It is incredible to think that today’s desktop computers are more powerful than machines that filled a whole room only a few years ago. This rapid scaling down is a striking example of how successful electronics based on semiconductors has been. Integrated circuits etched into tiny wafers of silicon pervade every part of our lives. A modern car engine is likely to be controlled by a computer containing a microprocessor, as are the latest passenger aircraft – so-called ‘fly-by-wire’ systems. Even the humble kitchen toaster often relies on a silicon microchip.
Nevertheless, physicists are trying to improve electronic devices. They are looking at semiconducting materials other than silicon. The most important of these are gallium arsenide (GaAs) and related compounds made from the elements in groups III and V of the Periodic Table. These include aluminium and indium in group III and phosphorus in group V. These so-called III-V materials have tremendous potential. They work at the fast speeds needed for the most powerful supercomputers. Gallium arsenide also operates at higher frequencies than silicon, providing communications systems that can carry more information and exploit previously inaccessible regions of the electromagnetic spectrum.
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Another important niche for gallium arsenide is optoelectronics, the interface between optics and electronics. Unlike silicon, gallium arsenide can both detect and generate light. Also, some optical computers rely on devices made by gallium arsenide.
The most exciting use of gallium arsenide and related materials, however, is in creating minute electronic structures that exploit the wave-like nature of electrons predicted in quantum mechanics. This contrasts with conventional devices, which can largely be understood with classical mechanics. Novel devices based on quantum mechanics should not only lead to smaller and faster computers and communications systems that consume less power, but they are already helping physicists to understand the subtle behaviour of electrons at the quantum level.
How do such devices work? All electronic devices depend on electrons moving about in some controlled way, so that there is either an electrical current or no current across the ‘active region’ of the device. In a computer, for example, this on-off switchng provides the means of passing and processing information in binary code consisting of 1s and 0s. How fast a device can respond depends on the time taken for the electrons to cross the active region. There are two ways to reduce the time – by making the electrons move faster or the device smaller.
In integrated circuits, the minimum size of the device is dictated by how easy it is to fabricate. You can now make silicon chips with features smaller than a micrometre. But there may be a minimum size below which conventional silicon devices will not work. We need new kinds of devices or materials if we are to break this limit. Gallium arsenide and other III-V compounds may provide both.
The properties of a semiconductor depend on how easily its electrons can move about. These electrons lie in ‘energy bands’ which control their freedom to move; a completely filled or completely empty band cannot conduct. It is now possible to ‘grow’ semiconductors so as to have bands with a particular energy – a technique called band engineering.
Energy bands in materials arise directly from the laws of quantum mechanics. In single atoms, electrons can occupy only certain energy levels. What is more, according to the Pauli exclusion principle, no two electrons can occupy the same energy state. The electrons fill up levels of increasing energy with the outer electrons being loosely bound enough to become involved in chemical bonding – the valence electrons. At higher energies, electrons are lost from the atoms altogether. In ths case, both the free electrons and the remaining charged atoms, or ions, can conduct electricity.
Things are slightly different if we bring together a large number of atoms, say of silicon, to form an organised array – a crystal. Then each atomic energy level is forced to split into a continuous series of levels so that each electron is at a slightly different energy in order to comply with the exclusion principle. This series of levels is called a band. Just as there are discrete electron energy levels in a single atom, so there are discrete energy bands in the solid (see Figure 1).
Imagine building up the solid by adding atoms one at a time. The electrons gradually fill up the bands. The highest completely filled band is called the valence band because these electrons hold the crystal together. Beyond the valence band, lies the conduction band. It is partly filled in metals which, therefore, can conduct electricity. In insulators, on the other hand, the conduction band is empty and separated from the full valence band by an energy gap (the band gap). It is difficult for electrons to cross this gap to the conduction band.
Semiconductors, by definition, lie between these extremes: they are insulators with narrow band gaps. We can easily control the number of free electrons to make them good insulators or good conductors. This is why semiconductors are so useful for electronic devices.
