Semiconductors : Junction Diodes and Transistors

Semiconductors : Junction Diodes and Transistors

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Semiconductors are at the heart of modern human civilization. Every word I type using this laptop is an implicit thank you to the incredible versatility and utility of semiconductors, as well as to the wonderful ingenuity of the scientists and engineers who have harnessed the potential of these magical materials to their fullest.

The following is part I of a brief overview of the physics of semiconductors. This is meant to be a starter pack, so to say. For deeper understanding, I suggest that you read a good textbook.

In this article, The Nerd Druid will talk about intrinsic and extrinsic semiconductors, p-n junctions, p-n junction diodes, and bipolar junction transistors and their applications.

Insulators and conductors

Let’s begin with sodium. Sodium is a metal. This means that it is a good conductor of heat and electricity. However, since sodium is very reactive, it isn’t very smart to use it to conduct electricity. Household wires are usually made of copper, which does a fine job of conducting current.

Image of sodium metal
Sodium metal

In comparison, nonmetallic elements and most compounds are poor conductors. Diamond, an allotrope of the nonmetal carbon, is a very good insulator. Ironically, graphite, another carbon allotrope, is a very good conductor. Graphene–atomic monolayers of graphite–is even better at this conduction business. 1 Air is good insulator, and it takes a huge voltage to pass electrons through air. Happens regularly around thunderstorms. Water is a decent conductor, since it has a lot of free protons (H+ cations) that carry the current.

Image of forked lightning. Extremely high potential differences between the Earth and thunderstorm clouds breaks down the insulation of air, forming forked lightning.
Forked lightning. Extremely high potential differences between the Earth and thunderstorm clouds breaks down the insulation of air, forming forked lightning.

Most natural materials found on Earth are either insulators or conductors.

Semiconductors

Intrinsic semiconductors

Some elements and compounds, however, do not identify themselves as either. Elements such as silicon and germanium, and binary compounds such as gallium arsenide and silicon carbide are semiconductors. When heated, semiconductors begin to conduct electricity. This behaviour is quite the opposite of conductors, where resistance increases with increasing temperature. These are intrinsic semiconductors.

Atomic orbitals

Before we proceed, a quick review of atomic orbitals might be helpful. A more detailed overview can be found here.

Electrons are arranged within atoms in orbitals. The energy of the electrons residing in them groups orbitals together in shells. Shells further away from the nucleus have higher energy than those closer to the nucleus. The most commonly encountered orbitals are s, p, and d. Each orbital can have at max 2 electrons.

Consider silicon. A neutral silicon atom has 14 electrons. These are arranged thus : 1s22s22p63s23p23d0. The first shell of silicon has 2 electrons (lowest energy) residing in the filled s-type orbital (1s). The second shell has 8 electrons (higher energy), 2 in the 2s and six in the 2p. The third shell has the remaining 4 electrons (highest energy); 2 in 3s and 2 is 3p. The 3d orbitals are completely vacant.

Image of silicon electronic configuration
Silicon electronic configuration

Extrinsic semiconductors

The behaviour of intrinsic semiconductors can be altered by adding small amounts of another element. For instance, silicon semiconductors can be thus doped using boron or phosphorus. Boron is trivalent, meaning it has three electrons in its outer shell (1s22s22p63s23p1); phosphorus is pentavalent, meaning it has five electrons in its outer shell (1s22s22p63s23p3). Since silicon has only four, phosphorus doped silicon has extra electrons which are free to move about. Similarly, boron doped silicon has fewer electrons, the absent electrons leaving behind holes, which are also free to hop about. The former is a n-type semiconductor, where electrons are the charge carriers 2. The latter is a p-type semiconductor, where the holes are the charge carriers 3 These extrinsic semiconductors are far more conductive than their undoped counterparts.

p-n junction

A single wafer of semiconductor can also be doped in two different ways; the boundary between the p-type and n-type regions form a p-n junction. When electrodes are attached to the two sides, this becomes the basic building block of all semiconducting electronic devices.

