Tag Archives: electrons

The Many Roads from P-N Junctions to Transistors

When I called p-n junctions the building blocks of digital electronics, I was referring to their key role in building transistors. A transistor is another circuit element, but it is active, meaning it can add energy to a circuit, instead of passive like resistors, capacitors, or inductors which only store or dissipate charge. The transistor has an input where current enters the device and an output where current leaves, but also has a control electrode which can be used to modify the transistor’s function. Transistors can act as a switch, an amplifier, and can change the gain of a circuit (i.e. how many electrons come out compared to how many went in). So where did the transistor come from, and how do you build one?

The earliest devices which acted as transistors were called ‘triodes’, for their three inputs, and were made using vacuum tubes. A current could be transmitted from one electrode to the other, across the airless vacuum inside the tube. But applying a voltage to the third electrode induces an electric field which diverts the current, meaning that the third electrode can be used as a switch to turn current on and off. Triodes were in wide use for the first half of the twentieth century, and enabled many radio and telephone innovations, and in fact are still used in some specialty applications that require very high voltages. But they are quite fragile and consume a lot of power, which is part of what pushed researchers to find alternate ways to build a transistor.

Recall that the p-n junction acts as a diode, passing current in one direction but not the other. Two p-n junctions back to back, which could be n-p-n or p-n-p, will pass no current in any direction, because one of the junctions will always block the flow of charge. However, applying a voltage to the point where the p-n junctions are connected modifies the electric field, allowing current to pass. This kind of device is called a bipolar junction transistor (or BJT), because the p-n junction diodes respond differently to positive voltage than to negative voltage which means they are sensitive to the polarity of the current. (Remember all those times in Star Trek that they tried reversing the polarity? Maybe they had some diodes in backward!) The input of a bipolar junction transistor is called the collector, the output is called the emitter, and the region where voltage is applied to switch the device on is called the base. These are drawn as C, E, and B in the schematic shown below.

Bipolar Junction Transistor

Looking at the geometry of a bipolar junction transistor, you might notice that without the base region, the device is just a block of doped semiconductor which would be able to conduct current. What if there were a way to insert or remove a differently doped region to create junctions as needed? This can be done with a slightly different geometry, as shown below with the input now marked S for source, the output marked D for drain, and the control electrode marked G for gate. Applying a voltage to the gate electrode widens the depletion region at the p-n interface, which pinches off current by reducing the cross-section of p-type semiconductor available for conduction. This is effectively a p-n-p junction where the interfaces can be moved by adjusting the depletion region. Since it’s the electric field due to the gate that makes the channel wider or narrower, this device is called a junction field-effect transistor, or JFET.

Junction Field Effect Transistor

Both types of junction transistor were in widespread use in electronics from about 1945-1975. But another kind of transistor has since leapt to prominence. Inverting the logic that lead us to the junction field effect transistor, we can imagine a device geometry where an electric field applied by a gate actually creates the conducting region in a semiconductor, as in the schematic below. This device is called a metal-oxide-semiconductor field-effect transistor (or MOSFET), because the metal gate electrode is separated from the semiconductor channel by a thin oxide layer. Using the oxide as an insulator is pretty clever, because interfaces between silicon and its native oxide have very few places for electrons to get stuck, compared to the interfaces between silicon and other insulating materials. This means that the whole device, with oxide, p-type silicon, and n-type silicon, can be made in a silicon fabrication facility, many of which had already been built in the first few decades of the electronics era.

These two advantages over junction transistors gave MOSFETs a definite edge, but one final development has cemented their dominance. The combination of an n-channel MOSFET and a p-channel MOSFET together enable the creation of an extremely useful set of basic circuits. Devices built using pairs of one n-channel and one p-channel MOSFET working together are called CMOS, as shorthand for complementary metal-oxide-semiconductor, and have both lower power consumption and increased noise tolerance when compared to junction transistors. You might be asking, what are these super important circuits that CMOS is the best way of building? They are the circuits for digital logic, which we will devote a post to shortly!

P-N Junctions: Building Blocks of Digital Electronics

Last time we mentioned n-type semiconductors, which have electrons as the charge carrier, and p-type semiconductors, which have holes as the charge carrier. But what happens when you put them together? The result is a device which underlies much of modern electronics!

