Vedantu’s Explanation on Band Theory
The band theory of metals is based on the valence band and conduction band. It is also known as the band theory of solids or zone theory of solids. It defines conductors, semiconductors and insulators very clearly and distinctly. Before understanding the band theory, you need to have knowledge of the following terms –
Valence Band- It is made up of those valence shell orbitals which have electrons in them. For example, a sodium valence band is made up of 3s1 orbital. The electronic configuration of sodium is 1s2, 2s2 2p6, 3s1.
Conduction Band- It is made up of those orbitals which are unoccupied by electrons either in valence shell or higher unoccupied shell. Thus, the orbitals of the conduction band are empty. Again, let’s take the example of sodium as after orbital 3s next orbital 3p is empty so it forms a conduction band.
Thus, in other words, we can say the highest energy band that is filled is known as the valence band. While the next available band in the energy structure which is empty is called the conduction band.
The band structure of sodium can be shown as follows –
Forbidden Gap – The gap or energy difference between the valence band and conduction band is called the forbidden gap.
Conductors – Those materials which allow electricity to pass through them are called conductors. Examples – copper, iron, zinc etc.
Semiconductors – Those materials which show conductivity between conductors and insulators are called semiconductors. Examples – Si, Ge, As etc.
Insulators – Those materials which do not allow electricity to pass through them are called insulators. Examples – wood, glass, stones etc. After understanding all these terms now, you are ready to understand band theory.
What is Band Theory?
In chemistry, according to the band theory of solids electrons jump from valence band to conduction band even at ordinary temperature and if this happens then the solid conducts electricity. Conductivity depends on the gap between the valence band and conduction band. If the gap or energy difference between the valence band and conduction band is more than or equal to 5ev then the material will behave as an insulator.
If the energy difference between the valence band and conduction band is equal to or less than 3ev then the material or solid is called a semiconductor. If the valence band and conduction band overlap each other then the solid is called conductors. The reasoning behind it is that electrons can jump from valence band to conduction band and thus conduct electricity. While if the gap is too much between the valence band and conduction band (more than or equal to 5ev) then electrons can’t jump from the valence band to the conduction band, hence these materials or solids can’t conduct electricity. If the valence band and conduction band are neither overlapping nor at too much distance then a few electrons may jump from the valence band to the conduction band and these materials are called semiconductors.
This was a brief of Band Theory, if you want to know more about the topic then register yourself on Vedantu or download the Vedantu learning app for classes 6-10, IITJEE and NEET.
FAQs on Band Theory
1. What is the band theory of solids?
Band theory is a quantum mechanical model that describes the electronic energy levels in a solid material. According to this theory, the interaction between a large number of atoms in a crystal lattice causes their individual atomic orbitals to merge and form continuous energy bands. These bands, separated by forbidden energy gaps, determine the electrical properties of the solid, explaining why some materials are conductors, some are insulators, and others are semiconductors.
2. How are energy bands formed from atomic orbitals in a solid?
In an isolated atom, electrons occupy discrete atomic orbitals. However, when a large number of atoms come together to form a solid crystal, their outermost orbitals begin to overlap. As per the Pauli Exclusion Principle, these overlapping orbitals split into a vast number of closely spaced molecular orbitals. This collection of infinitesimally close energy levels is called an energy band. The extent of this splitting depends on the degree of overlap, resulting in the formation of distinct bands like the valence band and conduction band.
3. What is the difference between a valence band, a conduction band, and a forbidden energy gap?
These three components are central to understanding band theory:
- Valence Band: This is the highest energy band that is completely or partially filled with valence electrons at 0 K temperature. Electrons in this band are typically bound to their atoms and do not contribute to electrical conduction.
- Conduction Band: This is the lowest energy band that is empty or unoccupied by electrons. For conduction to occur, electrons must gain enough energy to jump from the valence band to this conduction band, where they are free to move throughout the crystal.
- Forbidden Energy Gap (or Band Gap): This is the energy range between the top of the valence band and the bottom of the conduction band where no electron states can exist. The size of this gap is the primary factor that determines a solid's electrical conductivity.
4. How does band theory explain the difference between conductors, semiconductors, and insulators?
Band theory classifies solids based on the size of the forbidden energy gap between their valence and conduction bands:
- In conductors (like metals), the valence band and conduction band overlap, meaning there is no forbidden gap. Electrons can move freely into the conduction band with minimal energy, allowing for high electrical conductivity.
- In insulators (like diamond or glass), there is a very large forbidden energy gap (typically > 3 eV). It requires a huge amount of energy for an electron to jump from the valence band to the conduction band, so they do not conduct electricity under normal conditions.
- In semiconductors (like Silicon or Germanium), there is a small, finite forbidden energy gap (typically < 3 eV). At room temperature, some electrons gain enough thermal energy to jump this gap, enabling a small amount of electrical conduction.
5. Why are metals good conductors of electricity according to band theory?
Metals are excellent conductors because their electronic band structure features a valence band that directly overlaps with the conduction band. There is no forbidden energy gap separating them. This means the conduction band is partially filled with electrons even at absolute zero temperature. As a result, when an electric field is applied, these electrons can move into higher energy states within the same band with very little energy input, creating a flow of electric current.
6. How does an increase in temperature affect the conductivity of a semiconductor?
For a semiconductor, an increase in temperature significantly increases its electrical conductivity. According to band theory, the electrons in the valence band can gain enough thermal energy from the rising temperature to jump across the small forbidden gap into the conduction band. This process creates free electrons in the conduction band and leaves behind positively charged 'holes' in the valence band. Both the free electrons and holes act as charge carriers, thus increasing the material's overall conductivity.
7. What are intrinsic and extrinsic semiconductors, and how does band theory account for them?
Band theory explains both types of semiconductors based on the purity and energy levels within the band gap:
- An intrinsic semiconductor is a pure semiconductor (e.g., pure Si or Ge). Its conductivity is solely due to electrons thermally excited from the valence to the conduction band.
- An extrinsic semiconductor is created by intentionally adding impurity atoms (a process called doping). This introduces new, discrete energy levels within the forbidden gap. For n-type semiconductors, a 'donor level' is created just below the conduction band, making it easier for electrons to become charge carriers. For p-type semiconductors, an 'acceptor level' is created just above the valence band, making it easier to create holes.
