Semiconductor Theory: Atomic Structure, Energy Levels

SEMICONDUCTOR THEORY

The solid materials are classified into three types from the consideration of the current carrying capabilities: conductors, insulators and semiconductors. Conductors have an abudance of free electrons that act as charge carriers, which means that they have high conductivity. An insulator on the other hand, has hardly any free electrons and offers very low level of conductivity. A semiconductor is a material that has a conductivity level somewhere between extremes of an insulator and a conductor.

Atomic Structure

The most fundamental unit of all matter is the atom consisting of three basic particles; the electron, the proton and the neutron. Neutrons do not carry charge while protons and electrons are respectively positively and negatively charged. An atom contains the same number of electrons and protons. The atoms of various elements differ in number of sub‒atomic particles i.e., electrons, protons and neutrons they contain.

In the atomic lattice structure, neutron and proton are the heaviest particles, which make the core of the atom called nucleus. Electrons revolve around the nucleus in a fixed orbits. The orbits are denoted by principal quantum numbers or K, L, M, N shells. Each orbit represents an energy level. Electrons are arranged in order of 2n², where n is the orbit number. For example, first shell contains 2 electrons, second can 8, third can 18, and so on.

Bohr's model of the two common semiconductors, germanium and silicon are shown in fig. 1.24. The figure indicates that germanium atom has 32 orbiting electrons, while silicon has 14 orbiting electrons. In each case, there are 4 electrons in the outermost (valance) shell. Valance electrons are the electrons in the outermost shell. The potential (ionization potential) required to remove any of these 4 electrons is lower than that required for any other electron in the structure.

In a good conductor, the number of valance electrons will be 1 or 2 (eg. copper)

In an insulator, the outermost orbit will be completely filled. (eg. Xenon)

In a semiconductor, the outermost orbit will be partially filled. For example, the number of valance electrons is 4 in Germanium (Ge) and Silicon (Si).

Energy Levels

The range of energies that an electron may possess in an atom is known as the energy band. Energy band consists of a very large number of discrete energy levels, which are very closely spaced. These bands may be thought of as continuous. These energy bands are separated by forbidden energy gaps, i.e. no electron can have any energy value within forbidden bands. The three energy bands are explained below:

1. Types of energy bands

(i) Valance Band

The range of energy possessed by valance electrons is known as valance band.

(ii) Conduction Band

The range of energies possessed by conduction electrons is known as conduction band.

(iii) Forbidden Band

The energy band in between the conduction band and the valance band is called forbidden band.

2. Energy band diagrams for materials

The energy band diagrams of conductor, semiconductor and insulator are shown in fig 1.25.

(i) Conductor

In conductors, the conduction band and valance band overlap each other. Refer to fig 1.25 (a) forbidden energy gap energy gap (E_g = 0). So, a large number of valance electrons (≈ 10²² per cm³) are available for conduction in room temperature.

(ii) Insulator

In insulator forbidden energy gap Eg is very large (Eg ≈ 4 ‒ 8 eV) and very few electron‒hole pairs may be created by thermal process. Refer to fig 1.25 (c). Thus insulators or dielectrics are extremely poor conductors of electricity.

(iii) Semiconductor

Semiconductors are those substance whose electrical conductivity lies in between  conductors and insulators. In pure semiconductor, Eg lies in the range of 0.1‒3 eV. Refer to Fig 1.25 (b). Thus the appreciable number of electron‒hole is created by thermal process. Increasing temperature causes creation of more electron‒hole pairs hence resistivity falls. The number of electrons in conduction band or holes in valance band per unit volume is an ideally pure and perfect semiconductor crystal is called intrinsic carrier concentration.