Energy Bands Description
In gases, the arrangement of molecules is not at all close, that is, they are far away from each other, and are loosely packed. The molecular arrangement in liquids is moderate, that is, the molecules are a little far away from each other. When it comes to solids, the molecules are so tightly packed or arranged that the electrons (a sub-atomic particle with an electric charge of negative 1) tend to move towards the orbitals of the neighbouring atoms. Consequently, the electron orbitals overlap as and when the atoms come together. Because of the intermixing of atoms in the substances of the solid-state, there will be a formation of energy bands, instead of the single energy levels. The set of energy levels, which are closely or tightly packed, are what we call the Energy Bands.
Classification of Energy Bands
Valence Band
Although the electrons move in the atoms in certain energy levels, the energy of the electrons present in the innermost shell is higher than the energy of the electrons present in the outermost shell. Valence electrons are the electrons, which are present in the outermost shell. The valence electrons contain a series of energy levels and form an energy band known as the valence band. The valence band is the band, which has the highest occupied energy.
Conduction Band
The valence electrons are not held tightly or firmly to the nucleus, due to which, even at room temperature, a few of the valence electrons leave the valence band to become free. They are referred to as the free electrons because of the fact that they tend to move towards the neighbouring atoms. The free electrons conduct the current in the conductors and are therefore known as the conduction electrons. The conduction band is the one that contains the conduction electrons and has the lowest occupied energy levels.
Forbidden Energy Gap
The forbidden energy gap refers to the gap between the valence band and the conduction band. As the name suggests, the forbidden energy gap has no energy as a result of which no electron stays in this energy band. While going to the conduction band, the valence electrons pass through the forbidden energy gap. If the forbidden energy gap is greater, then the valence band electrons are tightly bound or firmly attached to the nucleus. For pushing the electrons out of the valence band, we require some amount of external energy equal to the forbidden energy gap.
The figure given below shows the conduction band, valence band, and the forbidden energy gap. Based on the size of the forbidden energy gap, the conductors, semiconductors, and insulators are formed.
Conductors
Conductors are the substances or materials that conduct electricity as they allow electricity to flow through them. The forbidden energy gap disappears in the conductors, as the conduction band and the valence band come close to each other and overlap. Copper, gold, and silver are a few examples of conductors. The figure given below shows the structure of energy bands in conductors.
The Characteristics of Conductors are as Follows:
There is no forbidden energy gap in a conductor.
The valence band and the conduction band overlap in conductors.
There are a high number of free electrons available for the conduction of electricity.
With a slight increase in voltage, there is an increase in the conduction as well.
No concept of hole formation is there because the continuous flow of electrons contributes to the current produced.
Insulators
Insulators are the substances or materials that don't conduct electricity as they don't allow electricity to flow through them. The forbidden energy gap in the insulators is large enough due to which the conduction of electricity can't take place. Rubber and wood are a few examples of insulators. The figure given below shows the structure of energy bands in insulators.
The Characteristics of Insulators are as Follows:
The forbidden energy gap is large enough in insulators with a value of 10eV.
The electrons in the valence band are tightly bound or firmly attached to atoms.
Some insulators might show conduction with an increase in the temperature.
Semiconductors
Semiconductors are substances or materials having conductivity between the conductors and the insulators. In semiconductors, the forbidden energy gap is small, and the conduction of electricity will take place only if we apply some external energy. Germanium and silicon are a few examples of semiconductors. The figure given below shows the structure of energy bands in semiconductors.
The Characteristics of Semiconductors are as Follows:
The forbidden energy gap is small in a semiconductor.
For Germanium (Ge), the value of the forbidden energy gap is 0.7eV, and for Silicon (Si), it is 1.1eV.
The conductivity of semiconductors increases with the rise in temperature.
Semiconductors are neither a good conductor or an insulator.
