by Brian Clegg
The simplest form of transistor is not dissimilar to a diode but has an extra connection to a central piece of material that is sandwiched between the two outer sections. In such a transistor, the layers are typically either n-type/p-type/n-type or p-type/n-type/p-type. With this type of set-up, changing the voltage that is applied to the middle section of the sandwich, called the base, enables the transistor to act either as an amplifier or as a switch.
When the transistor is in amplifier mode, small changes in the voltage applied to the base result in much bigger changes to the voltage across the two outer sections. When it acts as a switch, the difference between having a voltage on the base and having no voltage enables the transistor to switch off and on a current that is trying to flow through the outer parts.
In practice, modern circuits usually make use of a different type of transistor, called a field effect transistor. Here, instead of a central base, the switching part of the transistor, called a gate, is separated from the other parts by a thin insulating layer. In this type of transistor, it is the electrical field generated by the gate that allows it to control the flow through the device. In the case of graphene, as we shall see, this field effect is very pronounced, making it good for producing amplifying field effect transistors. However, the difficulty of getting it to stop conducting means that, alone, graphene isn’t suitable for making a switching transistor (though as we shall also see, there are a number of ways around this).
The reason the ability of a transistor to have a switch action is important is that switching is an essential aspect of the fundamental unit of computer hardware: the gate.
Jumping the gate
In physical terms, a computer chip usually contains a complex circuit, typically built up on a silicon wafer base – but in logical terms it is made up of gates. These are parts of the circuit that represent a logical operation, usually described using the terms of Boolean algebra. Named after the 19th-century English mathematician George Boole, Boolean algebra uses a relatively simple structure to combine true and false statements, and is fundamental in computing.
The key requirement to make a computer function is to be able to deal with the binary 0s and 1s that represent numbers and instructions bit by bit. (A ‘bit’ is just a ‘binary digit’.) While Boolean algebra was originally designed, well before the existence of the first electronic computers, to deal with problems involving ‘true’ and ‘false’, it proved equally effective in manipulating 0s and 1s – in both cases it’s a matter of dealing with a system that can have only one of two values. We can think of 0 as false and 1 as true.
Each type of logic gate in a computer manipulates numbers in different ways. Most combine two different inputs to produce one output, but the simplest gate merely transforms a single value to the opposite one. This is the NOT gate, which flips the bit. If the value is currently 0 it becomes 1; alternatively, if it’s 1, it becomes 0.
Moving on to the gates that combine two inputs, we start with AND and OR. The AND gate produces 0 in every possible combination of its two inputs (let’s call them A and B), except when both inputs are 1. If we think of 0 as false and 1 as true, the AND gate produces true only if both input A is true AND input B is true. You can think of this in logical terms by saying of a vehicle ‘This is a red bus.’ The statement is true only if the vehicle is red AND it is a bus. If it is just red but not a bus, or a bus but not red (or neither a bus, nor red) it is not a red bus.
The OR gate, by contrast, is less fussy in the way it operates. It will produce a 1 if either input A is 1 OR input B is 1 – and will also do so if both are 1. The only circumstance where it will produce a 0 is if both A and B are 0. In logical terms, it’s like looking for an object that is either red, or is a bus. A red postbox would be a true match, and either a green or red bus would also be true. But a yellow postbox would not match the criteria and so is false.
Each of the AND and the OR gates have negative alternatives, known as NAND and NOR. These produce exactly the same effect as putting the output of an AND or an OR gate through a NOT gate. So, where the AND gate produced 1 only if both A and B were 1, the NAND gate produces 1 unless both A and B are 1. Similarly, where the OR gate produces 1 except when both A and B are 0, the NOR gate produces 1 only if both A and B are 0.
Finally, we have a subtly different kind of OR – the XOR gate, which stands for ‘exclusive OR’. If you remember, the OR gate produces 1 if A is 1, if B is 1 and if both A and B are 1. The XOR gate, as the name suggests, requires an exclusive selection. It produces 1 as output if A is 1 or if B is 1 – but not if both are 1. A and B must be different. So, if both A and B are 1, it produces 0. This would be the equivalent of looking for something that was red, or a bus, but not a red bus. (There is also a negative version of this, the XNOR gate, which produces 1 if both A and B are 0 or both A and B are 1. It produces 1 when the inputs have the same value.)
Technically, there really is not a need for more than one kind of gate – we only need the electronic structure to produce a NOR gate or a NAND gate. Each of these, linked with more of the same kind, can produce all the other types of gate. For example, if you wanted a NOT gate, you could join together both inputs to a NOR gate. This would mean that both A and B would always have the same value. A NOR gate receiving two 0 values produces 1, while with two 1 values it produces 0. By linking the inputs, a NOR gate is forced to act as a NOT gate.
Gates make up both computer memory and the processors that do the hard work. The transistors in the circuit are arranged so that they make up different kinds of gate. For example, a NOT gate can be made from two transistors, while a more sophisticated gate like a NAND gate can require as many as four transistors. Before integrated circuits, printed circuit boards would be made up combining thousands of individual transistors in this way. In a modern computer, though, the whole memory unit or processor is combined on a single chip with layers of semiconductors, insulators and conductors replacing the individual components.