One obvious way of making a semiconductor conduct is by giving the electrons in its valence band energy in the form of heat to enable them to jump the bandgap into the conduction band. But this approach is not much good for electronic devices because the conduction then depends on the temperature. Another approach is to add electrons from outside by deliberately ‘doping’ the semiconductor with impurities. These come in two varieties. The first, called donors, have an extra electron compared with the semiconductor. This extra electron is weakly bound to the donor and can easily escape from it at room temperature using thermal energy. The electron goes into the bottom of the conduction band, because the valence band is full, leaving behind a fixed positive donor ion. The resulting doped semiconductor is called an n-type material.
The second type of impurity, called an acceptor, removes electrons from the top of the valence band, producing negative acceptor ions. Most of the states in the valence band remain filled, because the concentration of impurities is low, so it is much easier to keep track of which states are not filled rather than those that are. These unfilled states are called holes. They are usually treated as though they are genuine particles, in the same way as electrons, but they have a positive charge rather than a negative one. These semiconductors are called p-type materials.
Band gaps are not the only effect of quantum mechanics in a crystal. Holes and electrons in semiconductors behave as though they are less massive than a free electron. For example, electrons in gallium arsenide have an effective mass of 0.067 times that of a free electron. This is equivalent to putting a squash ball into gallium arsenide, and finding that it behaved like a ping pong ball. Because a ping pong ball is lighter, it is much easier to accelerate it than a squash ball, so by analogy it is easier to accelerate electrons in gallium arsenide than in free space. This effect is less marked in silicon where the electrons have an effective mass of 0.2. As a result, gallium arsenide produces faster devices.
Speedy gallium arsenide
Gallium arsenide and other III-V compounds can improve semiconducting devices which fall into two main categories. The first, called bipolar devices, need both electrons and holes to work. The simplest example is a p-n diode, a device that passes current in one direction but not the other .
The second category of devices uses only one kind of carrier. The most common type found in integrated circuits is the field-effect transistor, or FET (see Figure 2). It consists of two thin layers of semiconductor, one conducting (doped) and one insulating. Two electrodes called the source and drain are connected to the conducting layer. A third electrode called the gate is separated from the conducting layer by the insulating layer. A positive voltage on the gate causes current to flow down a channel in the conducting layer from the source to the drain. This current is controlled by varying the voltage on the gate. If the gate is made more positive, it pulls more negative electrons into the channel and the current increases. A more negative voltage on the gate repels electrons from the channel, so reducing the current.
The gate can be metal such as aluminium, or a highly doped semiconductor that conducts like a metal, such as polycrystalline silicon. The layer of semiconductor is usually silicon or gallium arsenide. In the commonest silicon FET, the insulator is silica (Si02). The device is called a metal-oxide-semiconductor FET, or MOSFET (see Figure 3). There may be thousands in your wristwatch and more than million on a large integrated circuit.
In the simplest device made from III-V compounds, the insulating layer is provided by what is called a depletion layer. This is formed because there are a large number of electronic ‘surface states’ on gallium arsenide, not present in silicon. These states attract electrons from the semiconductor beneath, forming the depletion region which contains almost no free electrons and so cannot conduct. This device is called a metal-semiconductor FET, or MESFET, as shown in Figure 4. A metal gate is deposited directly on top of a layer of n-type gallium arsenide. Electronics engineers have used MESFETS for some years in microwave circuits where the frequencies are too high for silcon devices.
There are, however, far more exciting ways to use gallium arsenide than simply as a faster conventional semiconductor. We can build much more complicated devices than MESFETs called heterostructures. These contain regions of differing chemical composition, obtained by using similar compounds such as gallium arsenide and aluminium arsenide and their alloys. These materials all have the crystal structure, so we can grow layers of gallium arsenide and, say, aluminium gallium arsenide (AIxGa1-xAs) on top of one another so that the structures match up. It is a bit like stacking up egg-trays so that the bumps and hollows line up. If the egg trays are slightly different sizes, then the holes and bumps do not quite match and the stack becomes unstable. Similarly, if the crystal lattices do not match, the conducting electrons become scattered or trapped, so ruining the electronic properties of the device. Special and expensive techniques such as molecular beam epitaxy and metal-organic chemical vapour deposition are needed (‘Metals with wings’, 91av, 14 April 1988) to grow thin layers of these heterostructures successfully.