Imagine a block of an n-type semiconductor pressed up to a block of a p-type semiconductor. What happens when the two make contact? Each material is electrically neutral, but the holes in the p-type material provide additional electron states which draw electrons from the n-type material. And when electrons travel into the p-type material, they leave holes behind them in the n-type material. Thus, at the interface the p-type semiconductor gains a negative charge, and the n-type semiconductor gains a positive charge. The region where this happens is called the space charge region. Even though this isn’t the lowest energy charge distribution, it is the lowest energy overall because it makes use of more available states for both electrons and holes. (The rigorous version of this argument involves entropy, which I hope to dedicate a post to very soon!) So now the interface looks like a cluster of positive charge next to a cluster of negative charge, which creates an electric field across the junction!

If we want to pass current through the p-n junction, that electric field is going to either help us or hurt us depending on which direction we want the current to flow. If the current flow is in the same direction as the force applied by the field, then current will be aided by the presence of the junction. But if the current flow is in the opposite direction, it will be impeded. This kind of device is called a diode, because it can either conduct current or block it depending on the direction of current flow.

Of course, since the size of the electric field in the junction is limited by the interface size and the charge carrier concentration, if we apply a strong enough external electric field then we will be able to pass current through the device in both directions. This is called breakdown, and while ideal diodes are assumed to never exhibit breakdown, real diodes do because of the physical nature of the system which in p-n junctions means the finite size of the junction’s electric field. So a p-n junction acts like a normal semiconductor with applied voltage in one direction, and in the other direction passes no current until a high enough voltage is reached to induce breakdown.

Diodes are a building block that can be used to make a more complex electronic circuit, just like inductors, resistors, and capacitors. But p-n junctions specifically are the building blocks of most digital circuits in silicon! More on that coming soon!

Electrons and Holes

So far when we’ve talked about electronic properties of materials, we have emphasized electrons as the carriers of charge through the material. As we know, in atoms, nuclei are big and mostly immobile, whereas electrons are small and exist in a probability cloud around the nuclei. Thus the mobility and number of electrons, plus the available energy states, are what determine how easily electrons can flow through a material. And this decides whether something is an insulator, a metal, or most interestingly a semiconductor.

But consider a material that has many, many electrons, one in which the band of electron states is nearly full with only a few vacancies. Even with an applied electric field, very few electrons will be able to go anywhere if there are not many available states to move into. A material like this would be nearly an insulator. But we may see one electron move over into an empty state, then a second electron move into the state vacated by the first, then a third electron move into the state vacated into the second, and so on. The motion of the electrons is causing a net charge flow, but no individual electron is able to get very far because of the dearth of available states. From a distance it might almost appear as if the empty space without an electron is what’s moving.

This is similar to a very common occurrence, in fizzy beverages such as soda or beer. Bubbles form, and once they detach from the sides of the container, they rise up through the liquid. But the force causing this motion is gravity, which doesn’t affect the gas in the bubbles as much as it affects the relatively dense liquid around them. In order for the liquid to fall, the bubble must rise. Or, imagine a row of seats, with a middle seat unoccupied but all the other seats full, in a narrow space that makes it difficult to get past occupied seats. A person next to the empty seat could move over, and then the person next to them can move over, and so on. It is the people that are doing the moving, but if we wanted to describe the motion it would almost be simpler to say that the empty seat moves to the edge of the row. There are lots of other examples of the same phenomenon, shown in the diagram below using marbles.

Thus, for the materials whose electron states are crowded but not quite full, the empty states are called ‘electron holes’ or just ‘holes’. Holes are quasiparticles, meaning we can treat them as individual particles even though they are really a collection of behavior exhibited by many particles. Conduction of charge still occurs via the movement of electrons, but conceptually and mathematically it is easier to describe the movement of holes in the system. So one can calculate the charge of a hole, which is the opposite of the charge of an electron, or the mass of a hole in various materials, or the hole mobility which describes how easy it is for a hole to traverse any given material. A material with holes as the charge carrier is called p-type, and a material with electrons as the charge carrier is called n-type,  because of the positive and negative charges of holes and electrons.

Practically, this is an important distinction between different types of semiconductor, and you’ll see how it comes into play in technology when we talk about p-n junctions and finally get to the transistor. But conceptually, I find it really cool that the emergent behavior of a bunch of electrons can be described as a quasiparticle, with its own mass, charge, and electronic properties. It’s elegant and weird, as nature often is.

