Conductivity of Semiconductors

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Conductivity of Semiconductors 

Every atom has an outer band of electrons, known as the valence band. In metals, the electrons from this valence band are not confined to the atom and are free to move throughout the metal lattice. This called “sea of electrons” which makes conduction possible. It is exactly the opposite in non-metals, where the electrons are held tightly that means tightly bound with nucleus of atom.

Semi-conductors act as non-metals at low temperatures ( that means Semiconductors act as insulator at 0K) – the electrons are trapped within the atom. As the temperature of the semi-conductor is increased,due to thermal agitation , the electrons in the valence band gain sufficient energy to escape from the confines of their atoms. As a result, in higher temperatures, a semi-conductor’s valence electrons are free , this cause conduction in semiconductors , As temperature increases conductivity of semiconductors increases and resistivity decreases

Semiconductors in their natural state are poor conductors because a current requires the flow of electrons, and semiconductors have their valence bands filled. There are several developed techniques that allow semiconducting materials to behave like conducting materials, such as doping or gating. These modifications have two outcomes: n-type and p-type These refer to the excess or shortage of electrons, respectively. An unbalanced number of electrons would cause a current to flow through the material 

So conductivity of semiconductors can be control ( increase or decrease ) by several means i.e. by temperature or by doping according to our requirement 

If we talk conductivity in terms of forbidden energy gap ( Eg) , for  as forbidden energy gap (Eg) decreases conductivity increases , forbidden energy gap for the semiconductors are smaller than insulators and larger than metals 

 

bandgapeEg

Consider silicon which, like carbon, has the diamond cubic cyrstal structure. The valance electrons are all covalently bonded in sp3 orbitals( in Valence Band- VB)  These orbitals are completely filled. However, in this case, the next available energy level (in the Conduction Band-CB) is 1.1 eV above the highest occupied level ( at room temperature ). 

siliconBandgap

Above figure indicate that we have to provide at least 1.1 eV Energy to the electrons in Valence band for the conduction ( Covalent bond will break due to thermal energy this causes conduction )
            

So the picture is exactly the same as that for the insulating materials, except that the the size of the energy gap( Eg) is smaller. Hence for Si, with an energy gap of 1.1 eV, at room temperature some electrons will be promoted into the conduction band which accounts for its intermediate value of conductivity. Furthermore, for every electron promoted into the conduction band, a “hole” ( white circle in VB)  is left in the valance band! 
                                            
These holes are also considered to be charge carriers. So there are two types of carriers for electrical conduction: electrons and holes. Electrons are called n-type carriers (for negative) and holes are called p-type carriers (for positive).
                                 
For intrinsic semiconductors (no impurities), the number of electrons will be equal to the number of holes (chart?cht=tx&chl=n %7B%7Be%7D%7D%20%3D%20n %7B%7Bh%7D%7D ). 

From mass action law for intrinsic Semiconductors 

chart?cht=tx&chl=n %7B%7Be%7D%7D%20%3D%20n %7B%7Bh%7D%7D%20%3Dn %7B%7Bi%7D%7D  

where chart?cht=tx&chl=n %7B%7Bi%7D%7D indicates intrinsic concentration this is a  fix value for for a intrinsic semiconductor 

Thus, the conductivity for an intrinsic semiconductor exist due to both electrons and holes can be calculated:
 chart?cht=tx&chl=%5Csigma%3D%20q(%5Cmu %7Be%7Dn %7Be%7D%2B%5Cmu %7Bh%7Dn %7Bh%7D) 

Above Expression give conductivity of Extrinsic Semiconductors 

where 

chart?cht=tx&chl=%5Cmu %7B%7Be%7D%7D = indicate mobility of electrons 

chart?cht=tx&chl=%5Cmu %7B%7Bh%7D%7D = indicate mobility of holes 

chart?cht=tx&chl=q    = magnitude of charge 

And since( chart?cht=tx&chl=n %7B%7Be%7D%7D%20%3D%20n %7B%7Bh%7D%7D%20%3Dn %7B%7Bi%7D%7D )the conductivity for an intrinsic semiconductor is given by

chart?cht=tx&chl=%5Csigma%20%3D%20qn %7B%7Bi%7D%7D(%5Cmu %7Be%7D%2B%5Cmu %7Bh%7D)

Overall Conclusion on the Conductivity of Semiconductors:

Semiconductors are semi-good electrical conductors because although their valence band is completely filled, the energy gap between the valance band and the conduction band is not too large. Hence some electrons can bridge it to become charge carriers. The difference between a semiconductors and an insulator is the magnitude of the energy gap. For semiconductors Eg< 3eV and for Insulators Eg > 3eV.

NOTE: Diamond is hardest Material with forbidden energy gap (Eg) 5 to 6 eV

In next Post we will know,Derivation of Conductivity chart?cht=tx&chl=%5Csigma%3D%20q(%5Cmu %7Be%7Dn %7Be%7D%2B%5Cmu %7Bh%7Dn %7Bh%7D) equation for extrinsic semiconductor