Depletion region

When a p-n junction is fabricated, there are more holes on the p-side and more electrons on the n-side. Immediately, holes and electrons begin migrating across the junction 4. This sets up a diffusion current pointing from the p-side to the n-side.

As holes diffuse over to the n-side, they leave behind negative bound ions. Similarly, diffusing electrons leave behind positive bound ions. Once on the n-side, the holes recombine with the electrons there and disappear. The electrons emulate this behaviour on the p-side. Soon enough, a region forms around the junction which has very few charge carriers. This is the depletion region.

Image showing formation of the depletion region in a p-n junction semiconductor
Formation of the depletion region in a p-n junction semiconductor

The cations and anions left behind set up an electric field pointing from the n-side to the p-side, thus opposing the diffusion current. Once a sufficient number of electrons and holes have diffused, this opposing field is strong enough to stop the diffusion current altogether, and set up its own drift current pointing from the n-side to the p-side.

p-n junction diode

Connect the p-n semiconductor to electrodes. This makes it a p-n junction diode. There are two ways this can be done.

Forward bias

In the first scenario, connect the anode (+ve electrode) to the p-side, and the cathode (-ve electrode) to the n-side. This is the forward bias condition.

The anode will inject holes into the p-side, while the cathode will inject electrons into the n-side. This will push and squeeze the depletion region so that it is narrow enough for electrons and holes to jump across. Once this happens, a current flows across the p-n semiconductor.

Illustration of forward bias in a diode. As the forward bias voltage increases, the deplection region gets narrower and finally collapses
As the forward bias voltage increases, the depletion region gets narrower and finally collapses. This allows current to flow through the diode.

Energetically speaking, the depletion region creates an energy barrier. In forward bias, if the voltage is not high enough, electrons and holes will not have sufficient energy to surmount the depletion barrier. Which is why the current-voltage graph of a p-n junction diode shows a knee in forward bias. The voltage above which the diode turns on is called the cut-in or the forward voltage (VF).

Reverse bias

In the second scenario, reverse the polarity 5. Connect the anode to the n-side and the cathode to the p-side. They will inject holes and electrons as before, though this time this will lead to greater recombinations and will serve to further widen the depletion region.

Illustration of reverse bias in a diode. Reverse bias widens the depletion region, making it almost impossible for current to flow through the diode.
Reverse bias widens the depletion region, making it almost impossible for current to flow through the diode.

Energetically, the reverse voltage will raise the height of the depletion region potential barrier. In this reverse bias state, the diode does not let current pass. Well, not unless the voltage is high enough so that the current flows in the opposite direction as before. That is breakdown. But we don’t want that to happen.

Transistors

Diodes are electronic valves; they allow current to pass in one direction. As such, they are very useful in circuits. However, they can be made much more useful if two p-n junction semiconductors are attached end-to-end in series, creating three separate zones. Attach electrodes to these three zones and you have a bipolar junction transistor (BJT).

There are two ways to do this; you either get a p-n-p transistor or an n-p-n transistor. The middle zone is called the base, and the ones on the two ends are called the collector and the emitter. Now, connect electrodes to each of these regions and apply potentials.

Image of an n-p-n transistor, with n-type collector and emitter, and p-type base.
An n-p-n transistor, with n-type collector and emitter, and p-type base.

Of course, BJTs are not the only type of transistor around. Field effect transistors work in a slightly different fashion. I’ll not be discussing FETs here.

Modes of operation : Switch and amplifier

The transistor can operate in four modes. One can control this by tuning the base voltage VB, the emitter voltage VE and the collector voltage VC. In what follows, I shall use an n-p-n transistor to illustrate the mechanism. You can convert this into a p-n-p by merely flipping the “>” signs and reversing the current.