The reason for making heterostructures is that they provide a way of controlling the motion of the electrons. In heterostructures, the different materials have conduction and valence bands at different energies (see Figure 6). In particular, the bottom of the conduction band in aluminium gallium arsenide is at a higher energy than that in gallium arsenide. This difference is usually about 0.3 electronvolts. A thin layer of aluminium gallium arsenide on top of a thin layer of gallium arsenide wil trap electrons in gallium arsenide unless they can gain the extra energy needed to enter the conduction band of aluminium gallium arsenide. Layers of aluminium gallium arsenide can, therefore, be used to confine electrons in gallium arsenide.
A clever use of heterostructures is in modulation doping. A conventional n-doped material contains donors to supply the electrons needed for conduction. A fixed positive ion is left behind when an electron leaves a donor to go into a conduction band. Because the ions and electrons attract each other, the electrons are scattered by the donor ions as they pass through the crystal lattice. This slows down the electrons, so that the device is less effective.
In modulation-doped materials, the donors are put into a layer of n-doped aluminium gallium arsenide grown next to undoped gallium arsenide. Electrons from the donors in aluminium gallium arsenide can travel into the gallium arsenide, where they lose energy. The separation of the negative electrons from the positive donors sets up an electric field that tries to drive the electrons back again. But the energy gap between the two conduction bands prevents this. All the electric field can do is to squeeze the electrons tightly against the interface between the two layers. The confined electrons are much less scattered because they are separated from their donor ions, and can move very quickly in just two dimensions.
The electrons are squeezed so tightly against the interface that their motion has to be described in quantum mechanical terms. This shows that the electrons are obliged to occupy a small number of energy levels, like electrons bound in an atom. Although all the electrons are stuck in the same state for motion normal to the interface, they are in different states for motion parallel to the interface, and can move. This is called a two-dimensional electron gas, usually abbreviated to 2DEG (see Figure 7).
A 2DEG can be turned into an FET by putting a metal gate on top of the layer of n-doped aluminium gallium arsenide. This layer has the uncomfortable role of acting as the insulator between the gate and the channel in the gallium arsenide as well as providing electrons in the 2DEG. The resulting device has many names, including modulation-doped FET (MODFET), and high electron mobility transistor (HEMT). MODFETS are the fastest transistors available (see Figure 8). Because the electrons are less scattered, MODFETS generate less electrical noise – a vital feature for microwave devices. Some receivers for satellite television contain a MODFET, probably the first consumer application of these so-called low dimensional devices.
The major problem with quantum devices is that they can pass only a limited current because the 2DEG is so thin. Also, at room, or higher temperatures, the vibrations of the crystal lattice may scatter the electrons. In fact, that is the problem with such quantum devices – they work best at liquid helium temperatures.
Could we go one step further and make electrons move in just one dimension rather than two dimensions? The answer is yes. Take a MODFET and cut a slit of about 1 micrometre out of the middle of the gate and apply a negative voltage to the gates to repel the electrons from the area beneath them. This leaves a narrow channel under the slit, only 25 nanometres wide, where the electrons are confined. They can move freely parallel to the slit but quantum mechanics prevents them from moving in other directions. For that reason such devices are called quantum wires (see Figure 9).
What is more, the conducting capacity (conductance), depends on the width of the channel but not in a smooth way. Experiments at the University of Delft and Philips Research Laboratories in the Netherlands, and at the University of Cambridge, show that the conductance is quantised, varying in steps whose values depend only on the electronic charge and Planck’s constant. Such a structure would be an ideal candidate for a digital device. This is only the beginning of an active area of research that will flourish for some years to come .
