by Brian Cox
Whilst all this is a little intricate, the net effect is very straightforward: we are to imagine a current of electricity through a semiconductor material as being representative of the flow of charge, and this flow can be made up of conduction band electrons moving in one direction and valence band holes moving in the opposite direction. This is to be contrasted with the flow of current in a conductor – in that case, the current is dominated by the flow of a large number of electrons in the conduction band, and the extra current coming from electron–hole pair production is negligible.
To understand the utility of semiconductor materials is to appreciate that the current flowing in a semiconductor is not like an uncontrollable flood of electrons down a wire, as it is in a conductor. Instead, it is a much more delicate combination of electron and hole currents and, with a little clever engineering, that delicate combination can be exploited to produce tiny devices that are capable of exquisitely controlling the flow of current through a circuit.
What follows is an inspiring example of applied physics and engineering. The idea is to deliberately contaminate a piece of pure silicon or germanium so as to induce some new available energy levels for the electrons. These new levels will allow us to control the flow of electrons and holes through our semiconductor just as we might control the flow of water through a network of pipes using valves. Of course, anyone can control the flow of electricity through a wire – just pull the plug. But that is not what we are talking about – rather we are talking about making tiny switches that allow the current to be controlled dynamically within a circuit. Tiny switches are the building blocks of logic gates, and logic gates are the building blocks of microprocessors. So how does that all work out?
Figure 9.2. The new energy levels induced in a n-type semiconductor (on the left) and a p-type semiconductor (on the right).
The left-hand part of Figure 9.2 illustrates what happens if a piece of silicon is contaminated with phosphorous. The degree of contamination can be controlled with precision and this is very important. Suppose that every now and then within a crystal of pure silicon an atom is removed and replaced with a phosphorous atom. The phosphorous atom snuggles neatly into the spot vacated by the silicon atom, the only difference being that phosphorous has one more electron than silicon. That extra electron is very weakly bound to its host atom, but it is not entirely free and so it occupies an energy level lying just below the conduction band. At low temperatures the conduction band is empty, and the extra electrons donated by the phosphorous atoms reside in the donor level marked in the figure. At room temperature, electron–hole pair creation in the silicon is very rare, and only about one electron in every trillion gets enough energy from the thermal vibrations of the lattice to jump out of the valence band and into the conduction band. In contrast, because the donor electron in phosphorous is so weakly bound to its host, it is very likely that it will make the small hop from the donor level into the conduction band. So at room temperature, for levels of doping greater than one phosphorous atom for every trillion silicon atoms, the conduction band will be dominated by the presence of the electrons donated by the phosphorous atoms. This means it is possible to control very precisely the number of mobile electrons that are available to conduct electricity, simply by varying the degree of phosphorous contamination. Because it is electrons roaming in the conduction band that are free to carry the current, we say that this type of contaminated silicon is ‘n-type’ (‘n’ for ‘negatively charged’).
The right-hand part of Figure 9.2 shows what happens if instead we contaminate the silicon with atoms of aluminium. Again, the aluminium atoms are sprinkled sparingly around among the silicon atoms, and again they snuggle nicely into the spaces where silicon atoms would otherwise be. The difference comes because aluminium has one fewer electron than silicon. This introduces holes into the otherwise pure crystal, just as phosphorous added electrons. These holes are located in the vicinity of the aluminium atoms, and they can be filled in by electrons hopping out of the valence band of neighbouring silicon atoms. The ‘hole-filled’ acceptor level is illustrated in the figure, and it sits just above the valence band because it is easy for a valence electron in the silicon to hop into the hole made by the aluminium atom. In this case, we can naturally regard the electric current as being propagated by the holes, and for that reason this kind of contaminated silicon is known as ‘p-type’ (‘p’ for ‘positively charged’). As before, at room temperature, the level of aluminium contamination does not need to be much more than one part per trillion before the current due to the motion of the holes from the aluminium is dominant.
So far we have simply said that it is possible to make a lump of silicon which is able to transmit a current, either by allowing electrons donated by phosphorous atoms to sail along in the conduction band or by allowing holes donated by aluminium atoms to sail along in the valence band. What is the big deal?
Figure 9.3. A junction formed by joining together a piece of n-type and a piece of p-type silicon.
Figure 9.3 illustrates that we are on to something because it shows what happens if we join together two pieces of silicon; one n-type and the other p-type. Initially, the n-type region is awash with electrons from the phosphorous and the p-type region is awash with holes from the aluminium. As a result, electrons from the n-type region drift over into the p-type region, and holes from the p-type region drift over into the n-type region. There is nothing mysterious about this; the electrons and holes simply meander across the junction between the two materials just as a drop of ink spreads out in a bath of water. But as the electrons and holes drift in opposite directions, they leave behind regions of net positive charge (in the n-type region) and net negative charge (in the p-type region). This build up of charge opposes further migration by the ‘like sign charges repel’ rule, until eventually there is a balance, and no further net migration occurs.