I’m With The Band Theory

We have already talked about the mechanical aspects of how a solid is assembled from individual atoms, when the atoms are in a repeating periodic structure called a crystal lattice. The lattice type can determine many of the material properties, but one of the most interesting and useful properties to think about is electrical conduction. One of the simplest ways to measure conduction is by creating a potential difference, so that one side of the material is more energetically favorable to charged particles than the other. This is called applying a voltage, named after Alessandro Volta who invented the battery, a device that uses chemical differences to create a voltage. When there is a voltage applied, electrons are drawn through the material, but how many electrons flow (which determines how large the measured electrical current is) varies widely by material. In some solids where electrons move freely, it’s easy to pass a lot of electrons through, creating an electrical current. This is characteristic of a metal, where electrical conduction is easy. But in other solids, it takes a lot of energy to move electrons through so electrical conduction is difficult, and we say these materials are insulators. And there is a third class of material, a semiconductor, which can be switched between conducting and non-conducting states.

To understand what causes the different electrical behaviors, we can think about how the atomic energy states available to electrons scale up to a bulk material. Each individual atom has a set of available electron states, that can be mathematically described using quantum mechanics. Some of these states are occupied by electrons, and some are not. A collection of atoms will have a collection of states, some occupied and some free, and an electron has to have available states that it can move between in order to traverse a solid. If there are no available states, it doesn’t matter how energetically favorable it is for the electron to go somewhere else, it has no way of getting there.

For a solid made up of only one kind of atom, the electronic states in each atom will be similar but may vary slightly due to varying conditions throughout a non-perfect crystal. This means that if we sum up all the states, instead of the precisely delineated states we found in a single atom, we’ll have smeared out bands of available states and forbidden regions which give a rough approximation of what energies electrons can have. As usual, the lowest energy states will be mostly occupied, and the highest energy states will be mostly empty. It’s the states right at the top of the electron occupancy which turn out to be the most useful for conduction, because of the minimal energy cost involved in moving electrons. (The line demarcating this is called the Fermi energy or Fermi level.) And how these available electron states look when we depict them as a function of energy can be very different, as shown below:

The various bands of allowed electronic states can overlap with each other, can have a small separation in energy, or can have a large separation in energy. Overlapping bands mean that in both bands, electrons have many available states to transition to, and that is why materials with overlapping bands have high electrical conductivity. These are metals, like gold or copper. For materials with a large separation between bands, the lower energy band is completely full and the higher energy band is completely empty. If an electron in the full band is tempted to move through the material, it must first scrounge up the energy to jump up to an available state, which is so considerable a task that most electrons can’t manage it. These are insulators, which may only pass one electron for every 1030 (a billion billion billion, or more electrons than stars in the universe) that pass through a metal at the same potential.

But the most interesting case, at least as far as modern electronics is concerned, is the material with a small separation between bands, the semiconductor. Only a small energy is needed to boost an electron from the full band to the empty band, and if the energy required is provided by thermal energy at room temperature, semiconductors can have significant electrical conduction at room temperature. But the most useful semiconductors are not quite conductive under normal conditions, but can easily be turned on by applying an electric field. That means they can operate as an electrical switch, acting as a metal or an insulator depending on what’s required. Silicon is the most widely used semiconductor in the present day,

Where the bands of available states fall exactly is determined by the crystal lattice type and the interatomic spacing, two factors which are themselves determined by the outer electrons of the atoms themselves. And for amorphous solids without a periodic structure, like glass, we still get energy bands. In fact, one way to think of the transparency of glass is that visible photons entering the material do not have enough energy to excite electrons from a filled band into an empty band, so they pass through the material without interacting with it. And that’s why you can see through glass!

All the justification for band theory involves a lot of math, of course. But just the basic idea, that bulk materials have bands of available states for electrons and the energy and grouping of these states determines electrical behavior, is pretty amazing because it puts a framework around the broad variety of electrical behaviors that we see in materials in nature. And, if you want to understand how electronics work, band theory is the first big piece of that puzzle.

Spin, Rotation, and a Plate Trick

In my introduction to the quantum number spin, I mentioned that particles can have half-integer or integer spin, and that which they have deeply affects their behavior. This is not an easy statement to understand, especially without seeing the math. The allowed values for spin come from solutions to quantum mechanical energy equations. But what do differences in these values mean? How does a spin-1/2 particle behave differently than a spin-0 particle?

