Semiconductors
Those materials which acts as insulators at low temperature & behave as conductors at room temperature or at higher temperature, are known as semiconductor.
Semiconductors could be:
(i) Elemental semiconductors: Si and Ge
(ii) Compound semiconductors: Examples are:
• Inorganic: CdS, GaAs, CdSe, InP, etc.
• Organic: anthracene, doped pthalocyanines, etc.
• Organic polymers: polypyrole, polyaniline, polythiophene, etc.
Most of the currently available semiconductor devices are based on elemental semiconductors Si or Ge and compound inorganic semiconductors.
However, after 1990, a few organic semiconductors and semiconducting polymers have been developed. This indicates the birth of a future technology of polymerelectronics and molecular-electronics.
There are only two materials which act as semiconductor in pure form.
- Si – 1s2 2s2 2p6 3s2 3p2
- Ge – 1s2 2s2 2p6 3s2 3d10 4s2 4p2
Both the semi conducting materials are having 4 valence electrons in outermost orbit of their atoms.
Band theory of solids
According to the Bohr atomic model, in an isolated atom the energy of any of its electrons is decided by the orbit in which it revolves. But when the atoms come together to form a solid they are close to each other. So the outer orbits of electrons (valance electrons) from neighbouring atoms would come very close or could even overlap. This would make the nature of electron motion in a solid very different from that in an isolated atom.
Inside the crystal each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges (Charges of nuclei of surrounding atoms and other electrons). Because of this, each electron will have a different energy level. These different energy levels with continuous energy variation form what are called energy bands. The energy band which includes the energy levels of the valence electrons is called the valence band. The energy band above the valence band is called the conduction band. With no external energy (at very low temperature, ~0K), all the valence electrons will reside in the valence band. Normally the conduction band is empty at very low temperature.
Let us consider what happens in the case of Si or Ge crystal containing N atoms. For Si, the outermost orbit is the third orbit (n = 3), while for Ge it is the fourth orbit (n = 4). The number of electrons in the outermost orbit is 4 (2s and 2p electrons). Hence, the total number of outer electrons in the crystal is 4N. The maximum possible number of electrons in the
outermost orbit is 8 (2s + 6p electrons). So, for the4N valence electrons there are 8N available energy states. These 8N discrete energy levels can either form a continuous band or they may be grouped in different bands depending upon the distance between the atoms in the crystal.
For Si and Ge crystal lattices the distance between the atoms is such that the energy band of these 8N states is split apart into two which are separated by an energy gap Eg ( See Fig.1). The lower band which is completely occupied by the 4N valence electrons at temperature of absolute zero is the valence band. The other band consisting of 4N energy states, called the conduction band, is completely empty at absolute zero.
The lowest energy level in the conduction band is shown as EC and highest energy level in the valence band is shown as EV. Above EC and below EV there are a large number of closely spaced energy levels (as shown in Fig.1).
The gap between the top of the valence band and bottom of the conduction band
is called the energy band gap (Energy gap Eg). It may be large, small, or zero, depending upon the nature of the material.
Basic Definitions
- Valence band: The energy band in a solid, which is completely filled by valence electrons at low temperature (at zero Kelvin).
- Conduction band – Energy band in a crystal, which is empty at low temperature (at zero Kelvin). But when an electron goes to this band, it freely participates in conduction process.
- Forbidden gap – This is an energy gap below the conduction band & above the valence band such that no electrons can posses these energies while present in the crystal.
Band Theory of Solids
(In Hindi + English mix Language)
Question.1 Distinguish between conductors, insulators or semiconductor, on the basis of energy band theory of solids?
1) Insulator
In a insulator the inter-atomic separation is such that, at low temperature, we get a narrow valance band, a narrow conduction band & a wide forbidden gap (Eg< 3 eV). In this case the energy gap is so large that electrons cannot be excited from the valence band to the conduction band by thermal excitation.
2) Conductors
In a conductor the inter-atomic separation is such that there is a wide V.B. (which is completely filled by valence electrons at low temperature) and a wide conduction band, such that the two bands overlap each other. In conductor there is no forbidden gap. So in conductor even at low temperature we get free electrons present in conduction band, which can participate in conduction process. (VB & CB overlap to each other, thus Eg disappears)
3) Semiconductor
In Semiconductor the inter-atomic separation is such that there is a wide V.B. (Completely filled by valence electrons at low temperature) and a wide conduction band is separated by a narrow forbidden gap.( Eg< 3 eV) [Eg for Si ⇒ 1.1 eV ; Eg for Ge ⇒ 0.74 eV]
Because of the small band gap, at room temperature some electrons from valence band can acquire enough energy to cross the energy gap and enter the conduction band. These electrons (though small in numbers) can move in the conduction band.