FAQs on Energy Bands - Classification and Explanation
1. What is an energy band in solid-state physics?
An energy band is a range of closely spaced energy levels that electrons are allowed to occupy within a solid crystal. According to quantum mechanics, when individual atoms are brought close together to form a solid, their discrete atomic orbitals overlap. This interaction causes the single energy levels to split and form these continuous bands of allowed energy.
2. What are the main types of energy bands found in solids?
The two most important types of energy bands that determine a solid's electrical properties are:
- Valence Band: This is the highest energy band that is completely filled with electrons at absolute zero temperature. Electrons in this band are generally bound to their atoms and do not contribute to electric current.
- Conduction Band: This is the lowest energy band that is either empty or partially filled. Electrons that move into this band are free to travel throughout the crystal and act as charge carriers, enabling electrical conduction.
3. How are energy bands formed in a solid crystal?
Energy bands are formed due to the interaction between electrons of neighbouring atoms in a crystal lattice. When isolated atoms combine to form a solid, the Pauli exclusion principle states that no two electrons can occupy the identical energy state. This forces the discrete energy levels of the individual atoms to split into a vast number of very closely spaced energy levels, which effectively merge to form a continuous range known as an energy band.
4. How does an energy band diagram explain the difference between conductors, semiconductors, and insulators?
An energy band diagram visually represents the difference between materials based on the forbidden energy gap (Eg) that separates the valence and conduction bands:
- Conductors: The valence and conduction bands overlap, resulting in no energy gap. Electrons can move freely into the conduction band with minimal energy, allowing for high conductivity.
- Insulators: There is a very large forbidden energy gap (typically > 3 eV). A significant amount of energy is required to excite an electron from the valence to the conduction band, so they conduct very poorly.
- Semiconductors: The forbidden energy gap is relatively small (typically < 3 eV). At room temperature, some electrons can gain enough thermal energy to jump the gap, allowing for moderate and controllable conductivity.
5. Why is there a 'forbidden energy gap' between the valence and conduction bands?
The forbidden energy gap represents a range of energy values that electrons within the crystal lattice cannot possess. This gap is a direct consequence of the wave-like nature of electrons and the periodic potential created by the atoms in the crystal. The allowed energy levels for electrons group into bands, and the energy regions between these bands are 'forbidden,' meaning there are no available or stable quantum states for an electron to occupy.
6. How does temperature affect the conductivity of a semiconductor based on its energy bands?
As the temperature of a semiconductor increases, its atoms vibrate more intensely, providing thermal energy to electrons in the valence band. This added energy allows a greater number of electrons to overcome the small forbidden energy gap and jump into the conduction band. The presence of more electrons in the conduction band (and the corresponding 'holes' left in the valence band) significantly increases the density of charge carriers, thereby increasing the semiconductor's electrical conductivity.
7. What is the most important difference between the energy band structure of a conductor and an insulator?
The key difference is the size of the forbidden energy gap. In a conductor, the valence band and conduction band overlap, meaning there is no energy gap that electrons need to overcome to conduct electricity. In contrast, an insulator features a very wide forbidden energy gap (Eg > 3 eV), which makes it extremely difficult for an electron in the valence band to acquire enough energy to jump into the conduction band under normal conditions.
8. Can an electron exist within the forbidden energy gap?
No, an electron cannot have a stable existence within the forbidden energy gap of a perfect crystal. This gap represents a range of energy levels for which there are no allowed solutions to the Schrödinger equation for an electron in the periodic potential of the lattice. An electron must possess an energy value that falls either within the valence band or the conduction band. It can be excited across the gap, but it cannot reside within it.
9. Is the conduction band of a semiconductor always empty?
No. The conduction band of a pure semiconductor is only completely empty at absolute zero temperature (0 Kelvin). At any temperature above absolute zero, some electrons will gain enough thermal energy to jump from the valence band to the conduction band, partially populating it and allowing the material to conduct electricity. The higher the temperature, the more electrons will be in the conduction band.
