Monthly Archives: June 2012

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!

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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.

Moving Charge, Magnetism, and Inductors

Last time I talked about how magnetization arises from the alignment of spins, which is favorable in some materials due to the quantum mechanical exchange interaction. But, there is another way to generate a magnetic field: it turns out that moving charges (i.e. an electric current) create a magnetic field as well! This was first observed experimentally by Ørsted, who noticed a compass needle moving in response to current running through a coiled wire. It was then incorporated into Maxwell’s Equations, which attempted to provide a unified framework for observed electric and magnetic phenomena.

But while the evidence that a moving charge generates a magnetic field was clear, explaining the mechanism by which this happens took some time. The key insight actually came from Einstein, who saw Maxwell’s Equations and had a question: why is the speed of light independent of the reference frame? That is to say, we know that if we are in a car that is passing another car, our car appears to be going only a bit faster than the other car, even though an observer standing on the sidewalk would say that both cars were moving fairly fast. The observed speed depends on the frame of reference of the observer! And so in classical mechanics, the speed of an object and the speed of its reference frame can be added together to give the total object speed. Why should it be any different for something moving at the speed of light? Well, the answer to that question gets into special relativity, but consider the same question with a moving charge from two frames of reference:

  1. From the reference frame of the charge, an electrical field is induced by a static charge.
  2. From the reference frame of a static observer, a magnetic field is induced by a moving charge.

The implication is that electric and magnetic fields, and forces, are simply two facets of the same phenomena, which is now called electromagnetism.

In fact, the magnetic field of the earth, shown above, is due to moving charge in the form of molten iron in the outer core of the planet. The charge flow is maintained because magnetics fields induce current flow, just as current flow induces magnetic fields, forming a feedback loop. The earth’s magnetic field is not very large, but it is enough to enable measurement devices such as compasses, which have long been used for navigation. Some animals are also able to sense the earth’s magnetic field to directly use for navigation, including homing pigeons, sharks, and even smaller organisms such as bacteria. Many different biological sensors for magnetic field seem to have evolved independently, likely due to the significant survival advantages associated with reliable navigation.

But another place where the magnetic field induced by a moving charge arises is in electronics. Any wire with a current running through it will generate a magnetic field proportional to the size of that current. That means that nearby objects that respond to magnetism may experience magnetic forces, or even have electric currents induced in them. Coaxial cable, which has an inner wire carrying current encased in an insulator and a cylindrical outer conductor, confines the magnetic field to the insulating region of the wire. It was developed specifically to shield the magnetic field of the current-carrying wire, and to shield the wire itself from stray external magnetic fields.

And there is a basic circuit component that makes use of this phenomenon as well, the inductor. An inductor, as you can see above, consists of wire coiled in a loop, possibly with many coils and possibly with a material lodged inside the coils of wire. The current on the wires induces a magnetic field in the center of the loop. The forces from this magnetic field act against any change in electric current, using the energy stored in the magnetic field. Because inductors are sensitive to changes in current over time, they are very useful in processing time-dependent electronic signals. The magnetic field of one inductor can also be coupled to the coils of a second inductor, inducing a second current which may be larger or smaller depending on the relative sizes of the coils of the two inductors. This is how a transformer is made, a device which inductively transfers electrical signals and is central to power transmission from the power grid to individual homes and businesses.

As you can see from all these examples, there are a lot of technologically useful things to do with the interplay between electricity and magnetism! And the realization that they were intertwined was a huge step forward for physics.

Magnets, How Do They Work?

Most of us have had some experience with magnetism, whether it’s finding north with a compass, posting a grocery list with refrigerator magnets, or playing with magnetic toys that snap satisfyingly together. And from those interactions we can glean some basic information about magnetism:

  1. Magnetic fields, even weak ones such as that of the earth, exert a magnetic force.
  2. Magnetic forces are experienced by some objects but not others.
  3. Magnets are cool.

But what causes magnetism in the first place? The answer is quantum mechanical in nature, and relates to an idea we discussed when we talked about the spin-statistics theorem. Recall that fundamental particles are indistinguishable, meaning that if we have two electrons and two available states, we cannot tell the difference between a system where electron 1 is in state 1 and electron 2 is in state 2, and a system where electron 1 is in state 2 and electron 2 is in state 1. In fact, we can’t even figure out which is electron 1 and which is electron 2; mathematically they are indistinguishable. This, of course, relies on the particles having identical physical properties such as charge and mass, but all electrons do. Another way of saying that particles are identical is to say that you can’t tell the difference if you swap two particles, which physicists call exchange symmetry. Mathematically, it becomes necessary to write equations for multiple particles so that the equation is not modified by exchanging the particles, and this adds a term due to the exchange interaction. We can think of the exchange interaction as another factor affecting the landscape of energy available to the physical system, much like gravity or electrical interactions are factors. Thus, how to minimize the energy of the system depends on the exchange interaction. And it turns out that for some materials, the exchange interaction term causes a system with aligned spins to be lower energy than a system where the spins are randomly oriented.

This is the origin of ferromagnetism, a property of objects that are permanently magnetized. Their spins align to minimize energy, creating a magnetic field that can interact with other magnetically sensitive objects. Some materials are susceptible to magnetism without being permanently magnetic, which usually occurs because small regions of the material magnetize but the regions never combine to create a material-wide magnetization. This is often the case with alloys that include iron or other magnetic materials, and the regions of magnetization are called domains. (Magnetic domains in a rare earth magnet are shown in a microscope image below.) So when you put a magnet on a refrigerator, you are placing a permanent ferromagnet on an alloy and aligning a small region of magnetic domains, creating a force that holds the two together. But the magnet can’t align the spins in a wooden cabinet door, because other terms besides the exchange interaction are more important in that material, so magnets won’t stick to wooden objects.

The polarity of magnets, which are usually described as having a north and a south pole, also stems from the aligned spins. Spins aligned in opposite directions, say one pointing north and one pointing south, are generating oppositely oriented magnetic fields. This is a very high energy configuration, as you know if you have ever tried to hold the south ends of two bar magnets together. But rather than one magnet reordering the other, the magnetic forces generated push the magnets apart.

You might be wondering, is there any way to change the magnetization of a ferromagnet? And actually, there is. While the exchange interaction is one factor controlling the configuration of many particles together, another factor is more mundane: temperature! At high temperatures, the high ordering of all the spins being aligned costs more and more energy to maintain, because there is plenty of thermal energy jostling the spins around. This is why sometimes people talk about ‘freezing in’ magnetism, because if you place some high-temperature materials with unaligned magnetic domains in a magnetic field and then let them cool, they will stay magnetized even after being removed from the magnetic field. And, conversely, if you melt a ferromagnet, it loses its magnetic alignment (but not its fundamental propensity to magnetize, which will return as soon as it cools back down!).

Compass needles are also ferromagnets, but the origin of the earth’s magnetic field is more complex, and ties into the use of magnetism in circuits. Next time!