To get graphene and other ultrathin materials to be able to produce the same kind of circuits – though in a much thinner and more flexible fashion, as we will see – it has been necessary both to think through the way to make these gates using the new materials and to deal with the pros and cons of the properties of the different materials – for example, graphene’s extremely high conductivity.
Ultrathin electronics were to pose a unique and intriguing set of challenges. But first we had to be able to make the materials – the graphene – which for so long had been considered impossible to manufacture.
Which takes us back to Andre Geim and Konstantin Novoselov.
* Strictly this refers not to a particle but a quantum system, which could include many particles, or indeed empty space with no particles present.
† More precisely, the square of the equation.
‡ Yes, that Carlsberg. Later on, the Danish Academy of Science would give Bohr tenancy of the Aeresbolig or House of Honour, a mansion provided to the Danish nation by Carlsberg, which came with a lifetime supply of lager.
§ Harald, two years younger than Niels, was a gifted mathematician with a talent for football, playing for Denmark in the 1908 Olympic Games. Niels, though not up to Harald’s standard, also had some success on the football field, as a goalkeeper.
¶ Ironically, given the way it’s used in ordinary English to imply a major change, a quantum leap is actually the smallest possible change that an electron can make.
|| This only applies to the electrons in the outer shell, the so-called ‘valence’ electrons that are involved in forming bonds. There is very little overlap with inner electrons, so their bands are negligible.
** As is often the case with quantum theory, things are not what they seem when it comes to spin. This property of quantum particles has nothing to do with rotation, and when measured along any chosen axis can only have one of two values, up or down. But it shares some similarities with the property of large-scale objects called angular momentum, a
nd so spin was used as a name, even though it is a distinctly misleading one.
†† Richard Feynman and his senior John Wheeler used the hypothetical backwards-in-time wave to deal with a problem whereby an electron seemed like it should be influenced by its own electrical field, causing problems for the mathematics.
‡‡ This may seem to contradict the idea we’ve already seen that an atom can have a number of electrons in the same shell. However, although these electrons occupy the same energy level, they must have other properties such as their spin with different values. The Dirac sea deals with all possible negative energy electrons.
§§ Doping a semiconductor is intentionally introducing impurities into it.
4
LIKE NOTHING WE’VE SEEN BEFORE
The road to Manchester
We have seen how Geim and Novoselov both moved to Manchester from the Netherlands. Geim had chosen the university because he preferred the British system and was offered a long-term post there. The fact that Manchester had offered his wife, Irina Grigorieva, a job as well, made the move more attractive than any alternative. Although Grigorieva had been a postdoc at Bristol, she had only found a role as a part-time teaching laboratory assistant at Nijmegen. But the board at Manchester were familiar with her Bristol work and she is now a well-established physicist in her own right, still based in Manchester. As for Geim and Novoselov, the pair may have first worked together in the Netherlands, but each had made a significant journey from his Russian origins.
Andre Geim was born in the Russian resort of Sochi on the Black Sea, near the border with Georgia. Now best known as the location of the 2014 Winter Olympics, in 1958, when Geim was born, Sochi was part of the USSR, a very different place from modern Russia, let alone the western European cities where he would later flourish. Geim spent his first few years living with his grandparents, as much of his family was incarcerated in the Gulag. His family were of German background and hence were considered potential enemies of the state in a part of the world still finding its feet little more than a decade after the end of the Second World War. Even though Stalin had implemented his own reign of terror, the dark hand of Germany was not forgotten.
Science had always been Geim’s passion – as a boy, he won a regional Chemistry Olympiad by memorising a 1,000-page dictionary, and proved as excellent at the experimental side as the theoretical. With glowing results from his school and a perfect score in the exams he took at age sixteen, he had looked forward to studying physics at the Moscow Engineering and Physics Institute. Unfortunately, despite his excellent qualifications, he was rejected. Although there is no direct evidence, Geim believes to this day that this was due to his German family background. The teenage Andre spent some time working at the same engineering factory as his father to pay for extra tutoring in maths and physics in order to give himself even more of an edge – only to be rejected by the Institute a second time.
Luckily, there was not the same level of discrimination on the selection board of the prestigious Moscow Institute of Physics and Technology, generally known in the USSR as PhysTech. In some ways, it’s a surprise that Geim did not apply to PhysTech in the first place. Set up at the end of the Second World War by leading Soviet scientists, the founding idea was to move away from the mass teaching methods used elsewhere in the USSR. Each of the students selected to attend would be given an individual programme of education, tailored to them and provided by leading figures in the field. This vision of a wholly independent institution foundered, as some of the scientists involved had been critical of the Soviet system, but they managed instead to set up PhysTech as a part of Moscow State University, where it was allowed a surprising degree of autonomy. Though Geim is rightly critical of the Soviet state, this institution’s approach seems to have benefited him.
