band theory long answer
Answers
A useful way to visualize the difference between conductors, insulators and
semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands . Crucial to the conduction process is whether or not there are electrons in the conduction band. In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap. With such a small gap, the presence of a small percentage of a doping material can increase conductivity dramatically.
An important parameter in the band theory is the Fermi level , the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties.
Alternate answer :-
Band Theory was developed with some help from the knowledge gained during the quantum revolution in science. In 1928, Felix Bloch had the idea to take the quantum theory and apply it to solids. In 1927, Walter Heitler and Fritz London discovered bands- very closely spaced orbitals with not much difference in energy.
In this image, orbitals are represented by the black horizontal lines, and they are being filled with an increasing number of electrons as their amount increases. Eventually, as more orbitals are added, the space in between them decreases to hardly anything, and as a result, a band is formed where the orbitals have been filled.
Different metals will produce different combinations of filled and half filled bands.
Sodium's bands are shown with the rectangles. Filled bands are colored in blue. As you can see, bands may overlap each other (the bands are shown askew to be able to tell the difference between different bands). The lowest unoccupied band is called the conduction band, and the highest occupied band is called the valence band.
Bands will follow a trend as you go across a period:
In Na, the 3s band is 1/2 full.
In Mg, the 3s band is full.
In Al, the 3s band is full and the 3p ban is 1/2 full... and so on.
The probability of finding an electron in the conduction band is shown by the equation:
\[ P= \dfrac{1}{e^{ \Delta E/RT}+1} \]
The ∆E in the equation stands for the change in energy or energy gap. t stands for the temperature, and R is a bonding constant. That equation and this table below show how the bigger difference in energy is, or gap, between the valence band and the conduction band, the less likely electrons are to be found in the conduction band. This is because they cannot be excited enough to make the jump up to the conduction band.
Because of the very large number of atoms that interact in a solid material, the energy levels are so closely spaced that they form bands. The highest energy filled band, which is analogous to the highest occupied molecular orbital in a molecule (HOMO), is called the valence band. The next higher band, which is analogous to the lowest unoccupied molecular orbital (LUMO) in a molecule, is called the conduction band . The energy separation between these bands is called the energy gap, Eg.
Idealized representation of energy bands and gaps
The filling of these bands and the size of the energy gap determine if a material is a conductor (a metal), a semiconductor, or an insulator. In metals there is no energy gap between filled and unfilled energy levels. A significant number of electrons are thermally excited into empty levels, creating holes in the filled band. The electrons in a conduction band and the holes in a valence band can move throughout the material, allowing it to easily conduct electricity. In semiconductors Eg is small, but large enough so that a fairly small number of electrons are in the conduction band due to thermal energy, and these materials conduct poorly. In insulators Eg is large so that electrons are not promoted to the conduction band due to thermal energy, and these materials do not conduct electricity.