Energy Band Theory

Molecules are arranged differently in solids, liquids, and gases. They have gathered closely together to form solids, which has caused the electrons in the molecule’s atoms to move into the orbitals of its neighbors. In liquids, the molecular organization is moderate, but it is not close in gases. As a result, the electron orbitals partially cover as the atoms get close to one another. Instead of single energy levels, the levels of energy bands are produced by the fusion of atoms within materials. A group of closely spaced energy levels is referred to as an energy band in energy band theory.

Formation of Energy Bands

The energy in each orbit of an isolated atom’s electrons is fixed. The energy level of the electrons in the outermost orbit, however, is influenced by the atoms nearby in solids.

The electrons in the outermost orbit feel an attractive force from the closest or neighboring atomic nucleus when two isolated charges are brought close to one another. The energy levels of the electrons are changed to a value that is greater or lower than the original energy level of the electron as a result, and they will not be at the same level.

Different energy levels can be seen in the electrons in the same orbit. The term “energy band” refers to this collection of various energy levels.

However, the presence of nearby atoms has no impact on the energy of the inner orbit electrons.

Energy Band Theory Visualization in Materials

Classification of Energy Bands

Valence Band

The term “valence electrons” refers to the electrons in the outermost shell. These valence electrons make up the valence band, an energy band that has a number of different energy levels. The maximum energy is occupied in the valence band.

Electrons can move from the valence band, which is a band of electron orbitals, into the conduction band when they are excited.

Conduction Band

A few of these valence electrons can escape the outermost orbit even at room temperature and become free electrons because they are not securely bound to the nucleus. The free electrons are referred to as conduction electrons because they may move current through conductors. The band with the lowest occupied energy levels is the one called the conduction band since it possesses conduction electrons.

Forbidden Energy Gap

The area between the conduction and valence bands is referred to as the forbidden gap. Due of its lack of energy, this band is not allowed to exist. Therefore, no electrons go through this band. This gap will enable electrons to transition from the valence to the conduction state.

If this gap is wider, there is a strong bond between the electrons in the valence band and the nucleus. The forbidden energy gap can be compared to the present situation where a small amount of external force is needed to force the electrons out of this band.

The diagram above shows the two bands as well as a forbidden gap. Based on the magnitude of the gap, semiconductors, conductors, and insulators are produced.

Conductors

All of these metals – Gold, Aluminum, Silver, and Copper—allow an electric current to flow through them.

Since there is no forbidden gap between the valence band and conduction band, both bands overlap. At normal temperature, there are a lot of free electrons available.

This overlapping indicates a large number of charge carriers available through conduction.

Conductors have the following characteristics:

In a conductors, there is no such thing as a prohibited energy gap.
In conductors, the valence band and the conduction band overlap.
There are a large number of free electrons accessible for power transmission.
When the voltage is increased slightly, the conduction increases as well.

Insulators

Examples of insulators include rubber, wood, and glass. These materials block the flow of electricity through them. They have an extremely poor conductivity and a high resistance.

The insulator has an extremely high energy gap of up to 15 eV. The inability of the electrons to travel from the valence band to the conduction band prevents the material from conducting.

Insulators have the following characteristics:

In the valence band, electrons are strongly bonded or firmly connected to atoms.
Conduction may occur in some insulators when the temperature rises.

Semiconductors

The two materials with electrical characteristics that fall between semiconductors and insulators are Germanium and Silicon. The valence band is fully filled and the conduction band is empty in the energy band diagram of semiconductors, however there is a very small (1eV) forbidden gap between the two bands. The forbidden energy gap in semiconductors is tiny, and electricity can only be conducted if external energy is applied.

At an absolute zero temperature (0 Kelvin), Semiconductors behave like perfect insulators.

Semiconductors have the following characteristics:

In a semiconductor, the prohibited energy gap is minimal.
The prohibited energy gap for Germanium (Ge) is 0.7eV, whereas for Silicon (Si) it is 1.1eV.
As the temperature rises, semiconductors become more conductive.
Semiconductors have neither strong conductivity nor good insulating properties.

