In 1948, Wiliam Shockley filed a patent for his new invention, the junction transistor. He had combined the theory of quantum mechanics from earlier in the century with the fast-growing knowledge of new materials and their uses. Ten years later, the electronic revolution began with the appearance of transistor radios and the first modern computers.
Since then, improved theory and technology have led to miniaturized devices of silicon, germanium, and, more recently, gallium arsenide and other semiconductor compounds. Some devices have only a few layers of atoms, so that conduction is effectively within a two-dimensional surface. Electronic equipment containing these tiny devices fills our homes and workplaces. It is not often in history that a single technological breakthrough has had such far-reaching effects.
What development will have such an impact in the future? Surely, maybe a superconductor that operates at room temperature. With such a device, we could in theory transmit electrical power over any distance with practically no energy losses. Physics will continue to have the potential for changing our world when applied with the right materials.
The ideas in this post
You see that this post is titled “Condensed matter’, but it might have been called ‘Solid state physics’. So why wasn’t it? Partly because ‘Condensed matter’ is more fashionable. But, more importantly, ‘solid’ obscures the fact that atoms and electrons in all materials are in constant motion, and ‘physics’ hides the need for an input from chemistry and the Periodic Table.
In this post, I shall look at the way quantum theory, as discussed before in some of my past posts, has led to a better understanding of how materials behave and how this in its turn has led to new devices hardly imagined before the arrival of the theory. I shall look at semiconductors, semiconductor lasers, superconductors, and magnetic material.
ATOMS AND THEIR OUTER ELECTRONS
All atoms consist of a nucleus of protons and neutrons surrounded by electrons. A simple model of the atom has electrons moving round the nucleus in a series of orbits, like planets orbiting the Sun. But the theory of this simple model could not justify precise orbits with electrons having fixed energies. With the arrival of quantum theory, electrons could be treated as waves confined around a circular path or, more accurately, as three-dimensional waves filling the near space around the nucleus. Just as we can set up standing waves on a string attached at one end with the other end fixed, so the waves associated with the electrons can be thought of as standing waves set up as if confined within a spherical box.
Many different modes of ‘vibration’ of the electron wave become possible, and each of these modes involves a different amount of energy. The different modes of vibration lead to a series of energy levels, which we can think of as the energies associated with a series of planets moving around a central body.
The properties of an atom (excluding properties due to the nucleus) rely on the possible energy levels that the electrons can occupy in their wave-like form. So I represent the atom as a series of available electronic energy levels. The number of electrons available to fill up the energy levels depends on the atomic number of the particular atom. If the atom is in its ground state, that is if it has not been excited, the electrons fill the levels one by one, starting from the bottom level. The bottom level corresponds to the level that, on average, is nearest to the nucleus. (If we go back to thinking of the electron as a particle, then it moves around very rapidly and we cannot be sure where it is at any one time, but we can say some on average are nearer to the nucleus than others.) Only two electrons can occupy each level; this comes from quantum theory. Even these two electrons themselves must have different properties. We can imagine them as spinning tops: the two electrons in any single energy level must spin in opposite directions. This is shown by tops spinning upright and upside-down in the figure. I show two tops representing two electrons filling the lowest level, one top representing an electron partially filling the second level, and then empty levels.
When atoms come together to form compounds, it is the outer valence electrons in the highest filled energy levels that interact. We can picture that above these are empty levels and below there are inner electrons that are more tightly bound. If two identical atoms are brought very close together, each with its outermost electron occupying the same energy level, then the two levels of equal height split in value, producing very slightly different levels for the electrons to sit within. When a very large number of atoms is brought together, then the same very large number of levels, very closely spaced, will exist for the electrons. We say that such a single energy level spreads out (in magnitude) to form an energy band.
METALS, INSULATORS AND SEMICONDUCTORS
CONDUCTION IN A METAL: Conduction in a metal arises because free electrons can circulate among a lattice of ions. The ions are the original atoms minus their ‘freed’ outer electrons which belong to no particular atom. There may be more than one outer electron per atom; it would be two for an atom of an element from Group 2 of the Periodic Table.
The electrons move very fast: their speed is about 105 ms-1. But their velocities are in all different directions so the electrons make no net progress in one direction along a conductor. However, when an e.m.f. is applied to the ends of a metal conductor, the electrons do move slowly round the circuit, forming a current. We say slowly as they move with a drift velocity which is typically 105 ms-1 but can vary by orders of magnitude depending on the cross-sectional area of the conductor and the current carried.
This model fits our band model. The electrons in the current are moving within an energy band. Just as people in a crowd cannot move around unless there is an area to move into, so electrons cannot move around within the energy bands unless there is a vacant energy space in which to move. If all energy states are filled, the electrons cannot change their energy.
To move around a circuit easily, an electron needs to be able to move within the energy bands as well as spatially through the material. So for good conduction in the metal, it is best to have a large number of filled and a large number of unfilled energy states. This can easily happen if filled and unfilled levels in isolated atoms spread apart and start to overlap when the atoms are brought close together. Below these overlapping levels, there are likely to be other completely filled levels. The number of levels depends on where the atoms are in the Periodic Table.
Now a model has been built up for the metal in which we have a lower filled band, a large energy gap where no electrons can exist, and the partially filled band in Which the electrons can move around, independent of any particular atom.
When the metal is heated, the electrons go faster, but only by a very small fraction of their initial speed. Meanwhile, the ions also warm up and vibrate with larger and larger amplitude. The circulating electrons make more collisions with the ions (the lattice) and are slowed down. So the conductivity of a metal decreases as the temperature increases.
CONDUCTION IN AN INSULATOR
An insulator has a lower, filled electron band, a bandgap that is quite large, and then another band which is empty. The electrons cannot move around in the filled band because there are no vacant energy states to move to, nor can electrons jump the gap to the unfilled band. Consequently, the insulator has a very low electrical conductivity. Even if we heat the insulator, we cannot excite electrons to move from the filled to the unfilled band because it requires too large an energy jump.
CONDUCTION IN A PURE SEMICONDUCTOR
Semiconductors have had a massive impact on the design and usefulness of electronic equipment. Computers are amongst the best known and most useful equipment that contain them. Computers are only of a manageable size and speed of operation because semiconductor devices can be made very small and so electrons have to move only tiny distances. As the name suggests, a semiconductor carries current less easily than a metal, but much better than an insulator. This is because it contains free charges which carry current, but fewer than in a metal.
At 0 K, the band structure of a semiconductor looks similar to that of an insulator; filled band, bandgap, and unfilled band. The difference between the semiconductor and the insulator is that the semiconductor’s bandgap is small. Electrons in the filled band require only a little energy to excite them into the higher band.
We can estimate whether electrons will be excited thermally by comparing the energy required to jump up through the energy gap with the magnitude of kT where k is Boltzmann’s constant and T is the temperature of the semiconductor measured in kelvin. Typically, the bandgap energy is quite a lot larger than kT, but sufficiently small for the thermal energy to excite a significant number of electrons to make the jump (I will explain more on this in my next post). Once electrons are excited into the upper band, they can move freely and so the semiconductor can carry electricity. This upper band is called the conduction band.
Till next time, when I explain the conduction electrons in an intrinsic semiconductor and some other examples of semiconductor materials, I remain my humble self, @emperorhassy.