Conduction in semiconductors – the tennis ball model

By Marcus Wilson 04/02/2015


Not so long ago, a tennis ball appeared in our garden. It's a rather distinctive red one. It doesn't belong to us. It was lying close by to the (low) fence between us and our neighbour, so I just chucked it back. 

Next morning, it was there again. I threw it back.

And, more or less immediately, it was back with us. Evidently, it didn't belong to next door. They were working on the assumption it belonged to us. The next-likely suspect was the house at the back of us, which has some rather energetic children. Over went the ball into their garden. 

Next day it was back with us. Not their ball, either. Suddenly, this ball has become highly mobile. It flits from garden to garden, and doesn't appear to be finding a home anywhere? Where did it come from?

I can't help thinking that this is a good analogy with conduction of electrons in n-type semiconductors. Although silicon underlies so much of modern electronics, it comes as a real surprise to many students to learn that silicon is really quite a lousy electrical conductor. That's unsurprising when you look at its structure – the silicon atoms are locked in a lattice, with each atom bonded by strong covalent bonds to four other atoms. There are no free electrons – all the outermost electrons that would contribute to conduction are tightly bound in chemical bonds. Without free, or losely bound, electrons, there's not going to be much electrical conduction. 

So how come silicon devices are at the heart of modern electronics? The key here (in the case of n-type silicon) is that extra electrons have been put into the lattice. This is done by adding impurity atoms with five, not four, electrons in their outer shell (e.g. phosphorus). These electrons aren't involved with bonding, and become extremely mobile, because none of the silicon atoms finds it favourable to take them on. They flit from atom to atom, finding a natural home nowhere, as does our tennis ball. Unlike a tennis ball, however, electrons are charged particles. Apply an electric field, and they have a purpose, and we suddenly have movement of electrical charge (which is simply what an electrical current is).

There's a second way to make silicon conduct, and that's the reverse. Rather than adding in electrons, we take them away. How does that work? Introduce now an atom into the lattice that only has three outer-shell electrons (e.g. boron). It is likely to grab one from a neighbour, to allow itself to make four covalent bonds. But now its neighbour is devoid of an electron. It will grab one from one of its neighbours. And so on. Now the 'lack of an electron', or 'hole', as its known in semiconductor physics, is what is mobile. Since electrons are positively charged, the lack of an electron (i.e., a hole) is positively charged. Apply an electric field and the hole moves – and we have electrical current again. This is 'p-type' silicon ('p' for positive, since conduction is through positively charged holes; contrast 'n' for negative, where conduction is through movement of negatively charged electrons). 

In our tennis ball analogy, the p-type lattice corresponds to a less desirable neighbourhood – someone on discovering that one of their tennis balls is missing makes up a complete set by sneaking round into the next-door garden to steal one, thus transferring the problem elsewhere.