Semi-conductors are essential components of modern technology. They are further subdivided into intrinsic and extrinsic semiconductors.

Intrinsic Semiconductor

A semiconductor that is exceedingly pure. According to the energy band theory, the conductivity of this semiconductor will be zero at ambient temperature. Si and Ge are two examples of intrinsic semiconductors.

Extrinsic Semiconductor

Extrinsic semiconductors are semiconductors that have had an impurity introduced to them at a regulated rate to make them conductive.

They can be created by doping intrinsic semiconductors, just as insulating materials can be doped to transform them into semiconductors.

What is Doping?

Doping is a purposeful addition of impurities to a semiconductor that is extremely pure or intrinsic in order to modify its electrical properties. The impurities differ depending on the type of semiconductor. Light to moderately doped semiconductors are known as extrinsic semiconductors. In most cases, one impurity atom is introduced to every 10⁸ semiconductor atoms. This process plays an effective role in energy band theory.

Impurity is used to enhance the number of free electrons or holes in a semiconductor crystal, making it more conductive. A significant number of free electrons will exist if a pentavalent impurity with five valence electrons is introduced to a pure semiconductor. A significant number of holes will exist in the semiconductor if a trivalent impurity with three valence electrons is introduced.

Because Ge and Si are Tetravalent in nature, doping impurities can be Trivalent or Pentavalent. (Trivalent impurities have three valence electrons, while pentavalent impurities have five valence electrons).

Due to doping, extrinsic semiconductors can be classified into two groups: those with more electrons (n-type for negative, from group V), and those with fewer electrons (p-type for positive, from group III).

n-TYPE SEMICONDUCTORS

n-type semiconductors are extrinsic semiconductors in which dopant atoms can provide additional conduction electrons to the host material (e.g. phosphorus in silicon).

Pentavalent impurities, or atoms with five valence electrons, are used to create these semiconductors. In these elements, holes make up the minority of charge carriers while electrons comprise the majority.

Ex: Phosphorous, Antimony, Bismuth, etc.

p-TYPE SEMICONDUCTORS

To enhance the number of free charge carriers, a p-type (p for “positive”) semiconductor is formed by adding a certain type of atom to the semiconductor.

These semiconductors are created by including a trivalent impurity (an atom with three valence electrons). A hole behaves like a positive charge. When a large enough number of acceptor atoms are supplied, thermally excited electrons are substantially outnumbered by holes. In p-type materials, holes are the majority carriers, whereas electrons are the minority carriers.

Ex: Gallium, Aluminum, Boron, etc.

Difference between Intrinsic & Extrinsic Semiconductors

The following are some of the key distinctions between extrinsic and intrinsic semiconductors:

Intrinsic semiconductors exist in their purest form at all times while Extrinsic semiconductors are created by doping impurities in pure semiconductors.
At room temperature, Intrinsic semiconductors have poor electrical conductivity while Extrinsic semiconductors have a high electrical conductivity compared to other materials.
The number of electrons equals the number of holes in Intrinsic semiconductors while numbers are unequal in Extrinsic semiconductors.
Intrinsic semiconductors are solely reliant on temperature while Extrinsic semiconductors are affected by temperature and the number of contaminants present.
Intrinsic semiconductors are not further classified while N-type and p-type semiconductors are two types of semiconductors in Extrinsic semiconductors.
Silicon and germanium are two examples of Intrinsic semiconductors while Si and Ge doped with Al, In, P, As, and other elements are examples of Extrinsic semiconductors.

According to Bohr’s theory, every shell of an atom contains a discrete amount of energy at different levels. Energy band theory explains the interaction of electrons between the outermost shell and the innermost shell.

The energy associated with forbidden band is called energy gap and it is measured in unit electron volt (eV).

1 eV = 1.6 × 10-19 J

The applied external energy in the form of heat or light must be equal to to the forbidden gap in order to push an electron from valence band to the conduction band.