In an extrinsic semiconductors, there are two types of materials n type
and p type. Let us obtain the expressions for the conductivity of n type
and p type materials.

__1.1 Conductivity of n Type Material__

It is known that in n type material, the free electrons are majority carriers while the holes are minority carriers.

Let n

_{n}= Concentration of free electrons in n type
p

_{n}= Concentration of holes in n type
N

_{D}= Concentration of donor atoms**Note**: In the symbol, main letter n or p indicates concentration of type of charge carrier electron or whole while the suffix indicates the type of material i.e. n type or p type. Thus n

_{n}indicates electron concentration in n type material while n

_{p}indicates electron concentration in p type material and so on.

From the basic equation of conductivity, the conductivity of n type material can be expressed as,

σ

_{n}= (n_{n}μ_{n }+ p_{n}μ_{p}) e ............(1)
But p

_{n}<< n_{n}as holes are in minority hence,
σ

_{n}≈ n_{n}μ_{n }e ................. (2)
The number of free electrons is dominantly controlled by donor atoms
added than the thermal generation at room temperature. Hence
concentration of donor atoms N

_{D}added can be approximately assumed to be equal to the concentration of free electrons n_{n}in n type materials.
Thus as N

_{D}>> n_{i}we can write,
n

_{n}≈ N_{D}................ (3)**.**σ

^{.}._{n}≈ N

_{D}μ

_{n }e ..................(4)

__1.2 Conductivity of p Type Material__

For a type material, holes are in majority and electrons are in minority.

Let n

_{p}= Concentration of free electrons in p type
p

_{p}= Concentration of holes in p type
N

_{A}= Concentration of acceptor atoms
Thus the conductivity of p type material can be expressed as,

σ

_{p}= (n_{p}μ_{n }+ p_{p}μ_{p}) e ................ (5)
But n

_{p}<< p_{p}as free electrons are in minority hence,
σ

_{p}≈ p_{p}μ_{p}e ........... (6)
The number of holes is dominantly controlled by added acceptor impurity
than the thermal generation. Each added impurity atom creats a hole
hence N

_{A}>> n_{i}. Thus all the holes generated p_{p}can be approximately assumed to be equal to the concentration of acceptor N_{A}. Thus,
p

_{p}≈ N_{A}............... (7)**.**σ

^{.}._{p}≈ N

_{A}μ

_{p}e ............. (8)

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