Semiconductors

Semiconductors started a tech revolution. Once a semiconductor transistor was invented – all hell breaks loose. Suddenly we were capable to make unimaginably complex electrical machines ‘engraved’ into a small chip of silicon.

Silicon

The reason why the pure silicon crystal is a bad conductor is a bit ‘scientific’. Simplified, electrons in the silicon crystal cannot have just any energy. Instead they are allowed only to have energies within some energy bands. Moreover, in silicon crystal it happens that all that energy bands are either almost completely full of electrons or almost completely free of electrons.

In the above picture we see the distribution of electron energies in a silicon crystal. All bands of allowed energies above certain energy level are (almost) completely empty, while all bands below it are (almost) completely full. The fact is that if a band of energies is completely full, electrons inside it cannot carry electricity (simplified: electrons cannot ‘move’). The reason for this, I was told, includes the Pauli Exclusion Principle. The Pauli Exclusion Principle is a monster from quantum mechanics and we should immediately stop asking further ‘why’ questions if we want to at least retain the feeling that we know anything!

The reason why the silicon crystal is not a real insulator is because the gap between the last full band and the first empty band is not that large. Because of this, some electrons will ‘jump’ the distance and the crystal will gain some conductivity. Note that electrons in both bands (almost empty one and almost full one) will now be able to conduct electricity. Of course, because at room temperature only small number of electrons will jump over the gap, the conductivity of the pure silicon crystal will be very small. You might heat the silicon crystal to make it somewhat more conductive.

Doping

There are other, more effective, ways to make silicon more conductive – use doping. That is, you can insert several non-silicon atoms inside the silicon crystal. Some of them (like phosphorus) will add electrons to the empty band, while others (like boron) will extract electrons from the full band. In either case the conductivity will be greatly increased even if a very small amount of doping atoms is added – say 0.01%.

In the picture above we see the energy-distribution of electrons in a n-doped and a p-doped silicon crystal. The n-doped silicon is a good conductor because it contains fairly good amount of electrons in its higher-energy band. The p-doped silicon is also a fairly good conductor because it contains lots of ‘holes’ in its lower-energy band.

Note however that even n-doped silicon has some small amount of holes in the lower-energy band, and that p-doped silicon has some small amount of electrons in the higher-energy band (This is for the exactly same reason the pure silicon would have it – because of temperature). Therefore, for the n-doped silicon we can call electrons ‘majority carriers’ of electric current, while we can call holes ‘minority carriers’ of electric current (because in the n-doped silicon, holes only carry a small percentage of current). Likewise, for the p-doped silicon we can call holes the ‘majority carriers’, wile electrons the ‘minority’ carriers.

Hold a moment! What holes are we talking about? The concept of a hole (that is, a non-electron) is very useful to simplify understanding of semiconductors. We can think of a hole as a positively charged ‘electron’. Look at the schematics below:

The picture shows pure, n-doped and p-doped silicon crystals. The pure silicon only has very few electrons (red circle) and holes (green circle) to carry electricity. The n-doped silicon has much more electrons than holes available to carry electricity. The p-doped silicon has much more holes than electrons available to carry electricity. Note that only those electrons are shown that are available (moveable) to carry the electricity.

One thing I need to say about the doped silicon. As we said, phosphorous atoms in a n-doped silicon will ‘donate’ one electron to the crystal and this electron will then become moveable and thus able to carry electricity. As a result, the phosphorous atom will remain positively charged as it is now missing one electron. This of course doesn’t mean that the whole crystal will be charged because those electrons are still present inside the crystal. The similar is true for boron atoms that become negatively charged by borrowing one electron from crystal (that is, ‘by donating one hole’).

Finally it must be noted that the situation inside the doped silicon crystal is dynamic - a phosphorous atom will often recapture an electron and then release it soon enough. A boron atom will often release an electron just to capture another one soon after that. On average, however, the situation will be as described above.

The p-n junction

But first we need to note one very important fact. As we said, in a silicon crystal there are both electrons and holes capable to move around and thus capable to carry electricity. There are always both, electrons and holes, but there are much more electrons in a n-doped silicon and much more holes in a p-doped silicon. The important thing is: not only are those electrons/holes capable to move around, but they are randomly moving around all the time (driven by heat). Very much the same way as molecules in a gas move around.

So, what will happen at the p-n junction? Obviously, electrons from the n-doped region will move (diffuse) toward p-doped region, while holes from p-doped region will diffuse toward n-doped region. This is the same thing that would happen if we open a door between two gas containers – molecules in gases would start mixing because of their random movement.

One might think that eventually both, holes and electrons, will mix evenly inside the crystal, but this is not what will happen. First, when electrons and holes meet they mostly recombine and only very few of them remain. That is, electrons from n-doped region fill up holes in the p-doped region creating a region with neither many holes nor many electrons (the depleted region). Second, some electric field will soon be established in the depleted region that will prevent any further mixing of electrons and holes.

The complex picture above (silicon atoms are omitted for clarity) shows what happens at the p-n junction. Some electrons (red circles) diffused into the p-doped region, while some holes (green circles) diffused into the n-doped region. There both of them recombined with native majority carriers (crossed out red-green circle pairs) creating the depleted region where not many holes and electrons exist any more. However, this depletion exposes positive phosphorous atoms (ions) and negative boron atoms – an electric field (gray arrows) is therefore created across the depleted region.

This electric field prevents electrons from n-doped side to reach the p-doped side because it asserts the opposing force on them. The same is true for holes from the p-doped side trying to diffuse into the n-doped side.

