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 * **energy band **
 * Energy Band Splitting and Band Gap. **

 The analysis of periodic potentials is required to find the energy levels in a semiconductor. This requires the use of periodic wave functions, called Bloch functions .The result of this analysis is that the energy levels are grouped in bands, separated by energy band gaps. The behavior of electrons at the bottom of such a band is similar to that of a free electron. However, the electrons are affected by the presence of the periodic potential. The combined effect of the periodic potential is included by adjusting the value of the electron mass. This mass will be referred to as the effective mass.

 The effect of a periodic arrangement on the electron energy levels is illustrated by Figure 1. Shown are the energy levels of electrons in a carbon crystal with the atoms arranged in a diamond lattice. These energy levels are plotted as a function of the lattice constant, //a//.Isolated carbon atoms contain six electrons, which occupy the 1s, 2s and 2p orbital in pairs. The energy of an electron occupying the 2s and 2p orbital is indicated on the figure. The energy of the 1s orbital is not shown. As the lattice constant is reduced, there is an overlap of the electron wavefunctions occupying adjacent atoms. This leads to a splitting of the energy levels consistent with the Pauli exclusion principle. The splitting results in an energy band containing 2N states in the 2s band and 6N states in the 2p band, where N is the number of atoms in the crystal. A further reduction of the lattice constant causes the 2s and 2p energy bands to merge and split again into two bands containing 4N states each. At zero Kelvin, the lower band is completely filled with electrons and labeled as the valence band. The upper band is empty and labeled as the conduction band.



 Figure1:Energy bands for diamond vsl attice constant.



 Figure2:Energy bands for semiconductor.

 The above diagram shows the band splitting due to the variable potential energy based on Kronig Penny model. Energy levels are discrete in nature. Figure 2 shows that thing.



 Figure3:Energy bands for semiconductor.

 Figure 3 shows the difference between conductor, semiconductor and insulator based on energy gap. Conductor has no energy gap and valance band overlap on conduction band so electron can easily transfer from valance band to conduction band.So, conductivity is highest among three. Top of Form

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