The structures that I have described are called horizontal structures because the electrons flow parallel to the surface. We can also make vertical structures where the electrons flow across the interfaces from one material to another. A simple structure consists of a sandwich with gallium arsenide on either side of a single insulating layer of aluminium gallium arsenide. This acts as what is called a rectangular barrier. According to classical mechanics, an electron in gallium arsenide cannot cross through the insulating layer because of the energy gap. However, because the barrier is so narrow, quantum mechanics comes into play. The wave-like character of the electron allows it to tunnel through.
Another structure has a layer of gallium arsenide sandwiched between two layers of aluminium gallium arsenide. In this case the electron is trapped in a ‘potential well’. Again, the well is so narrow that quantum mechanics must be used to calculate the allowed energy levels in it. These are discrete, like those of an atom, and the well is analogous to a one-dimensional atom.
An electron remains in one of the allowed levels of an isolated well for ever, but this is not true if the aluminium gallium arsenide layers on either side are made thin instead of infinitely thick. In this case, the electron can escape by tunnelling through the barriers, and we talk of a resonant state rather than a bound state (see Figure 10). This has a startling effect on the transmission of electrons through the resulting double barrier. If electrons are ‘fired’ at a barrier, they have some probability of tunnelling through, or they will be reflected. You might expect that electrons would find it more difficult to get through two barriers than one. This is usually true, and most electrons are reflected. But if the energy of the electron matches that of the resonant level, as in Figure 10 (b), all the electrons pass through the double barrier, and none is reflected. The double barrier acts as an ‘energy filter’, because it allows through only those electrons whose energy is close to that of the resonant level. We can move the resonant level in and out of the incoming electrons to create a fast switch, oscillator or amplifier.
This double barrier with a resonant state is used in a device called a resonant tunnellng diode. The outer layers of gallium arsenide are n-doped to introduce electrons. The barriers normally prevent the electrons from moving out of the layer so no current flows. If you apply a voltage such that the electrons are pushed into the resonant level then the electrons can pass through, and a large current flows. It is also possible to make resonant tunnelling structures in a 2DEG, using a MODFET, with a more complicated gate, as shown in the micrograph at the beginning of this article. In this case, the barriers come from a negative voltage on two gates rather than from different materials.
By creating a sequence of alternating wells and barriers, we can produce a material with a particular band structure called a superlattice. The atoms of the semiconductors form a lattice with a certain band structure, as does the regular sequence of wells and barriers, except that the bands are much narrower. But this lattice is only one-dimensional and its band structure depends on the length of the wells and the thickness of the barriers. This means that we can grow the band structure of the superlattice with a particular specification. There are many optical applications but superlattices have not been widely exploited in electronic devices.
As the size of devices decreases, so does the number of active electrons, and the goal of miniaturisation is to have only a single active electron. This goal has been reached in the past couple of years with structures controlled by the ‘Coulomb blockade’. These are so small that only one electron can occupy the device at a time – the electrostatic, or Coulomb repulsion between electrons prevents others entering. Physicists have developed an ‘electron turnstile’ which passes one electron when a voltage pulse is applied to a gate electrode. Most devices today are tunnelling barriers, but the barrier is an oxide film between metals rather than a semiconductor. Structures made from III-V semiconductors are also being developed, and this adds another component to the ‘toolbox’ of effects that can be used to build novel devices in heterostructures.
Despite all these exotic possibilities, gallium arsenide and other III-V semiconductors suffer from a reputation that they ‘were, are and will always be the materials of the future’. Devices made from silicon perform so well that gallium arsenide is restricted to devices for high frequencies such as receivers for satellite television or as radio transmitters.
Optoelectronics is the area where III-V devices are most likely to be successful as optical communications become more important. This alone should ensure the success for gallium arsenide and its relations. Low-dimensional devices such as the MODFET, as well as the more way-out quantum devices could find wider application – although engineers are unlikely to be satisfied with devices that work only at liquid helium temperatures.
