As the number of holes are …

Considering  an equilibrium  established between the number of holes and the number of free electrons in a semiconductor at a particullar temperature.at  equilibrium let

, n_o    be the equilibrium free electron concentration in conduction  band  ,,  [ cm^-3 ]

p_o    be the equilibrium  hole concentration  in valency band  ,   [ cm^-3 ]

Certainly , then in intrinsic semiconductor :

.............n_o   =  p_o   =    n_i    

where,   n_i   represents  intrinsic - carrier concentration.

As  T  increases , then  n_i   increases .

As   E_g   increases   ,     n_i   decreases.

    We can consider this equilibria .........bond <---------->   e^-      +      h⁺        using an anology to chemical reaction  H₂O  <------------>   H⁺     +     OH^-    

Applying law of mass action ,

..................................................................K   =   [ e^- ] [  h⁺ ]  /  [ bond ]...................................................................&  K   =   [ H⁺ ] [ OH^- ]   /  [ H₂ O ]

........................................................................{tex}\approx{/tex}  exp [ - E_g  /  k T ]...................................................................................{tex}\approx{/tex}  [ - E  / k T ]

where , [ bonds ] is the concentration of unbroken bonds  ,  k is rate constant  &  E  , E_g   represents  respective  activation energies..

again , since [ bonds ]  >> n_o , p_o    

..................{tex}\therefore{/tex} [ bonds ]  =  constant

In general  , relatively few bonds are broken to form an electron hole , therefore, the number of bonds  are approximately constant .Hence ,

......................Number of holes   are equal to  number of free electrons