Saturation mode : VB > VC , VB > VE

Recall that the transistor is n-p-n, so that the base is p and the emitter and collector are n. Thus, VBE > 0 and VBC > 0 imply that both the base-emitter (BE) and base-collector (BC) junctions are in forward bias mode. This setup behaves like a closed circuit; current flows freely between the collector and the emitter. For n-p-n, the collector current IC points from the collector to the emitter. Electrons, the majority carriers in n-p-n, are emitted by the emitter and collected by the collector 6.

The transistor is now ON.

Cut-off mode : VB < VC , VB < VE

The signs are reversed; VBE < 0 and VBC < 0. Both the BE and BC junctions are reverse biased. No current flows in the transistor, and it behaves like an open circuit.

The transistor is now OFF.

By reversing the voltages, one can thus use the transistor as a switch.

Forward active mode : VC > VB > VE

Here, VBE > 0 but VBC < 0; the BE junction is forward biased, while the BC junction is reverse biased. In this mode, the transistor acts as an amplifier–a small input base current IB gives rise to a very large output collector current IC.

IC = β IE

where β is large, usually 100.

Image of a transistor in forward active mode, acting as an amplifier. The n-type emitter emits electrons, a majority of which reach the collector due to the large potential difference between C and E.
A transistor in forward active mode, acting as an amplifier. The n-type emitter emits electrons, a majority of which reach the collector due to the large potential difference between C and E.
Reverse active mode : VC < VB < VE

This is basically the same as forward active, except β is much smaller. This mode is seldom used in practice.

Schematic of the four modes of a transistor; saturation (ON), cutoff (OFF), forward active (amplifier), and reverse active.
The four modes of a transistor; saturation (ON), cutoff (OFF), forward active (amplifier), and reverse active.

Applications

Transistors are the basic building blocks of computers and modern electronics, and have wide-ranging applications.

As a switch

Keep the transistor in switch mode and assign labels to the states of the switch; 0 for OFF, 1 for ON. The transistor now functions as a bit, the fundamental unit of classical computing.

You can string a few transistor switches together and form logic gates. These follow Boolean algebra, and allow you to perform OR, AND and NOT operations. More complex combinations of transistors give NOR, NAND, and XOR gates.

Bits and logic gates can be used together to implement a series of instructions. This implementation of an algorithm is a computer program.

Finally, by connecting transistors together in certain ways, it is possible to make it stay either in the saturation or the cut-off states until a new input has been applied. Such flip-flops can either be in 0 or 1 states, and thus can store bits. These are the building blocks of computer memory.

As an amplifier

Hearing aids are wonderful applications of transistor amplifiers. The microphone converts sounds into electrical current. It then feeds this into the base of a transistor which is operating in the active mode. The collector current, greatly amplified, feeds into a loudspeaker. Prof Calculus (in moon rocket mode) would greatly approve.

A panel from the tintin book Destination Moon, showing Professor Calculus and Captain Haddock
Professor Calculus and Captain Haddock, from Destination Moon.

References and Further Reading

  1. All About Circuits
  2. ExplainThatStuff
  3. SparkFun
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Footnotes

  1. This graphene is actually a most interesting material, boasting high flexibility, high thermal and electrical conductivity, and exceptional strength.
  2. Actually the majority carriers. n-types do have holes that carry charge too, just that their concentration is quite a bit lower
  3. For instance, the direction of current in a circuit is conventionally taken to be from the positive terminal to the negative terminal. In reality, of course, electrons move in the opposite direction.
  4. Well, only the electrons actually move. They jump across the junction from n to p to fill up holes. But for all practical purposes, it is ok to imagine that electrons move from n to p and displace (not fill up) holes, while holes move from p to n to displace electrons. In fact, if one does enough quantum condensed matter physics, one realises that holes are just as real as electrons.
  5. Of the electron flow. Not neutrons. That would be Doctor Who.
  6. The reverse happens in p-n-p. Holes are the majority carriers there. The emitter emits holes, the collector collects them.

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