Electronics Topics - Energy Band Structures

ENERGY BAND STRUCTURES

Insulator is a very poor conductor of electricity. Ex: Diamond

Resistivity, p > 10⁹  Ω- cm

Free electron Concentration, n ≈10⁷ electrons/m3

Energy Gap, E_G>>1 eV

Metal is an excellent conductor of electricity. Ex: AI, Ag, Copper

p < 10^-3 n - cm 
Free electron concentration, n = 10²⁸ electrons/m3

Energy Gap, E_G = 0

Semiconductor is a substance whose conductivity lies between these two. Ex: C, Si, Ge, GaAs etc.

 

INSULATOR

For diamond, the value of energy gap E_G is 6 eV. This large forbidden band separates the filled valence band region from the vacant conduction band. The energy, which can be supplied to an electron from an applied field, is too small to carry the particle from the filled valence band into the vacant conduction band. Since the electron cannot acquire externally applied energy, conduction is impossible and hence diamond is an insulator.

SEMICONDUCTOR

For Semiconducting materials, the value of energy gap E_G will be about 1 eV.

Germanium ( Ge ) has E_G = 0.785 eV, and Silicon is 1.21 eV at 0⁰K. Electron can not acquire this much Energy to travel from valence band to conduction band. Hence conduction will not take place. But E_G is a function of temperature T. As T increases, E_G decreases.

For Silicon ( Si ) E_G decreases at the rate of 3.6 x 10^-4 eV /⁰K

For Germanium E_G decreases at the rate of 2.23 x 10^-4 eV/⁰K

For Si, E_G = 1.21- 3.6 x 10^-4 x T

For Ge, E_G = 0.785 - 2.23 x 10^-4 x T.

The absence of an electron in the semiconductor is represented as hole.

METAL(SEMICONDUCTOR)

In a metal, the valence band may extend into the Conduction Band itself. There is no forbidden band, under the influence of an applied field, the electron will acquire additional energy and move into higher states. Since these mobile electrons constitute a current, this substance is a conductor.

When an electron moves from valence band into conduction band in a metal, the vacancy so created in the valence band cannot act as a hole. Since, in the case of metals, the valence electrons are loosely bound to parent atom. When they are also in conduction, the atom can pull another electron to fill its place.

In the energy band diagram, the y-axis is energy. The x-axis is wave vector K, since the energy levels of different electrons are being compared. The Ge has structure of,

1s² 2s² 2p⁶ 3s² 3p⁶ 3d^l0 4s² 4p²

The two electrons in the s sub shell and 2 in the p sub shell are the 4 electrons in the

Outermost 4th shell. The Germanium has a crystalline structure such that these 4 electrons are shared by 4 other Germanium atoms. For insulators the valence shell is completely filled. So there are no free electrons available in the outermost shell. For conductors say Copper, there is one electron 10 the outermost shell which is loosely bound to the parent atom. Hence the conductivity of Copper is high.