The basic semiconductor

In the media, there are two kinds of physics which are the most hyped: the physics of the very big, and the physics of the very small.  Namely, cosmology and particle physics.  These fields are really exciting, but what about the physics of everything in the middle?  In the middle, there is Condensed matter physics.  Condensed matter is one of the biggest fields of physics, and also one of the most practical.  Practically every piece of electronics uses it.

In particular, nearly all modern electronics rely on the transistor, considered to be one of the most important inventions of the 20th century.  But I will leave my explanation of the transistor for another day.  For now, I will explain the basic physics of semiconductors, which form an essential component of transistors.

A semiconductor is basically a material whose electrical conductivity is somewhere in the middle between conductors and insulator.  An example of a conductor would be a copper wire, while an example insulator is the rubbery stuff around that wire.  We use conductors for wires because we want want electricity to move as freely as possible through the wires.  We use insulators to cover wires because we don't want the electricity to jump between crossed wires.  An example of a semiconductor is silicon.  Silicon is used in electronic devices because it allows us more control over whether electricity can pass through or not.

Insulators, conductors, and semiconductors are all important for electronics

What makes these materials behave so differently?  The difference comes from what's called the "electronic band structure".

Many of you are familiar with the electron energy levels of atoms.  Electrons are allowed to be at certain energy levels but not others.  There's an energy level 1, and energy level 2, but no electrons can exist between.  Furthermore, each energy level can only contain a certain number of electrons, because by the Pauli Exclusion Principle, no two electrons may be in the exact same state.  After the energy level is filled up with electrons, any additional electrons must occupy higher energy levels.

(Image credit)

Of course, the atom doesn't really look like this, but the energy levels are indeed discrete

In order to make a wire or a microchip, we can't just use one atom.  We need thousands of billions of billions of atoms.  When there is such a large collection of atoms, most of the quantum weirdness disappears.  There are still energy levels 1, 2, 3, and so on, but they're so close together that we might as well describe the energy as a continuous spectrum.

But the energy isn't entirely continuous.  Sometimes it's continuous, and sometimes there are gaps.

The electronic band structure.  The further an electron is to the right, the more energy it has.  Figure not to scale.

This is what's called the electronic band structure of the material.  There are energy bands where the energy is continuous, but there are also gaps between the energy bands.  No electrons can exist in these band gaps.  Also note that the energy bands can only contain a certain number of electrons.  Once an energy band is filled with electrons, any additional electrons must occupy a higher energy band.

I should mention that there's a reason why there are band gaps, but it's one that requires a much deeper understanding of quantum mechanics than will ever appear on my blog.  Suffice it to say that it is caused by the repeating crystal structure of the material.

The band structure has everything to do with the difference between insulators, conductors, and semiconductors.  First I will explain insulators.

An insulator has exactly enough electrons to fill up to one of the band gaps

In the band structure of an insulator, there are exactly enough electrons that all the energy bands are either completely filled or completely empty.  Let's say we tried to make a wire out of this insulating material.  Any given energy band consists of a specific set of states.  Exactly half of those states are moving forward through the wire, while the other half are moving backwards through the wire.  So if an energy band is completely filled, then half the electrons must be moving forwards while the other half are moving backwards.  The total current through the wire is precisely zero.

If we wanted to push current through the wire, we would have to give some electrons enough energy that they jump up to the next band.  But this is a very large energy barrier!  And that's why it's hard to send current through an insulator.

In a conductor, there is an energy band which partially filled and partially empty.  Or perhaps there are two energy bands which overlap.  In any case, there is no large energy barrier stopping us from sending current through a conductor.  The only thing slowing down the electrons are collisions with atoms and stuff of that sort.

Semiconductors have something rather different going on.  In a semiconductor, the electrons fill up to one of the band gaps, but the band gap is very small.  In particular, the band gap is small enough that thermal fluctuations will overcome the gap.

In a semiconductor, the temperature smears electrons across a band gap

Temperature has the effect of smearing the electron energies across a certain range.  So at high temperatures, electrons don't always fall to the lowest energy available.  So even if there are exactly enough electrons to fill up an energy band, some of those electrons jump up to the next band anyways.  This occurs only if the temperature is high enough and the band gap is small enough.

There are some interesting consequences to the semiconductor's band structure.  One consequence is that the conductivity increases with temperature.  As the temperature increases, the electrons smear over the gap even more, allowing more current.  Contrast to conductors, which decrease in conductivity as the temperature increases.

Another consequence is conduction by "holes" (much like the holes discussed earlier).  Because there is an energy band which is almost, but not quite filled, it's best to describe it with holes.  These holes, unlike electrons, have positive charge, and may have a different mass too.  The current through a semiconductor will be carried by a mix of electrons and holes.

A final consequence that I will briefly discuss is sensitivity to "doping".  If you add certain impurities to a semiconductor (such as arsenic impurities in silicon), it may very slightly increase or decrease the number of electrons.  If the impurity increases the number of electrons, it's called "n-doping".  If the impurity decreases the number of electrons (or increases the number of holes), it's called "p-doping".  This may not seem that exciting, but I mention it because it is tremendously important.  P-type and n-type semiconductors are essential to the transistor, among other things.  But that's outside the scope of this blog post, so I'll just leave it at that.