Conductivity of a Semi conductor

In a pure Semi conductor number of electrons = number of holes. Thermal agitation (increase in temperature) produces new electron-hole pairs and these electron-hole pair combines produces new charge particles.

one particle is of negative charge which is known as free electron with mobility \mu _{n} another in with positive charge known as free hole with mobility \mu _{p}.

two particles moves in opposite direction in an electric field \overrightarrow{E} and constitutes a current.

The total current density (J) with in the semi conductor.

\overrightarrow{J} = \overrightarrow{J_{n}} + \overrightarrow{J_{p}}

Total conduction current density = conduction current density due to electrons + conduction current density due to holes.

J_{n}= nq\mu _{n}E.

J_{p}= pq\mu _{p}E.

n- number of electrons/Unit-Volume.

p-number of holes/Unit-Volume.

E- applied Electric field strength V/m.

q-charge of electron/hole \approx 1.6X10^{-19}C.

J = nq\mu _{n}E +pq\mu _{p}E.

J = (n\mu _n +p\mu _{p})qE.

J=\sigma E.

where \sigma = (n\mu _{n}+p\mu _{p})q is the conductivity of semi conductor.

Intrinsic Semi conductor:-

In an  intrinsic semi conductor n=p=n_{i}

\therefore conductivity \sigma _{i}= (n_{i}\mu _{n}+ n_{i}\mu _{p})q

\sigma _{i}= n_{i}(\mu _{n}+ \mu _{p})q

where J_{i} is the current density in an intrinsic semi conductor J_{i} = \sigma _{i} E

Conductivity in N-type semi conductor:-

In N-type n> > p 

number of electrons > > number of holes

\therefore \sigma _{N}\simeq n\mu _{n}q

J _{N}= n\mu _{n}q.

Conductivity in P-type semi conductor:-

In P-type p> > n

number of holes > > number of electrons

\therefore \sigma _{p} \approx p\mu _{p}q.

J_{P}= p\mu _{p}q E.

 

 

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Author: Lakshmi Prasanna

Completed M.Tech in Digital Electronics and Communication Systems and currently working as a faculty.