The second of the three pictures in Figure 9.3 illustrates how we might think of this using the language of potentials. What is shown is how the electric potential varies across the junction. Deep in the n-type region, the effect of the junction is unimportant, and since the junction has settled into a state of equilibrium, no current flows. That means the potential is constant inside this region. Before moving on we should once again be clear what the potential is doing for us: it is simply telling us what forces act on the electrons and holes. If the potential is flat, then, just as a ball sitting on flat ground will not roll, an electron will not move.
If the potential dips down then we might suppose that an electron placed in the vicinity of the falling potential will ‘roll downhill’. Inconveniently, convention has it the other way and a downhill potential means ‘uphill’ for an electron, i.e. electrons will flow uphill. In other words, a falling potential acts as a barrier to an electron, and this is what we’ve drawn in the figure. There is a force pushing the electron away from the p-type region as a result of the build up of negative charge that has occurred by earlier electron migration. This force is what prevents any further net migration of electrons from the n-type to the p-type silicon. Using downhill potentials to represent an uphill journey for an electron is actually not as silly as it seems, because things now make sense from the point of view of the holes, i.e. holes naturally flow downhill. So now we can also see that the way we drew the potential (i.e. going from the high ground on the left to low ground on the right) also correctly accounts for the fact that holes are prevented from escaping from the p-type region by the step in the potential.
The third picture in the figure illustrates the flowing water analogy. The electrons on the left are ready and willing to flow down the wire but they are prevented from doing so by a barrier. Likewise the holes in the p-type region are stranded on the wrong side of the barrier; the water barrier and the step in the potential are just two different ways of speaking about the same thing. This is how things are if we simply stick together an n-type piece of silicon and a p-type piece. Actually, the act of stick
ing them together takes more care than we are suggesting – the two cannot simply be glued together, because then the junction will not allow the electrons and holes to flow freely from one region to the other.
Interesting things start to happen if we now connect this ‘pn junction’ up to a battery, which allows us to raise or lower the potential barrier between the n-type and p-type regions. If we lower the potential of the p-type region then we steepen the step and make it even harder for the electrons and holes to flow across the junction. But raising the potential of the p-type region (or lowering the potential of the n-type region) is just like lowering the dam that was holding back the water. Immediately, electrons will flood from n-type to p-type and holes will flood in the opposite direction. In this way a pn-junction can be used as a diode – it can allow a current to flow, but only in one direction. Diodes are, however, not where our ultimate interest resides.
Figure 9.4 is a sketch of the device that changed the world – the transistor. It shows what happens if we make a sandwich, with a layer of p-type silicon in between two layers of n-type silicon. Our explanation of a diode will serve us well here, because the ideas are basically the same. Electrons drift from the n-type regions into the p-type region and holes drift the other way until this diffusion is eventually halted by the potential steps at the junctions between the layers. In isolation, it is as if there are two reservoirs of electrons held apart by a barrier, and a single reservoir of holes that sits brim-full in between.
Figure 9.4: A transistor.
The interesting action occurs when we apply voltages to the n-type region on one side and the p-type region in the middle. Applying positive voltages causes the plateau on the left to rise (by an amount Vc) and likewise the plateau in the p-type region (by an amount Vb). We’ve indicated this by the solid line in the middle diagram in the figure. This way of arranging the potentials has a dramatic effect, because it creates a waterfall of electrons as they flood over the lowered central barrier and into the n-type region on the left (remember, electrons flow ‘uphill’). Providing that Vc is larger than Vb, the flow of electrons is one-way and the electrons on the left remain unable to flow across the p-type region. This all might sound rather innocuous, but we have just described an electronic valve. By applying a voltage to the p-type region we are able to turn on and off the electron current.
Now comes the finale – we are ready to recognize the full potential of the humble transistor. In Figure 9.5 we illustrate the action of a transistor by once again drawing parallels with flowing water. The ‘valve closed’ situation is entirely analogous to what happens if no voltage is applied to the p-type region. Applying a voltage corresponds to opening up the valve. Below the two pipes, we have also drawn the symbol that is often used to represent a transistor and, with a little imagination, it even looks a little like a valve.
What can we do with valves and pipes? The answer is that we can build a computer and if those pipes and valves can be made small enough then we can make a serious computer. Figure 9.6 illustrates conceptually how we can use a pipe with two valves to construct something called a ‘logic gate’. The pipe on the left has both valves open and as a result water flows out of the bottom. The pipe in the middle and the pipe on the right both have one valve closed and obviously no water can then flow out of the bottom. We have not bothered to show the fourth possibility, when both valves are closed. If we were to represent the flow of water out of the bottom of our pipes by the digit ‘1’ and the absence of flow by the digit ‘0’, and if we assign the digit ‘1’ to an open valve and the digit ‘0’ to a closed valve, then we can summarize the action of the four pipes (three drawn and one not) by the equations ‘1 AND 1 = 1’, ‘1 AND 0 = 0’, ‘0 AND 1 = 0’ and ‘0 AND 0 = 0’. The word ‘AND’ is here a logical operation and it is being used in a technical way – the system of pipe and valves we just described is called an ‘AND gate’. The gate takes two inputs (the state of the two valves) and returns a single output (whether water flows or not) and the only way to get a ‘1’ out is to feed a ‘1’ and a ‘1’ in. We hope it is clear how we can use a pair of transistors connected in series to built an AND gate – the circuit diagram is illustrated in the figure. We see that only if both transistors are turned on (i.e. by applying positive voltages to the p-type regions, Vb1 and Vb2) is it possible for a current to flow, which is just what is needed to implement an AND gate.
