Extrinsic Doping :

Imperities could be incorporated into the crystal which could either contribute extre electrons or could accept electrons.In the former,afer the contribution of the electron/s the impurity itself becomes positively charged(as it was neutral to start with)and into concentration is called ND+.In the latter case the impurity after accepting electron/s becomes negatively charged and its concentration is called NA -

Assuming uniform doping under equilibrium

, Donors produce +ve ions, Acceptors produce -ve ions.

if

, this is the charge neutrality relation.

Relationship for    and  

Now let N D = no. of donor atoms

and = no. of donor atoms ionized

is the ratio of no. of empty states to total no. of states in donor energy

g D = 2(standard value)

Similarly, g A = 2(standard value)

In the above expressions, g D and g A are the degeneracy factors

From charge neutrality condition.

We have

solving this equation given N V , N c , N A , E c , E v , T, E D , E A we can find E F etc

Free-out/Extrinsic T

Suppose N D > > N A and N D > > n:

electron concentration > > hole concentration. Also .

where (a computable constant at a given T)

Therefore,

Solving this quadratic equation,

, (+ve root chosen as )

or,

Similar result can be obtained for acceptor doped material.

is typically much grater than N D

, p doped Si, T = 300 k

n = 0.9996 , So 99.96% of P atoms are ionized at room temperature

At T = 77 K i.e Liquid N 2 temperature,

Special case of High Temperature

When a semiconductor is kept at a high temperature, most dopants area ionized

But we know that  

Therefore,     

and

donor doped

acceptor doped