The equilibrium is reached – any random diffusion of electrons and holes (due to thermal moving) is exactly canceled by drifting forces caused by the electric field. We say the diffusion current and the drift current remain in equilibrium. This is the crucial moment to understand.

Notes:

• The depleted region does not really have sharp boundaries.
• Even in the middle of the depleted region there exist always some small amount of carriers (holes and electrons)
• The most important thing about the depleted region is the existence of the electric field

The diode

Now the charming part… we are going to make two experiments…

EXPERIMENT 1: let us add several electrons to the n-doped side and simultaneously add several holes to (that is, remove several electrons from) the p-doped side. What happens? Adding the negative charge to the n-doped side and adding positive charge to the n-doped side will decrease the strength of the internal electric field. Therefore the diffusion current will prevail over the drift current component and several electrons will be able to move to the other side while several holes will do the same in the opposite direction – both will soon recombine and the resulting state will be the same as before we added any charge.

Experiment 1B: what if we are constantly keep adding electrons to the n-doped side and simultaneously removing electrons (adding holes) to the p-doped side? We can easily do this by connecting a battery to the crystal – connect the battery plus pole to the p-doped side and connect the battery minus pole to the n-doped side. Obviously, the internal electric field will constantly remain decreased. This will enable electrons and holes to move through it by diffusion. Then electrons and holes will recombine. In other word, the current will flow! Note that the current moves through the depleted region (the barrier) by diffusion of carriers.

EXPERIMENT 2: what if we remove some electrons from the n-doped side and simultaneously remove some holes from the p-doped side? The electric field will increase because now we are helping it. As a result, no carrier will be able to cross the depletion region. This is very different than in the first experiment because in this case the difference in charge between n-doped and p-doped side will be sustained forever (well, in reality it will not really last forever, but for some quite long time).

The current cannot flow if we connect the plus pole of battery to the n-doped side and minus pole of battery to the p-doped side. We created a diode! Charming! [Note that some current will still flow even in this case - as we said minority carriers are also always present at both sides and they don’t see the electric field, that is, minority carriers do not see the barrier and are able to move through it even in ‘wrong’ direction. However as there is very small number of minority carriers, only a very small current will flow. The funny thing is that this current doesn’t depend much on the voltage applied.]

The bipolar-junction transistor (BJT)

A bipolar-junction npn transistor has two p-n junctions and thus two depleted regions. The structure on the picture above is symmetric, but for clarity I decided to name the left n-doped region ‘collector’, the central p-doped region ‘base’ and the right n-doped region ‘emitter’ (to improve efficiency, real transistors are in fact not that symmetric and you should not exchange emitter and collector).

EXPERIMENT 3: We connect the collector at some positive voltage, but we keep the base and the emitter at zero volt. What happens? Nothing much – the internal electric field of the collector-base boundary grows stronger preventing any diffusion current from collector toward base. The current does not follow (as in the experiment 2). See the picture below.

EXPERIMENT 4: We now connect the collector to positive voltage; we also connect the base to some small positive voltage; we connect emitter to zero volt. What happens now? Many, many things… First of all, the base is now positive compared to the emitter. As a result, the internal electric field at the base-emitter boundary decreases and therefore some diffuse electron current will start flowing from emitter to base. In other words, because the internal electric field is now weaker, many electrons from the emitter will wander (by diffusion) into the base region where some of them will recombine with holes in base… But this is nothing new; we saw the same effect in the Experiment 1B.

What is new is that not all of electrons that diffuse (wander) into the base region from the emitter side gets recombined with the holes. This is because the recombination takes some time, but the base is a very narrow place. Many of electrons that come from emitter will wander through the whole width of the base without recombining. Then, once they find themselves very near the collector-base depleted region they will start ‘feeling’ the internal electric field of the collector-base junction. This electric field will pull them over to the collector side!

In fact, most of electrons will be pulled to the collector side. Only small portion (maybe 1%) will recombine in the base. Those electrons that do recombine in the base make the base current. Other electrons that are pulled through the collector-base barrier make the collector current. The collector current is therefore stronger than the base current, but is proportional to it.

The picture below shows how electrons flow through an n-p-n transistor. Note that arrows display the direction of electrons, not the direction of the electric current (the electric current has the opposite direction by convention – you know already about this issue, don’t you?).

Notes:

• Electrons from emitter move to the base due to the diffusion
• Electrons from base move further to the collector due to the electric field between base and collector. The strength of this field doesn’t influence the intensity o the collector current much.
• Instead, the collector current intensity only depends on the number of electrons that cross (by diffusion) the emitter-base boundary. This number in turn depends on the strength (weakness) of the internal electric field at the emitter-base boundary.
• Therefore, by applying some base-emitter voltage we can adjust the strength of the internal emitter-base electric field, and thus we can control the collector current
• The base current and the collector current are proportional. The factor depends on the percentage of electrons that recombine in the base. To make high-gain transistors, the base width must be small so that most electrons diffuse through base without recombining.
• The number of electrons that diffuse through emitter-base boundary is rather sensitive to the base-emitter voltage and other parameters. As a result, it would be hard to regulate the collector current by the base-emitter voltage. Instead, much better approach is to regulate the base current (the base-emitter voltage will ‘self-adjust’ if regulate the base current). Therefore we say: a bipolar-junction transistor is a current-controlled current-regulating element.

All written above is very simplified but is useful to understand how it is possible to use semiconductors to amplify signals.

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See also the gasoline vs diesel engine comparation article.