Figure 9.5. The ‘water in a pipe’ analogy with a transistor.
Figure 9.6. An ‘AND’ gate built using a water pipe and two valves (left) or a pair of transistors (right). The latter is much better suited to building computers.
Figure 9.7. An ‘OR’ gate built using water pipes and two valves (left) or a pair of transistors (right).
Figure 9.7 illustrates a different logic gate. This time water will flow out of the bottom if either valve is open and only if both are closed will it not flow. This is called an ‘OR’ gate and, using the same notation as before, ‘1 OR 1 = 1’, ‘1 OR 0 = 1’, ‘0 OR 1 = 1’ and ‘0 OR 0 = 0’. The corresponding transistor circuit is also illustrated in the figure and now a current will flow in all cases except when both transistors are switched off.
Logic gates like these are the secret behind the power of digital electronic devices. Starting from these modest building blocks one can assemble combinations of logic gates in order to implement arbitrarily sophisticated algorithms. We can imagine specifying a list of inputs into some logical circuits (a series of ‘0’s and ‘1’s), sending these inputs through some sophisticated configuration of transistors that spits out a list of outputs (again a series of ‘0’s and ‘1’s). In that way we can build circuits to perform complicated mathematical calculations, or to make decisions based on which keys are pressed on a keyboard, and feed that information to a unit which then displays the corresponding characters on a screen, or to trigger an alarm if an intruder breaks into a house, or to send a stream of text characters down a fibre optic cable (encoded as a series of binary digits) to the other side of the world, or … in fact, anything you can think of, because virtually every electrical device you possess is crammed full of transistors.
The potential is limitless, and we have already exploited the transistor to change the world enormously. It is probably not overstating things to say that the transistor is the most important invention of the last 100 years – the modern world is built on and shaped by semiconductor technologies. On a practical level, these technologies have saved millions of lives – we might point in particular to the applications of computing devices in hospitals, the benefits of rapid, reliable and global communication systems and the uses of computers in scientific research and in controlling complex industrial processes.
William B. Shockley, John Bardeen and Walter H. Brattain were awarded the Nobel Prize in Physics in 1956 ‘for their researches on semiconductors and their discovery of the transistor effect’. There has probably never been a Nobel Prize awarded for work that directly touches so many people’s lives.
10. Interaction
In the opening chapters we set up the framework to explain how tiny particles move around. They hop around, exploring the vastness of space without any prejudice, metaphorically carrying their tiny clocks with them as they go. When we add together the multitude of clocks corresponding to the different ways that a particle can arrive at some particular point in space, we obtain one definitive clock whose size informs us of the chance of finding the particle ‘there’. From this wild, anarchic display of quantum leaping emerges the more familiar properties of everyday objects. In a sense, every electron, every proton and every neutron in your body is constantly exploring the Universe at large, and only when the sum total of all those explorations is computed do we arrive at a world in which the atoms in your body, fortunately, tend to stay in a reasonably stable arrangement – at least for a century or so. What we have not yet addressed in any detail is the nature of the interactions between particles. We have managed to make a lot of progre
ss without being specific about how particles actually talk to each other, in particular by exploiting the concept of a potential. But what is a potential? If the world is made up solely of particles, then surely we should be able to replace the vague notion that particles move ‘in the potential’ created by other particles, and speak instead about how the particles move and interact with each other.
The modern approach to fundamental physics, known as quantum field theory, does just this by supplementing the rules for how particles hop around with a new set of rules that explain how those particles interact with each other. These rules turn out to be no more complicated than the rules we’ve met so far, and it is one of the wonders of modern science that, despite the intricate complexity of the natural world, there are not many of them. ‘The eternal mystery of the world is its comprehensibility,’ Albert Einstein wrote, and ‘the fact that it is comprehensible is a miracle.’
Let’s start by articulating the rules of the first quantum field theory to be discovered – quantum electrodynamics, or QED. The origins of the theory can be traced all the way back to the 1920s, when Dirac in particular had an initial burst of success in quantizing Maxwell’s electromagnetic field. We’ve already met the quantum of the electromagnetic field many times in this book – it is the photon – but there were many problems associated with the new theory that were apparent but remained unsolved throughout the 1920s and 1930s. How exactly does an electron emit a photon when it moves between the energy levels in an atom, for example? And, for that matter, what happens to a photon when it is absorbed by an electron, allowing the electron to jump to a higher energy level in the first place? Photons can obviously be created and destroyed in atomic processes, and the means by which this happens is not addressed in the ‘old-fashioned’ quantum theory that we have met so far in this book.