As was common with PhysTech students, Geim went on to join a section of the Russian Academy of Sciences, in his case, the Institute of Solid State Physics, where he gained his doctorate. After this, Geim worked mostly in the West at universities in Nottingham (where he first realised just how many obstacles faced those doing science in the Soviet system), Bath and Copenhagen, becoming an associate professor at Radboud University Nijmegen in the Netherlands in 1994. His move to Manchester in 2001, he claims, was in part due to the hierarchical, backbiting nature of the Dutch academic system, which he found less constructive than that of British universities.
In Nijmegen, as we have seen, one of Geim’s doctoral students would be Konstantin Novoselov. Sixteen years younger than Geim, Novoselov was born on the eastern side of Russia in Nizhny Tagil, an industrial city where railway and military engineering dominated. While Novoselov was not initially the same kind of standout student as Geim, he exhibited an unusual level of curiosity about electricity and magnetism. Given a rather smart German train set at the age of eight, he was more excited by the DC controller for the set than the actual trains. With this he had a variable power supply, which he used to experiment over the years with electromagnets and electrolysis.
Like Geim, Novoselov won a place at PhysTech, still a significant force in Russian physics, from where he went straight to work under Geim in the Netherlands. The two hit it off, not just from having a common background, but in their approach to science. It seemed only natural that Novoselov should travel with Geim to Manchester, putting in place the second essential piece in the creative game that would result in the creation of graphene. (He continued to be officially registered in the Netherlands until 2004, when his doctorate was awarded there.)
From discovery to Nobel
Although there is no doubt that there was a sudden and significant mental shift when the Scotch tape method was dreamed up and proved successful, this doesn’t mean that Geim and Novoselov went straight from their early Friday night experiments to winning the Nobel Prize. The initial breakthrough was followed by many months of solid work.
Novoselov, looking back on the first year that followed the 2003 discovery, has described it as ‘a whole year of continuous excitement’. In real life (as opposed to TV and movies) science usually has many long periods with nothing much happening. But during that year, the pace was intense. Novoselov again: ‘For a typical piece of work, novel results and experiments come maybe on a weekly or daily basis. At that time, it was on an hourly basis.’
Graphene opened up so many possibilities that there was constantly something new to be investigated. And after the Manchester lab published their first paper in 2004, interest worldwide in this wonder material shot through the roof. It was only a matter of time before the two Mancunian Russians were awarded the Nobel Prize for Physics, winning it in 2010 for ‘groundbreaking experiments regarding the two-dimensional material graphene.’
Referring to graphene as a two-dimensional material might seem an exaggerated boast. Any substance does, of course, have some depth, even if it is measured as a fraction of a nanometre. It is part of a three-dimensional world. However, while graphene may not be two-dimensional in the pure mathematical sense, there is no way to make anything thinner – it is as thin as you can get, the next stage in removing a slice being no atoms at all. This means that it shares some properties with theoretical two-dimensional objects and behaves in ways that its three-dimensional counterpart, graphite, can’t.
The Nobel Prize has come to be recognised as the ultimate mark of excellence in the disciplines it covers, though it’s worth remembering that many of history’s greatest scientists have not won Nobels. The Physics prize is limited to a maximum of three people, who must be alive at the time of the award. It was first given out in 1901 to the German physicist William Röntgen ‘in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him’. As it happens, the Nobel committee got one thing here wrong – the suggestion that the ‘remarkable rays’ would be named after their discoverer. The term ‘Röntgen rays’ was a non-starter as Röntgen’s original description of these then-mysterious rays as �
�X-Strahlen’ or X-rays proved much more popular. Effects in physics are often named after the discoverer – but not fundamental phenomena.
Given the date of the first award in 1901, great names such as Galileo, Newton or Maxwell of course never featured. And it is worth remembering that the selection process for the Nobels is a very human one, which has resulted in some distinct oddities, notably the 1912 prize, won by the Swedish scientist Gustaf Dalén for the dubious honour of having invented a better gas regulator for lighthouses, just at the time when lighthouses were converting to electricity.
The process of nomination for the prize is not secret, even though the detail of who was nominated is kept under wraps for 50 years, so we do not know, for example, whether the Manchester pair were nominated before the 2010 prize – or how many nominations they received. It’s a shame that this data isn’t available earlier, with the person making the nomination anonymised. Looking back at the historical nominations gives a good feel for the way a nominee’s work became recognised over time.
Take, for example, Albert Einstein, who won the 1921 prize in 1922, primarily for work he had done during 1905. His first nomination, a single one, came in 1910. He had two in 1912, and three in 1913. It’s possible not only to see the number of nominations grow, but also the prestige of the nominators. By 1920 he had six nominators, including the leading Dutch physicist Heike Kamerlingh Onnes, and in 1921 there were fourteen nominations including names such as Eddington and Planck. Even this didn’t persuade the committee, which unusually decided that no one deserved the 1921 prize. But in 1922, the pressure was so great, with seventeen nominations for Einstein, that the Nobel committee gave in and retrospectively awarded the previous year’s prize to him.