One major difference is in the behavior under rotation. When we try to calculate how rotation affects a particle with spin-0, we find that it doesn’t matter: the particle is indistinguishable before and after any rotation. However, a spin-1 particle requires a 360° rotation to return to its initial state, and a spin-2 particle requires a 180° rotation to return to its initial state. This may seem strange, but what it means is that the spin value describes the symmetry of the particle. If you imagine a deck of cards, the spin-2 particles are like face cards that look the same when rotated 180°. Spin-1 particles are like number cards which must be rotated 360° to look the same as they did when they started. Particles with integer spin are called bosons, after the Indian physicist Satyendra Bose.

There are no playing cards which must be rotated 720° in order to look the same, and yet this is the case with spin-1/2 particles. There are few macroscopic objects that can demonstrate this property, but one of them is your hand! Place any object on your hand, palm up, and rotate it without dropping your palm. After 360° you will find your arm to be pretty contorted, but after 720° of rotation your arm has regained its initial position! Another way to think of it is that, instead of a 360° rotation bringing the object back to its initial state, which would be like multiplying by 1, the 360° brings the object to another state like multiplying by -1, and then an additional 360° rotation multiplies by (-1)*(-1) which equals 1. Every spin-1/2 particle shares this behavior, such as quarks (the constituents of protons and neutrons) and electrons. We call these particles fermions, after the physicist Enrico Fermi.

That factor of -1 becomes important because of the idea in quantum mechanics that particles are interchangeable or identical. That is, we cannot tell one specific electron from another. Mathematically, you can state this by writing a function that describes the positions of two particles, and seeing what happens to that function when you exchange the particles. If you do this, what you find is that bosons are symmetric under particle interchange and the function stays the same, but fermions are antisymmetric under particle exchange, and the function is multiplied by -1.

This idea, that bosons are symmetric and fermions are antisymmetric under exchange of identical particles, is called the spin-statistics theorem. A thorough proof requires relativity and quantum field theory, but the fundamental cause is the differing rotational behavior due to spin as a measure of symmetry. One very important consequence of all of this is that if you have two fermions occupying the same state, and you exchange them, you find that the function describing their position cancels out to zero. This is a mathematical statement of the Pauli exclusion principle forbidding two fermions from being in the same quantum mechanical state!

On the other hand, we find that bosons are perfectly happy to all pile into the same quantum mechanical state, at least at low temperatures. This is the concept behind the Bose-Einstein condensate, the state of matter experimentally realized only 30 years ago in which bosons can be cooled into occupying the same state.

I hope this makes the connections between spin, the Pauli exclusion principle, and particle types clearer. But if nothing else, the rotational exercise with an object on your hand, better known as Feynman’s plate trick, is fun at parties.

The Rainbow of Bonds

Now that we have looked at the broader picture of what a bond is, we can go a little deeper. Bonds can be easy or hard to break, they can involve particle exchange between atoms, they can be the result of transient forces, and they can react in a variety of ways. There is a rainbow of bond types to explore, but we can focus on a few primary examples.

We’ll start with the stronger sort of bonds: those that involve direct transfer of electrons between atoms. For example, say we have two neighboring atoms, one with an empty low-energy state and one with an outer electron that’s all alone at a high-energy state. If the states are similarly shaped, both atoms can lower their overall energy when the extra electron moves to the low-energy state. The atom that gave up the electron is now positively charged, and the atom that accepted the electron is negatively charged, so there is an electrostatic force attracting them. Charged atoms are also called ions, so we say that these two atoms have an ionic bond. And it’s possible to have ionic bonds involving more than one electron, if an atom has two or three electrons to donate which another atom can accept. A common example of ionic bonding is table salt, which has a sodium atom donate an electron to a chlorine atom.

It’s also possible for two atoms to share a pair of electrons, so that the electron cloud overlaps with both atomic nuclei. If the electrons in question have oppositely aligned spins, they can have the same energy without being in the same quantum mechanical state. This is called covalent bonding. It happens most often when the two atoms in question are comparably attractive to electrons, for example if they are the same type of atom. Graphite, or pencil lead, is one form of carbon that has covalent bonds. So is graphene, the atomically thin version of graphite whose discovery (and extraordinary properties) recently garnered a Nobel prize in physics.

Ionic and covalent bonds tie atoms together very tightly, and can be linked together to form complexes with many bonded atoms. These complexes are known as molecules. But large numbers of atoms can also share electrons diffusely, so that the electrons aren’t localized to a single atom or a pair of atoms. This is called metallic bonding, so-called because delocalized electrons are found in metals. The free electrons move around the atomic nuclei like a sea moving around rocks, only weakly bound to them. The mobility that electrons have in metals is why we say that metals have high ‘electrical conductivity’: it is easy to pass an electrical current, which just consists of individual electrons, through a metal. As a special case of metallic bonding, it’s also possible to have partially delocalized electrons in small molecules, which is the basis of organic chemistry.

