Basics of SemiConductors:

All consumer electronics rely on the use of semiconductors to function.

The physics that governs the movement of electrons (which are extremely tiny objects) is based on quantum mechanics and not classical Newtonian physics.

This is not a course about quantum mechanics so don't suddenly freak out. Rather, we will use some important principles quantum mechanics to better understand how semiconductors work.

To begin with, we will consider a solid (like a semi-conductor) as any material in which the atoms are arranged in an ordered fashion. Such ordered is usually referred to as a crystal or a lattice. Let's consider the case of silicon.

Silicon has 14 electrons, but only the outer most 4 are available as "valence" electrons to help bond with other atoms.

In its solid form, each silicon atom normally shares one of its four valence electrons in a covalent bond with each of four neighboring silicon atoms. The solid thus consists of basic units of five silicon atoms: the original atom plus the four other atoms with which it shares valence electrons. The image below visually represents this 5 Atom Silicon Crystal:

In two dimensions we can represent silicon as below

Each silicon atom shares its four valence electrons with valence electrons from four nearest neighbors, filling the shell to 8 electrons, and forming a stable, periodic structure. The outer shells of all of the atoms blend together and form what is called a band. This band is called the conduction band . Electrons that are still bound in atoms are said to be in the valence band .The difference in energy between these two bands is called the bandgap energy

Once the atoms have been arranged like this, the outer valence electrons are no longer strongly bound to the host atom. Therefore, in principle, these outer electrons can easily be "freed" from the lattice and move through the material. The movement of electrons through material is a current.

In real materials, the constant interaction between electrons and nuclei which are "fixed" at periodic locations in the materal gives rise to a host of physical difficulties. For instance, as the electrons move through the material, they are exposed to different (quasi-periodic) electric fields and potentials. While this material is well beyond the scope of this class we can illustrate the basic point below:

Consider the diagram below which shows two bands of some substance, where the second band is of higher energy than the first band. The energy difference between the two bands is the Band Gap.

The cups in the figure represent the allowed states that electrons can occupy in a periodic solid. Note, that these allowed states are grouped within relatively small energy ranges. As you move up in energy you encounter the first energy band, with very few allowed states (e.g. 1 cup). The "center" of that energy band has the most allowable states (e.g. 4 cups) and as you move away from that center band energy, the number of allowable states decreases. Then you enter the band gap region which has no cups (e.g. no allowable states). The you enter another band, with an energy distribution of allowable states (e.g. the cup configuration) that is similar to the previous band. Most materials have several of these bands, not just 2.
Now there is a rule: each band has exactly 2N allowed states in it, where N is the total number of atoms in the particular crystal. For our schematic case, N=5 so that 2N = 10, so that there are 10 cups in each band. Into each band we must now distribute all of the valence electrons associated with the atoms. However, there is a very important restriction only one electron can occupy each allowed state This means to occupy the next cup in an energy band an electron needs to gain energy until all the cups are full
So if the first cup in the first band is filled, then an electron necessarily must move to a higher energy to fill another state (cup). For silicon, which has 4 valence electrons per atom, then, since we have 5 atoms, we would simply fill all 20 cups with valence electrons in the first two states. So what about the third gap and its 10 states? (only the first 7 are shown in the top of the figure) In this case we have run out of electrons to fill the cups in the third band. To get the cups in the third band filled, the electrons in silicon would have to acquire a relatively large amount of energy. Where would this energy come to force filling this third band? One way is to apply a voltage to the silicon crystal which will create an electric field. The potential energy in this field would have to be higher than the band gap energy between the second and third bands - thus electrons in silicon can not easily gain energy and this makes it a poor conductor of electricity under normal circumstances. So how can we cause silicon to be a conductor at all?
Well, the schematic case demonstrated of the first 20 cups being full for silicon really only occurs at zero temperature. At room temperature, the electrons gain some thermal energy and move to the higher energy band. This is called "hopping the gap" and is shown schematically to the right. In silicon at room temperature, about 10 billion electrons per cc are thermally excited from the valence band to the conduction band. Well if this process were efficient, then we can turn silicon into a good conductor of electricity just by heating it up. But we can't really do that since as we heat it up the nuclei in the crystal lattice move faster and interfere with the electrons trying to flow through the material thus increasing resistance. To get around this problem we have to modify silicon but introducing doping atoms (often Boron) at key locations to facilitate more donor electrons to become current. We will talk about doping later, but this process doping silicon is the main reason that clean room handling of silicon processing is required.