Extrinsic semiconductors
So far, we have discussed pure semiconductors, such as pure silicon. In this case, the charge carriers are a result of electrons in the valence band being excited to the conduction band, creating an electron-hole pair. These are known as intrinsic semiconductors. What makes semiconductors really useful for many applications is that their electronic properties can be changed by introducing impurity atoms which result in either free electrons or holes. These are known as extrinsic semiconductors because the charge carriers are not intrinsic to the host lattice. The process of adding impurity atoms to semiconductors is known as doping.
Imagine a silicon lattice that has been doped with a small amount of aluminum. Aluminum has one fewer valence electrons than silicon (it is directly to silicon's left on the periodic table. So, as depicted on the left of Figure 13.11.1, one of the bonds with the surrounding silicon atoms will be missing an electron. This is a hole which can conduct electricity and it is not intrinsic to the silicon material. Hence, it is an extrinsic charge carrier. Semiconductors that have been doped to have holes are known as p-type ("p" for positive, since holes have a positive charge).
We can also dope silicon with an element like phosphorous which has one more valence electron than silicon. The extra electron can't participate in the four bonds with surrounding silicon atoms, because those bonds are already full with two electrons each. So, the extra electron delocalizes around the phosphorous atom as depicted on the right of Figure 13.11.1. Semiconductors that have been doped to have extra free electrons are known as n-type ("n" for negative, since electrons have a negative charge).
Note that the lattice is still electrically neutral. For each aluminum atom in a silicon crystal, there is one positive hole introduced, but the aluminum atom has one fewer protons compared to silicon, so there is no net positive charge added to the lattice as whole. The opposite is true for phosphorus added to silicon. There is a free electron introduce to the lattice, but the phosphorous nucleus has an extra proton compared to silicon which balances out the electron. P-type and n-type refer to the charge carriers in an extrinsic semiconductor, not to the charge of the material as whole, which is always neutral.
Figure 13.11.1 (a) A silicon crystal with a substitutional aluminum atom. Aluminum has one fewer valence electron than silicon, resulting in an extrinsic hole. (b) A silicon crystal with a substitutional phosphorous atom. Phosphorous has one more valence electron than silicon, resulting in an extrinsic free electron.
Band diagrams of dopants
Although we say an n-type dopant introduces a free electron, it isn't quite free. In the case of silicon doped with phosphorous, the phosphorous atoms is more electronegative than the silicon atoms. So, even though the extra electron will delocalize around the phosphorous atom, it more attracted to the phosphorous atom than the silicon atoms. Thus, a small amount of energy is needed to make an n-type extrinsic semiconductor conduct electricity. This is visualized in band diagrams by placing the "donated" electron state slightly below the conduction band, indicating that it still requires a little bit energy to start conducting, as shown in Figure 13.11.2 below.
A similar effect holds for a p-type dopant. In the case of silicon doped with aluminum, there is a hole as a result of one of the bonds being fractional. Aluminum is less electronegative than silicon, so it will attract the hole more than the silicon atoms will. So, it takes a little bit of energy to separate the hole from the aluminum atom. If you want to think of it in terms of electrons, then the electron from a neighboring Si-Si bond needs to move to one of the Si-Al bonds. Since Al is less electronegative than Si, this bond is higher energy than the Si-Si bond. So for an electron to move from the Si-Si bond to fill the hole in the Si-Al bond, requires some energy. This is visualized in band diagrams by placing the an acceptor state slightly above the valence band, indicating that it requires a little bit of energy to move an electron into that state after which the hole can participate in conduction, as shown in Figure 13.11.3 below.
Figure 13.11.2 (a) In an n-type semiconductor, the dopant adds donor states only a small amount of energy below the conduction band. (b) With a small amount of energy, the electron is excited into the conduction band where it is now free to conduct electricity.
Figure 13.11.3 (a) In a p-type semiconductor, the dopant introduces an acceptor states only a small amount of energy above the the valence band. (b) With a small amount of energy, an electron from a neighboring atom is excited into the acceptor state and the hole left behind in the conduction band is now free to conduct electricity.
Figure 13.11.4 A generic band diagram.
Free electron and hole model of extrinsic semiconductors
NetLogo model 13.11.1 adds one element to our free electron and hole model of intrinsic semiconductors: doping. The doping slider adds a certain concentration of either free holes or electrons. The background changes color depending on the amount of doping to indicate that the composition of the underlying lattice changes with doping.