Another way to weakly bind atoms comes from the fact that charge is separated in an atom, between the positively charged nucleus and the negatively charged electron cloud. Imagine that the cloud is slightly distorted, by a passing electrical field or by a random fluctuation. If the electron cloud is not symmetric around the nucleus at that moment, there will be a distance between the center of the positive charge and the center of the negative charge, and a force because of the opposite charges. This is called a dipole in electromagnetism, because of the two oppositely charged poles. And if you have two next to each other, they will try to align so that the negative side of one dipole is near the positive side of the other. What starts as a small fluctuation can cause a slight reordering over a large material, because of the dipoles attempting to align. This dipole-dipole interaction is another weak form of bonding. It can happen with induced dipoles, as I’ve described, or between permanent dipoles which are common in molecules.

There is also a lone form of chemical bonding which doesn’t rely solely on electrons. The hydrogen atom, with its single proton and single electron, is pretty small and pretty reactive. So it’s actually possible for two atoms to share a third atom, hydrogen, which means that both the electron and the proton are in energy states that minimize the total system energy. The hydrogen bond is partly covalent, since the hydrogen electron is usually paired with a second electron. But the separation of the proton and electron also induces a dipole, making hydrogen bonding a dipole-dipole interaction. Hydrogen bonding may sound like a strange beast, and it is, but it is an important factor in the chemical behavior of water which is essential to life as we know it.

What is spin?

First the basics: spin is an intrinsic property of matter, like charge or mass. It is measurable in the real world by observing interactions with magnetism, and is the basis of technologies like MRI and hard disk drives!

We of course recognize the verb ‘to spin’, which means to rotate around a fixed axis the way that wheels, figure skaters, and the Earth do. But the word spin is also used to describe a fundamental property of particles. We have already talked a little about a fundamental property, charge, which was useful because a lot of the important forces at the atomic scale are electromagnetic and thus related to charge. And we remember that mass, another fundamental property, determines how matter interacts via the gravitational force. Spin is a bit different.

The idea of particles having an intrinsic spin first arose during the development of quantum mechanics, when Wolfgang Pauli and others noticed that part of the mathematical solution for particle states resembled angular motion, as if the particles were physically spinning around an axis. But unlike spinning at the macroscopic scale, quantum spin can only occur at a few discrete values: integer and half-integer multiples of ħ, the reduced Planck constant. The allowed values of spin are clustered around zero, and the ħ factor is dropped by convention because particle physicists like to make things look simple. So a photon, the quantum of light, has spin 0, whereas electrons and quarks, which make up protons and neutrons, have spin 1/2. There are also particles with spin 1, 3/2, and 2. As with charge, spin is reminiscent of a behavior we see in the macroscopic world, but its values are quantized into a few allowed values.

Spin can have one of two polarities, meaning we can have an electron with spin +1/2 and one with spin -1/2. And charged particles like the electron actually respond to magnetic fields differently if they have positive or negative spin! This is because the motion of a charged particle creates a small magnetic moment, which will be aligned in one direction for positive spin and the opposite direction for negative spin. This is the basis of the famous Stern-Gerlach experiment, in which atoms with one free electron are sorted by their spin under the influence of a magnetic field. But it’s also the basis of nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI), two related techniques for determining the composition and structure of either chemical substances or human patients! Strong magnetic fields can be used to align spins within any object, and how quickly the spins decay back to their original orientation gives information about what is inside the object. Currently, researchers are trying to build circuits that use spin instead of charge to carry information, which is called ‘spintronics’.

But at a more basic level, when we talked about chemical bonds we skipped over the importance of spin. The reason spin matters for bonding is due to the Pauli exclusion principle, the idea that no two electrons can share the same quantum state. In the development of quantum mechanics, it became clear from the data that even if all the available energy states were mathematically accounted for, there still seemed to be a degeneracy in which two electrons shared what was thought to be the same quantum state. This can be explained with a new quantum number, which we call spin. So spin is another factor of the electron cloud shape and is critical in the understanding of chemical bonding.

But there are actually even more strange things about spin than I can fit in this post, including the fact that the Pauli exclusion principle only applies to particles with half-integer spin! Half-integer and whole-integer spin particles are fundamentally different from each other, in some pretty interesting ways, but why is a story for another time!