Tag Archives: electronics

Active and Passive Circuit Components

Now that we have several different circuit components under our belts, it’s helpful to try to classify the behavior that we’ve seen so far. Resistors, capacitors, and inductors respond in a reliable way to any applied voltage that induces an electric field. Resistors dissipate heat, capacitors store charge, and inductors store magnetic flux.  These responses always occur and cannot be manipulated without manipulating the very structure of the material which causes the response. They don’t add energy or electrons to a circuit, but merely redirect the electrons provided by an external source. Thus these are called “passive circuit components”.

Transistors also have a predictable response to a given voltage, but that response can be changed by tuning the gate voltage in order to open or close the conducting channel. Effectively, the transistor can be in one of two states:

  1. Functioning like a wire with a small resistance, passing most current through while dissipating a small amount of heat.
  2. Functioning like an insulator with a high resistance, blocking most current and dissipating more heat.

The controlling gate which allows us to pick between these two states can actually add energy to the system, increasing the current output, thus the transistor is called an “active circuit component”. Circuits that do calculations or perform operations are usually a combination of active and passive circuit components, where the active components add energy and act as controls, whereas the passive components process the current in a predetermined way. There are other system analogues to this, such as hydrodynamic machines. Instead of controlling the flow of electrons, we can control the flow of water to provide energy, remove waste products, and even perform calculations. An active component would be a place where water was added or accelerated, whereas a passive component might be a wheel turned by the water or a gate that redirects the water. But in electronics, with electrons as the medium, active components add energy and passive components modify existing signals.

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Electronics: The Bigger Picture

In our exploration of electronics, we started at the atomic level with the fundamental properties of subatomic particles. We looked at emergent properties of collections of atoms, like the origins of chemical bonding and electronic behavior of materials. Recently we have started to move up in scale, seeing that individual circuit components affect the flow and storage of electrons in different ways. At this point I think it is worthwhile to take a step back and look at the larger picture. While individual electrons are governed by local interactions that minimize energy, we can figure out global rules for a circuit component that tell us how collections of electrons are affected by a resistor or some other building block, creating the macroscopic quantity we call current. From there we can create collections of circuit components that perform various operations on the current passing through them. These operations can again be combined, and where we may have started with a simple switch, we can end up with a computer or a display or a control circuit.

One way to picture it is like a complex canal system for water: we have a resource whose movement we want to manipulate, to extract physical work and perhaps perform calculations. At a small scale, we can inject dye into a bit of water and watch its progress through the system as it responds to local forces. But we can look at water currents at a larger scale by adding up the behavior of many small amounts of water. In fact, scale is a type of context, a lens through which a system can look quite different! Electrical engineers who design complex circuits for a living tend to work at a much higher level of abstraction than do scientists working on experimental electronic devices. The electrical engineers have to be able to imagine and simulate the function of impressive numbers of transistors, resistors, and other components, as shown below. Whereas a device physicist focuses on the detailed physics in a single circuit component, to learn what its best use might be. They are each working with the same system, but in different and complementary ways.

When I first started writing here, I talked about science as a lens through which we can view the world: a set of perspectives that let us see the things around us in a different way than we are used to. But there are lots of different worldviews and perspectives within science, depending on scale as well as other contexts. A discussion of electrical current, for example, could be handled quite differently depending on whether electrons are moving through a polar solvent like water, or synapses in the brain, or a metal wire connecting a capacitor to an inductor. Scientists who have trained in different fields like physics, chemistry, or biology can imagine very different contexts for discussions of the same phenomenon, so that even when the fundamental science is the same, the narrative and implications may change between contexts.

But in the end, whether you are a scientist or just interested in science, it helps to know not only that an electron is a tiny charged particle, but also how it behaves in electronic circuits, in chemical bonds between atoms, and in biological systems. And to know that it’s possible to build computers out of gears, billiard balls, or even crabs! But the size and properties of electronic computers have led them to dominate, at least for now.

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.

How Resistors and Capacitors Work

Now that we have started out with atoms and gone all the way to electronic band theory, which uses available energy states to explain why some materials are good at conducting electrons and others are not, we can start to discuss actual electronic devices! After all, fancy materials aren’t much good unless you have some way to use them.

Broadly speaking, we want devices that do something worthwhile, like light a room, make calculations, or power a motor. Most electrical devices work by manipulating a flow of electrons to extract some useful behavior. If we apply an electrical potential (which is also called voltage) to a device, then it will be energetically favorable for electrons to move through the device; this charge flow is called electrical current. The potential difference is often provided by something like a battery, where the differing chemical potential within the battery provides the voltage, and the device itself is connected to both terminals of the battery. Connecting a device to a battery forms a physical loop that electrons travel through, hence the name circuit. The battery itself is a circuit element, and so is the device that does something useful. There are quite a few interesting circuit elements but let’s start simple.

While the high electrical conduction of metals is extremely useful, sometimes it can be useful to have something that does not conduct electrons quite so well. Why? Because poor conductors offer the opportunity to convert electrical energy into other forms of energy, such as light or heat. This is the idea behind resistors, circuit elements that resist the flow of electrons without quite stopping it. Some resistor materials convert excess energy into heat, which can be the basis of electric heaters or electric stovetops. And the filament in an incandescent light bulb is acting as a resistor, one which heats up so much that it emits light (the reason for this is a whole other sack of beans). Resistors can be made by combining a conductive material with a non-conductive material, and are manufactured across an incredibly broad range of resistances. And independent of their heating or light-emitting properties, they are often used because the electrical current through them depends linearly on voltage.

And what happens if we push resistance to its limit, such that no electrons can actually pass through an insulating device? Applying a voltage drop would cause electrons to build up on one side of the device, attempting to pass through, until the repulsive force from the assembled electrons was enough to deter additional electrons from building up. The charge imbalance creates an electric field across the device, and this is what we call a capacitor. You can build a capacitor by bringing two parallel conducting plates close to each other and applying voltage. Since current can’t cross the gap between the plates, charge is stored on the capacitor plates, which can be discharged upon connection to a circuit. This is somewhat similar to a battery, although most batteries have stored chemical energy rather than electrical, and the speed of the chemical reaction which discharges a battery is usually much slower than the speed of electrons rushing to equilibrium when a capacitor is discharged. An older example of a capacitor is shown below; modern capacitors use thin films to create an insulating gap, and are considerably smaller than the capacitor pictured.

Resistors and capacitors are two of the most basic pieces that you can put into a circuit, and two of the most widely used. But some of the more complicated elements are interesting as well, and we’ll get into those in the next few posts!

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.