which an electron can transition. This easy access to unoccupied energy states is what makes a conductor a conductor.

12. As mentioned above, electrons in a material (either a conductor or insulator) can be ejected into the vacuum, but they have to overcome a potential barrier (similar to overcoming the bandgap in an insulator). This potential barrier is known as the work function, and it is usually a few electron volts. It's because of this work function barrier that a vacuum can be thought of as an insulator.

13. Here is an article discussing the effects various work functions on the life and performance of vacuum tubes. It quotes cesium as being used in some vacuum tubes and having a work function of 1.6 eV. Compare that to Si, which has a native band gap of 1.2 eV, and you can see how a low-work-function material in a vacuum tube might be used similarly to a semiconductor**.

*Note—technically the work function is the energy difference between the lowest energy state of the vacuum and the highest energy level in the material. It's also defined as the minimum energy required to remove an electron from the material.

**Note that most semiconductor devices (like p-n junctions) are doped with impurities, which essentially add states to the electronic structure. these states are typically in the bandgap, which makes the effective barrier much smaller than the native bandgap. See the second cartoon.