Physicists are developing new materials to overcome this restriction. One example is the alloy indium gallium arsenide, which can be used instead of a gallium arsenide in the channel of a MODFET. This alloy has a lower effective mass than gallium arsenide so that the electrons can be accelerated more easily, and a larger conduction band energy, so that electrons are better confined within the channel. The lower effective mass also makes the quantum effects easier to observe. There remains a huge amount of work to be done before these quantum devices find their way into wristwatches, but a lot of exciting physics will certainly be found along the way.
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Bipolar devices – the p-n diode
A diode is formed by a junction between an n-type and p-type semiconductor (see Figure 5a). An n-type material has free electrons in the conduction band, while p-type material has holes (missing electrons) in the valence band. If an electron and hole meet, the electron can fall into the hole in the conduction band – the two particles ‘recombine’ and emit energy (just as electrons and positrons annihilate at much higher energies in machines like the Large Electron Positron Collider at CERN in Switzerland).
When the n- and p-type materials are brought together, electrons and holes diffuse across the junction and recombine. This produces a ‘depletion region’ where there are no free electrons or holes – effectively an insulating region (see Figure 5b). This region is limited because the electrons and holes leave charged donor and acceptor ions behind, and these set up an electric field that opposes the diffusion.
If we connect a battery so that the n-type material is made positive, and the p-type side is negative, the diode is ‘reverse biased’. The electrons and holes are attracted away from each other by the battery and the insulating depletion region becomes bigger (as in Figure 5c). Almost no current flows. The opposite happens if we connect the battery the other way round, giving ‘forward bias’. Electrons and holes are attracted across the depletion region, which gets smaller (as in Figure 5d), and current flows. Thus a diode allows current to flow in one direction but not the other – a ‘one-way valve’.
The simplest use of a diode is in converting an alternating current – one whose sign keeps changing, like ordinary household electricity – to a direct current, whose sign is constant. Diodes are found in the power supply of any electronics. Another important use is in radios, where they convert the rapidly oscillating radio waves into audible signals.
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Quantum wires to guide electrons
Complicated and potentially useful structures can be made using quantum wires as building blocks. They are also called ‘electron waveguides’ because they resemble waveguides used to carry microwaves. There is a big difference in size – microwave guides are metal tubes with a rectangular cross section, tyically two centimetres across, while electron waveguides are a million times narrower. Many devices have been proposed that are electronic analogues of microwave devices.
Possibly, the simplest is the ‘stub tuner’ on a waveguide, simply a side-branch whose length can be varied (as in Figure 11). Its operation depends on resonances that build up in the side-branch or stub, in the same way as they build up in a bottle if you blow across the mouth and making it ‘sing’. Depending on the lengh of the stud, these resonances can allow electrons to be transmitted down the main waveguide, or all electrons can be reflected back out the way they came in. The length of the stub can be controlled with a gate like that of a MODFET to make a quantum mechanical switch.
Another device that relies on interference is the ring in Figure 12 above. It shows a peculiar quantum phenomenon called the Aharonov-Bohm effect. Here, the electrons are affected by a magnetic field even though they do not pass through it. The electron waves come down the input wire, split to go either way around the loop, and recombine at the exit. They interfere constructively and go down the exit waveguide, provided that the structure is perfectly symmetrical and the electrons travel exactly the same distance round either side of the ring.
If a magnetic field is applied through the hole in the ring, the waves that go along the two paths around the ring gain phase shifts of opposite sign. The waves interfere destructively at the exit if the field has the correct value, and the current through the device should fall to zero. This has been observed, although present devices are far from perfect and the current does not drop to zero. Again, we have a quantum mechanical switch. A magnetic field is inconvenient in practice, but you can use an all electric field instead.
John Davies is a lecturer in the department of electrical engineering at Glasgow University. He researches on the theory and modelling of semiconductor devices, particularly those based on quantum wires.
Further reading ‘Nanoscale and ultrafast devices,’ special issue Physics Today, February 1990; ‘Gallium arsenide transistors’, Scientific American, August 1987, p 80; ‘Fabricating minute devices’, J H Davies, Physics World, April 1989, p 47.