# Doping Semiconductors

I have two questions on semiconductors that I hope someone will be able to help me with.

1. I have been told that a semiconductor is classed as N-Type when it's donor density is greater than its acceptor density and that it is classed as P-Type when its acceptor density is greater than it's donor density. So far so good, but I have also been taught that trivalent atoms are acceptors and pentavalent atoms are donors.

This seems to conflict with the first part because if I introduce a trivalent atom into silicon then either the acceptor density is lower or silicon is the acceptor. Could someone clarify this for me please?

2. So far I have only covered introducing impurities with 3 or 5 outer electrons into silicon with 4 outer electrons. If the impurity of the atom has 2 electrons in the outer shell rather than three in the case of p-type or 6 rather than 5 in the case of n-type does this emphasize the effect? Or does something else entirely happen?

Non-organic semiconductors are used in crystalline form. The definition of a crystal is not that it looks like a gem, though that is a common result, it's that the constituent atoms are arranged in a regular pattern known as a lattice. A crystal of silicon forms a diamond-cubic lattice structure like this:

If you look carefully (and understand that this is just one cell; it replicates on all sides) you'll notice that each atom has 4 bonds. Each bond involves one electron from each atom. In normal silicon, some electrons do dissociate from their parent atoms and leave holes behind (this is $n_i$, the intrisic carrier concentration). However, the normal pattern is for a bond to more-or-less permanently link an electron and a hole.

The reason that trivalent and pentavalent atoms are acceptors and donors is that this bond structure is maintained when impurities replace atoms in this lattice. If you add a trivalent atom to this structure, you still require four bonds but you only have three valence electrons to work with. This is an acceptor. Each trivalent acceptor atom (in a unit volume) increases $N_A$ by one. Silicon cannot be a donor because it only has four valence electrons; if it donates an electron to fill this bond then that leaves a hole on the silicon atom. If you add a pentavalent atom to the structure, four of its electrons will form bonds but the fifth cannot form a bond. It becomes a donor, and each pentavalent donor atom increases $N_D$ by one.

If you added an impurity with two or six valence electrons, the same thing would happen, but two electrons or two holes would be added per atom. However, this is more likely to cause a break in the crystal structure and isn't really very common in industry as far as I know.

• +1 Very good. I haven't heard either of 2- and 6-electron per atom impurities, and I would also say that one of the reasons is mechanical stability. – Telaclavo Apr 30 '12 at 17:01
• @KevinVermeer, thanks that's a very clear explanation. I'm still unsure of the which is the donor and which is the acceptor, is the silicon always the acceptor or does this depend on the impurity. – DNN Apr 30 '12 at 18:15
• @DNN - Donors and acceptors aren't one-and-one; you can add trivalent atoms to a crystal and it will have as many acceptors as trivalent atoms. There are no donors in the resulting crystal (at a first approximation). – Kevin Vermeer Apr 30 '12 at 18:24
• @DNN The donor or acceptor is always the impurity. Never the silicon. – Telaclavo Apr 30 '12 at 23:17

So far so good, but I have also been taught that trivalent atoms are acceptors and pentavalent atoms are donors.

I think the key thing here is that each nucleus has a set of available "states" for electrons available around it, whether the atom provides electrons to fill those states or not.

So a trivalent atom (like bismuth, IIRC) provides just as many possible states for electrons to take, but it doesn't provide as many electrons to fill them. That's what makes the column III atom an acceptor site.

Similarly, a pentavalent atom provides roughly the same set of states, but also provides extra electrons compared to a silicon atom. Since the energy levels of these extra electrons are relatively close to the conduction-band energy levels of the silicon crystal, its relatively easy for these "extra" electrons to get freed up from their nucleus and become conducting electrons in the crystal. And so we call the column V impurity a "donor" site.