We saw there are two energy bands associated with a silicon lattice: valence and conduction bands. At 0K, all the energy states within the valence band are filled and all the energy states in the conduction band are empty. Silicon at 0K is therefore an insulator because there are no free charge carriers. However, there are ways to excite electrons to the conduction band and create free charge carriers to conduct electricity.
Below you see the valence and conduction bands (energy domain) and on the right you see a Si lattice in real space.
Hover over the two bands to see how many electrons exist in each energy state.
Light can be used to excite electrons in the valence band to the conduction band.
For silicon, the band gap is 1.1eV. Which photons are able to excite electrons to the conduction band?
Wavelength
Energy
When an electron is excited to the conduction band, it leaves its bond and moves freely in the lattice. In the process it generates a vacant space in the lattice, called a hole.
Other electrons in the valence band can move to occupy this hole, generating a hole in their original position. This mimics the effect of a hole moving across the lattice
We consider the hole to be a positively charged carrier, and it moves freely in the lattice similar to the free electron.
The motion of these two carriers is responsible for conduction in semiconductors.
In a perfect lattice, electrons and holes move freely in straight lines and nothing interfere with their movement. However, any non-ideality such as replacement of an atom by another kind of atom (impurity), can scatter electrons and holes. These impurities are called defects.
As we will see, scattering can also take place because of the vibration of the atoms at temperatures above 0K.
A free electron in the conduction band can return back to the vallance band filling an empty state. This way, both the free electron and hole are annihilated. The lost energy may result in emission of a photon or it may heat the lattice.
Click on the recombine button below to recombine the two charge carriers.
Just like shining light, an electron can also get excited to the conduction band by the thermal energy of the lattice. As one increases the temperature, the densities of electrons and holes increase drastically.
A higher temperature also means more lattice vibration; hence, more frequent carrier scatterings. Carriers also move faster on average as temperature rises.
Temperature (K):
In this manner, the band gap determines the conductivity of various materials.
Conductors don't have a band gap,so electrons can get excited even at 0K. Semi-conductors have moderate band gaps, so they conduct at higher temperatures. Insulators have very large band gaps, so they never conduct electricity.